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NLP Centre, Faculty of Informatics, Masaryk University 14

aqua_rat__A7bivZpwoIxXaYQj

What is the remainder when 750*810*830*790 is divided by 13? Choose the correct answer. A) 4 B) 9 C) 10 D) 8 E) 6

OA is 'C'. OE: take the remainder from each of 750/15, 810/15 and so on.. 750/13 gives remainder = 9 810/13 gives remainder = 4 830/13 gives remainder = 11 790/13 gives remainder = 10 the net remainder is the product of above individual remainders. i.e = 9*4*11*10 break them into pairs 9*4/13 gives remainder 10 and 11*10/13 gives remainder 6 so 10*6/13 gives remainder 8. Answer: 10 <result>C</result>

C

What is the remainder when 750*810*830*790 is divided by 13?

aqua_rat__8tBlhFSpQ22ngGln

If a and b are the two values of t that satisfy the equation t^2 – 10t + 16 = 0, with a > b, what is the value of a – b? Choose the correct choice from the following A) 2 B) 4 C) 6 D) 8 E) 10

Factor the left side of the equation: t^2 – 10t + 16 = 0 (t – 2)(t – 8) = 0 t = 2, t = 8 Thus, a = 8 and b = 2. So a – b = 8 – 2 = 6. The answer is 6. <result>C</result>

C

If a and b are the two values of t that satisfy the equation t^2 – 10t + 16 = 0, with a > b, what is the value of a – b?

aqua_rat__hDWvzMmW2STHg7QF

k = 2^n + 5, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9? Choose the correct choice from the following choices: A) 2^n - 8 B) 2^n - 4 C) 2^n D) 2^n + 4 E) 2^n + 5

Given: k, M and N are integers If k is a divisor of both N and M, then k is a divisor of N+M (and N–M and M–N) We're told that 9 is a divisor of 2^n + 5 We also know that 9 is a divisor of9. So, applying the aboverule, 9 is a divisor of 2^n + 5 +9, and 9 is a divisor of 2^n + 5 -9 = 2^n-4 2^n - 4 <result>B</result>

B

k = 2^n + 5, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9?

aqua_rat__l5ry1UEiGgpehsFc

A certain distance is covered by a cyclist at a certain speed. I a jogger covers half the distance in double the time, the ratio of the speed of the jogger to that of the cyclist is: Choices A) 1:2 B) 2:1 C) 1:4 D) 4:1 E) None of these

let the distance covered by the cyclist be x and the time taken be y. Then, Required ratio=1/2x/2y:x/y=1/4:1=1:4. 1:4orrect Option: 1:4 <result>C</result>

C

A certain distance is covered by a cyclist at a certain speed. I a jogger covers half the distance in double the time, the ratio of the speed of the jogger to that of the cyclist is:

aqua_rat__XuxJ7qmncXtMSlmi

The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square? Select. A) 5:18 B) 5:12 C) 5:10 D) 5:11 E) 5:16

Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm. a2 = 4096 = 212 a = (212)1/2 = 26 = 64 L = 2a and b = a - 24 b : l = a - 24 : 2a = 40 : 128 = 5:16 Answer:5:16 <result>E</result>

E

The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square?

aqua_rat__gncvgYCavhV1VTLo

A and B start a business, with A investing the total capital of Rs.100000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.10000 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year? Choose the correct choice from the following choices: A) A)2520000 B) B)2620000 C) C)2820000 D) D)2920000 E) E)2420000

Interest received by A from B = 10% of half of Rs.100000 = 10% * 50000 = 5000. Amount received by A per annum for being a working partner = 10000 * 12 = Rs.120000. Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (5000+ 120000 + P) Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally. Income of A = Twice the income of 2620000 (5000 + 120000 + P) = 2(P) P = 125000 Total profit = 2P + 120000 = 2*125000 + 120000 = 2620000 Answer:2620000 <result>B</result>

B

A and B start a business, with A investing the total capital of Rs.100000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.10000 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?

aqua_rat__yI53tp3wlzmLXpst

An amount of Rs.1638 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of B? Choose the correct choice. A) 360 B) 358 C) 356 D) 514 E) 504

Let the shares of A, B and C be a, b and c respectively. a : b : c = 1/2 : 1/3 : 1/4 Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12. a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3. Share of B = 4/13 * 1638 = Rs. 504 Answer: 504 <result>E</result>

E

An amount of Rs.1638 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of B?

aqua_rat__mdMR6nHDYi9XUqr7

A school has received 60% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 50% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise? Select the correct option. A) $200 B) $333.33 C) $100.25 D) $277.78 E) $377.00

Let us suppose there are 100 people. 50% of them donated $25000 ( 500 * 50 ) $25000 is 60% of total amount. So total amount = 25000 * 100/60 Remaining amount is 40% of total amount. 40% of total amount = 25000 * (100/60) * (40/100) = 50000/3 This amount has to be divided by 50( remaining people are 50 ) So per head amount is 50000/3 / 50 = 32000/180 = 333.33; ANSWER:$333.33 <result>B</result>

B

A school has received 60% of the amount it needs for a new building by receiving a donation of $500 each from people already solicited. People already solicited represent 50% of the people from whom the school will solicit donations. How much average contribution is requited from the remaining targeted people to complete the fund raising exercise?

aqua_rat__l3ka6aY103xMKObm

In a company of 11 employees, 5 employees earn $32,000, 4 employees earn $45,000, and the 2 highest-paid employees earn the same amount. If the average annual salary for the 11 employees is $48,000, what is the annual salary for each of the highest-paid employees? Choose one. A) $90,000 B) $94,000 C) $98,000 D) $102,000 E) $106,000

5*32,000+4*45,000+2x=11*48,000 2x=528,000-160,000-180,000 2x=188,000 x=94,000 The answer is $94,000. <result>B</result>

B

In a company of 11 employees, 5 employees earn $32,000, 4 employees earn $45,000, and the 2 highest-paid employees earn the same amount. If the average annual salary for the 11 employees is $48,000, what is the annual salary for each of the highest-paid employees?

aqua_rat__QSyBujHefOcX3Qfi

Of 70 players on a football team, 46 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total? Pick one A) 54 B) 59 C) 63 D) 71 E) 62

Total = 70 Thrower = 46 Rest = 70 - 46= <gadget id="calculator">70 - 46</gadget> <output>24</output> 24 Left Handed= 24/3= <gadget id="calculator">24/3</gadget> <output>8</output> 8 Right handed= 16 If all Thrower are right handed then total right handed is 46 + 16= <gadget id="calculator"> 46 + 16</gadget> <output>62</output> 62 so E. 62 is the right answer <result>E</result>

E

Of 70 players on a football team, 46 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?

aqua_rat__pMP0coeRGLUFtGPr

The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is: Select the correct option. A) 70 km/hr B) 75 km/hr C) 84 km/hr D) 87.5 km/hr E) 77.5 km/hr

The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train = 400/4= <gadget id="calculator">400/4</gadget> <output>100</output> 100 kms/hr then the speed of the first train is:100*7/8= 700/8= <gadget id="calculator">700/8</gadget> <output>175/2 = around 87.5</output> 87.5 km/hr ANSWER:87.5 km/hr <result>D</result>

D

The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is:

aqua_rat__nUUzaWfLuYTIXGqN

One man traveled a distance of 61 km in 9hrs. He traveled partly on footat 4 km/hr and partly on bicycle ta 9 km/hr. The distance traveled on foot is? Select the correct option A) 11 km B) 13 km C) 16 km D) 18 km E) 19 km

Let the distance travelled on foot be x km. Then, distance travelled on bicycle = (61 -x) km. So, x + (61 -x) = 9 4 9 9x + 4(61 -x) = 9 x 36 5x = 80 x = 16 km. 16 km <result>C</result>

C

One man traveled a distance of 61 km in 9hrs. He traveled partly on footat 4 km/hr and partly on bicycle ta 9 km/hr. The distance traveled on foot is?

aqua_rat__aS66854sKedra2k8

Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make? Choose the correct answer. A) 9 B) 12 C) 14 D) 15 E) 60

Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make? 3! / 1!2! * 6! / 3!3! =3*20= <gadget id="calculator">3*20</gadget> <output>60</output> 60 E. 60 <result>E</result>

E

Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?

aqua_rat__KQ7LFlidZ3FZH8uw

There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability R that at least one will be orange? Choices. A) R=7/10 B) R=3/5 C) R=2/5 D) R=3/10 E) 1/10

Method 1 Probability R that at least one out of two marbles will be orange = 1 - Probability that both marbles are blue = 1- P(First marble is blue) * P (Second Marble is Blue) = 1- (3/5)(2/4) = 7/10 Method 2 Probability that at least one marble will be orange = P( First Marble is Orange)*P(Second Marble is Blue) + P (First Marble is Blue)*P(Second Marble is Orange) + P(First Marble is Orange) *P(Second Marble is Orange) = (2/5)*(3/4)*2 + (2/5)*(1/4) = 7/10 Method 3 Probabilty that at least one marble will be orange = 1 - Probability that both marbles are blue = 1 - (Number of ways 2 blue marbles out of 3 can be pulled)/(Number of ways 2 marbles out of 5 can be pulled) = 1 - 3C2/5C2 = 1-(3/10) = 7/10 R=7/10nswer :R=7/10 <result>A</result>

A

There are 5 marbles in a bag - 2 are orange and 3 are blue. If two marbles are pulled from the bag, what is the probability R that at least one will be orange?

aqua_rat__p4Gwtad3Uh6iCdfG

Which of the following options is an arithmetic sequence? I. m-9, n-5, o-9,p-9, q-9, r-9 II. m^5, n^5, o^5, p^5, q^5 III. 4m,4n,4o,4p,4q Answers: A) I only B) I and II C) I and III D) II and III E) III only

lets look at the three choices... I. m-9, n-5, o-9,p-9, q-9, r-9 since the difference is not constant, it is not an arithmetic sequence... II. m^5, n^5, o^5, p^5, q^5 since the difference is not constant, it is not an arithmetic sequence III. 4m,4n,4o,4p,4q since the difference is constant it is an arithmetic sequence... The answer is III only) <result>E</result>

E

Which of the following options is an arithmetic sequence? I. m-9, n-5, o-9,p-9, q-9, r-9 II. m^5, n^5, o^5, p^5, q^5 III. 4m,4n,4o,4p,4q

aqua_rat__tGaoZ5T5DksUiBtT

Average monthly income of a family of 3 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 650. The income of the deceased was? Choose one A) Rs. 692.80 B) Rs. 905 C) Rs. 990 D) Rs. 1385 E) None

Answer Income of the deceased = Total income of 4 members - total income of remaining 3 members. = 735 x 3 - 650 x 2 Rs. = 905 Rs. Correct Option: Rs. 905 <result>B</result>

B

Average monthly income of a family of 3 earning members was Rs. 735. One of the earning members died and therefore, the average income came down to Rs 650. The income of the deceased was?

aqua_rat__3Q83T8mJKoxSLH1d

In how many ways the word "RITUAL" can be arranged? Choose one: A) 120 B) 240 C) 720 D) None E) Cannot be determined

Explanation : The required number of ways = 6! = 720 Answer : 720 <result>C</result>

C

In how many ways the word "RITUAL" can be arranged?

aqua_rat__JBXg4ayWkMGdB7hU

210 reputed college students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers? Choose one A) 25 B) 40 C) 50 D) 60 E) 75

We are told that60 Students claimed that they preferred Mac to Windows, which means that 60 preferred Mac but NOT Windows, so # of students who preferred Mac (P(A) as you wrote), does not equal to 60, it equals to 60+20 (20 is # of students who equally preferred both brands). Also we are asked to find # of the students who preferred Windows to Mac, so if you denote x as those who prefer Windows then you should calculate x-20. So, if we use your formula it should be: 210={Mac}+{Windows}-{40oth}+{Neither}=(60+20)+x-20+90 --&gt; x=60 (# of student who prefer Windows) --&gt; # of the students who preferred Windows to Mac is x-20=40. <result>B</result>

B

210 reputed college students were asked in a survey if they preferred Windows or Mac brand computers. 60 Students claimed that they preferred Mac to Windows brand computers. One third as many of the students who preferred Mac to Windows, equally preferred both brands. 90 of the students had no preference. How many of the students in the survey preferred Windows to Mac brand computers?

aqua_rat__xPxtDEGO9LEoOtRH

5 identical snow plows can clear an iced parking lot in 24 hours. How long would it take 6 such snow plows to clear the same parking lot? Pick one A) 1 hour, 15 minutes B) 2 hours, 30 minutes C) 3 hours D) 7 hours, 30 minutes E) 20 hourss

6/5 as many plows will take 5/6 as many hours --&gt; 24*5/6=20 hours. Answer: 20 hourss.-- 24*5/6= <gadget id="calculator">-- 24*5/6</gadget> <output>20</output> 20 hours. Answer: 20 hourss. <result>E</result>

E

5 identical snow plows can clear an iced parking lot in 24 hours. How long would it take 6 such snow plows to clear the same parking lot?

aqua_rat__b8xmz3m9N9C0irkF

If a whole number n is divided by 4, we will get 3 as remainder. What will be the remainder if 2n is divided by 4 ? Choices: A) 4 B) 3 C) 2 D) 1 E) 0

Explanation: Let n ÷ 4 = p , remainder = 3 =&gt; n = 4p + 3 2n = 2(4p + 3) = 8p + 6 = 8p + 4 + 2 = 4(2p + 1) + 2 Hence, if 2n is divided by 4, we will get 2 as remainder. Answer: 2 <result>C</result>

C

If a whole number n is divided by 4, we will get 3 as remainder. What will be the remainder if 2n is divided by 4 ?

aqua_rat__TpZfzX5b9FhqB1NC

Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ? Choose the correct choice. A) 27 sec B) 87 sec C) 67 sec D) 47 sec E) 37 sec

Explanation: Time taken to meet for the first time anywhere on the track = length of the track / relative speed = 300 / (15 + 25)5/18 = 300x 18 / 40 x 5 = 27 seconds. 27 secnswer: 27 sec <result>A</result>

A

Two persons start running simultaneously around a circular track of length 300 m from the same point at speeds of 15 km/hr and 25 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions ?

aqua_rat__Ohc3TCDsgJUeQrTN

How many 6 digit numbers can be formed from the digits 1 to 6 which are divisible by the unit digit of that number. Choose the correct answer: A) 648 B) 720 C) 890 D) 980 E) None of these

Explanation : Since, there is no repetition, numbers 1 to 6 will always be present in the 6 digit number. We will go through this step by step. Divisible by 1 and 1 at the unit place: _ _ _ _ _ 1 This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers. Divisible by 2 and 2 at the unit place: _ _ _ _ _ 2 This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers. Divisible by 3 and 3 at the unit place: _ _ _ _ _ 3 Since, any number will have all the digits from 1 to 6 and the sum 1 + 2 + 3 + 4 + 5 + 6= <gadget id="calculator"> 1 + 2 + 3 + 4 + 5 + 6</gadget> <output>21</output> 21 is divisible by 3 This gives us total of 5 x 4 x 3 x 2 x 1= 120 numbers. Divisible by 4 and 4 at the unit place: _ _ _ _ _ 4 Here, there are two cases _ _ _ _ 2 4 This gives 4 x 3 x 2 x 1 = 24 numbers. _ _ _ _ 6 4 This gives 4 x 3 x 2 x 1 = 24 numbers. This gives us total of 24 + 24= <gadget id="calculator"> 24 + 24</gadget> <output>48</output> 48 numbers. Divisible by 5 and 5 at the unit place: _ _ _ _ _ 5 This gives us total of 5 x 4 x 3 x 2 x 1= 120 numbers. Divisible by 6 and 6 at the unit place: _ _ _ _ _ 6 As all 6 digit numbers formed with 1 to 6 digits(without repetition) are divisible by 3 and numbers with 6 at the unit place are even. This gives us total of 5 x 4 x 3 x 2 x 1 = 120 numbers. None of these cases will have numbers overlapping with each other. So, Total numbers = 120 + 120 + 120 + 48 + 120 + 120= <gadget id="calculator">120 + 120 + 120 + 48 + 120 + 120</gadget> <output>648</output> 648 648nswer : 648 <result>A</result>

A

How many 6 digit numbers can be formed from the digits 1 to 6 which are divisible by the unit digit of that number.

aqua_rat__5mwHurpFETHcPIEI

A car averages 35 miles per hour for the first 4 hours of a trip and averages 44 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 38 miles per hour, how many hours long is the trip? Choices: A) 6 B) 8 C) 10 D) 12 E) 14

Let T be the total time of the trip. 35*4 + 44(T-4) = 38T 6T = 176-140 T = 6 The answer is 6. <result>A</result>

A

A car averages 35 miles per hour for the first 4 hours of a trip and averages 44 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 38 miles per hour, how many hours long is the trip?

aqua_rat__OuZ1Jt8MFwtnz6P4

A store sells a certain product at a fixed price per unit. At the product's current price, v units cost a total of exactly $300. If the price were lowered by $5 from its current value, then v + 2n units would cost exactly $300; if the price were raised by $5, then v – n units would cost exactly $300. What is the value of v? Pick. A) 10 B) 15 C) 20 D) 25 E) 30

It got too complicated when I used algebra. Using plugging in, it was quite fast. Price Quantity total value p v pv = 300 p-5 v+2n (p-5)(v+2n) = 300 p+5 v-n (p+5)(v-n) = 300 Solving three equations for three unknowns. Tough!! Plugging in, I always start with C. 20 was the answer here, so saved calculation! Putting values in above equations: Price Quantity total value 15 20 300 10 20+2n 300 -&gt; 10(20 + 2n)=300 -&gt; 200 +20n = 300 -&gt; 20n = 100 -&gt; n =5 20 15 300 So v = 20 satisfies all equations!! <result>C</result>

C

A store sells a certain product at a fixed price per unit. At the product's current price, v units cost a total of exactly $300. If the price were lowered by $5 from its current value, then v + 2n units would cost exactly $300; if the price were raised by $5, then v – n units would cost exactly $300. What is the value of v?

aqua_rat__dIvWGTaxOqBmdGbc

It would take one machine 9 hours to complete a large production order and another machine 8 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order? Choose the correct choice. A) 72/17 B) 17/72 C) 14/24 D) 24/56 E) 34/56

The rate of the first machine is 1/9 job per hour; The rate of the second machine is 1/8 job per hour; Thus, the combined rate of the machines is 1/9+1/8=17/72 job per hour, which means that it takes 1/(17/72)=72/17 hours both machines to do the job. 72/17nswer: 72/17. <result>A</result>

A

It would take one machine 9 hours to complete a large production order and another machine 8 hours to complete the same order. How many hours would it take both machines, working simultaneously at their respective constant rates, to complete the order?

aqua_rat__OmFyOSK1ypcdEe9H

find the average of first 20 multiples of 7? Choose the correct choice: A) 73.5 B) 70.5 C) 63.5 D) 54.5 E) 40.5

Required average =7(1+2+3+…….+20)/20 (7*20*21)/(20*2) (147/2)=73.5. 73.5NSWER 73.5 73.5 <result>A</result>

A

find the average of first 20 multiples of 7?

aqua_rat__Nl4iXaXgkshdKBmj

Out of 8 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them? Choose the correct answer A) 7/8 B) 9/10 C) 11/12 D) 13/14 E) 15/16

P(no graduates) = 4C3 / 8C3 = 4/56 = 1/14 P(at least one graduate) = 1- 1/14 = 13/14 The answer is 13/14. <result>D</result>

D

Out of 8 people working on a project, 4 are graduates. If 3 people are selected at random, what is the probability that there is at least one graduate among them?

aqua_rat__esZ44ucY1jn80SHb

John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.51 more than Jane, what was the original price of the dish? Choose the correct choice from the following A) 24 B) 34 C) 37.8 D) 42 E) 84

The difference between the amounts John paid and Jane paid is the deference between 15% of p and 15% of 0.9p: 0.15p - 0.15*0.9p = 0.51--&gt; 15p - 13.5p = 51 --&gt; p = 34. Answer: 34. <result>B</result>

B

John and Jane went out for a dinner and they ordered the same dish. Both used a 10% discount coupon. John paid a 15% tip over the original price of the dish, while Jane paid the tip over the discounted price for the coupon. If John paid $0.51 more than Jane, what was the original price of the dish?

aqua_rat__xIxgcBThfIHqLvcz

Three grades of milk are 1 percent, 5 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z? Choose one. A) y + 3z B) (y +z) / 4 C) 5y + 3z D) 3y + z E) 3y + 4.5z

Soln: The resulting equation is =&gt; (.01x + .05y + .03z)/(x+y+z) = 1.5/100 =&gt; x + 5y + 3z = 1.5x + 1.5y + 1.5z taking x to one side and y and z to other side we get =&gt; x = 5y + 3z Ans is 5y + 3z <result>C</result>

C

Three grades of milk are 1 percent, 5 percent and 3 percent fat by volume. If x gallons of the 1 percent grade, y gallons of the 2 percent grade, and z gallons of the 3 percent grade are mixed to give x+y+z gallons of a 1.5 percent grade, what is x in terms of y and z?

aqua_rat__RCghDR00qglPa96S

If x is divisible by 3, 14, and 15, which of the following must be the least multiple of x? Choose the correct choice from the following answers A) 308 B) 210 C) 200 D) 120 E) 100

If x is divisible by 3, 14, and 15, then x must be a multiple of 3,14 and 5. Hence,the least multiple of x will be 3*14*5= <gadget id="calculator"> 3*14*5</gadget> <output>210</output> 210. ANSWER:210 <result>B</result>

B

If x is divisible by 3, 14, and 15, which of the following must be the least multiple of x?

aqua_rat__mpPdSaF2v7fanu6u

Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.1450? Pick. A) Rs.1000 B) Rs.1250 C) Rs.1010 D) Rs.10000 E) None of these

Explanation: 1450 = P [1 + (5*16/5)/100] P= 1250 Answer: Option Rs.1250 <result>B</result>

B

Find the principle on a certain sum of money at 5% per annum for 3 1/5 years if the amount being Rs.1450?

aqua_rat__WlUoZPGrUoG2qZov

How many different section of 4 books can be made from 10 different books if two particular books are always selected? Choices A) 36 B) 38/ C) 26 D) 28 E) 24

This means two books are seclected out of the remaining 8 books. Required number of ways = 8C2= 8!/6!x2!=28. Ans: 28. <result>D</result>

D

How many different section of 4 books can be made from 10 different books if two particular books are always selected?

aqua_rat__VUcLG09yFLbdRnK6

4 couples are seating at a round tables how many ways can the 4 women sit together Choose the correct choice from the following: A) 4!*4! B) 3!*4! C) 4!*3! D) 5!*4! E) 6!*4!

4 men can be arranged around a table in (4-1)= <gadget id="calculator">(4-1)</gadget> <output>3</output> 3! ways; Now, we can place 4 women in 4 slots between any two men and arrange these women in this slot in 4! ways. So, total # of ways is 3!*4*4!=4!*4! 4!*4!NS:4!*4! <result>A</result>

A

4 couples are seating at a round tables how many ways can the 4 women sit together

aqua_rat__mgqwCKVxEIFigFSK

If the radius of a circle is increased by 60% then the area is increased by: Choose the correct answer. A) 44% B) 120% C) 156% D) 40% E) None of the above

initially A=pi*r2 now R2=160/100r then area=Pi*(160R/100)2 area=256R/100 that is area increases from 100 to 256=increase in area=156% ANSWER:156% <result>C</result>

C

If the radius of a circle is increased by 60% then the area is increased by:

aqua_rat__H5hMU7j5C5YyIJqK

A daughter lent $750 to her mother to help pay her rent. At the end of the month, the daughter received y dollars more than than the amount that was lent due to interest. The mother also gave her daughter an additional $5 for goodwill. In terms of y, what fraction of the total amount that the daughter received was the goodwill amount? Pick. A) (5y-1)/(755-y) B) 5/(755+y) C) 5y/(755+y)-1 D) 5y/(755+y) E) 5y

The amount of money the daughter received was (750 + 5+ y) dollars. The $5 goodwill gift as a fraction of the amount received was, therefore, 5/(755+y). Answer: 5/(755+y). <result>B</result>

B

A daughter lent $750 to her mother to help pay her rent. At the end of the month, the daughter received y dollars more than than the amount that was lent due to interest. The mother also gave her daughter an additional $5 for goodwill. In terms of y, what fraction of the total amount that the daughter received was the goodwill amount?

aqua_rat__f0varFDWR7q3KLT2

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green? Choose the correct choice. A) 2/3 B) 8/21 C) 3/7 D) 9/22 E) None of these

Explanation: Total number of balls = (8 + 7 + 6)= <gadget id="calculator">(8 + 7 + 6)</gadget> <output>21</output> 21 Let E= event that the ball drawn is neither blue nor green =e vent that the ball drawn is red. Therefore, n(E) = 8. P(E) = 8/21. Answer: 8/21 <result>B</result>

B

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?

aqua_rat__mlDDWizcaeLJfNbd

From a pack of 52 playing cards, 2cards are drawn together at random. Find the probability of both the cards being king ? Choose the correct choice from the following: A) 1/212 B) 1/223 C) 1/221 D) 2/213 E) 3/313

Two cards can be drawn from a pack of 52 playing cards in 52C2 ways. i,e., 52 x 51 / 2 = 1326 ways. The event that two kings appear in a single drawn of cards is 4C2 ways, i.e 6 ways. ∴ The probability that the two cards drawn from a pack of 52 cards are kings = 6/1326 = 1/221 1/221 <result>C</result>

C

From a pack of 52 playing cards, 2cards are drawn together at random. Find the probability of both the cards being king ?

aqua_rat__WTg6UiXoRZnJbQYt

When p is divided by 9, the remainder is 8. All of the following are possible values of p, except for which of the following? Choose the correct answer A) 17 B) 35 C) 53 D) 61 E) 71

Four of these numbers can be expressed in the form of 9x+8, where x can be 0,1,2,3,4.... However, 61 = 9(6) + 7 The answer is 61. <result>D</result>

D

When p is divided by 9, the remainder is 8. All of the following are possible values of p, except for which of the following?

aqua_rat__FmD3dvqHD05TzBnl

A shop owner sells 30mtr of cloth and gains SP of 10 metres. Find the gain %? Choose the correct choice from the following choices: A) 30% B) 40% C) 50% D) 65% E) 72%

Here, selling price of 10 m cloth is obtained as profit. Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth) Selling price of 20 m cloth = Selling Price of 30 m of cloth Let cost of each metre be Rs. 100. Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. Rs. 3000 Profit% = 10 × 100 = 50% 20 Profit of 50 % was made by the merchant. 50% <result>C</result>

C

A shop owner sells 30mtr of cloth and gains SP of 10 metres. Find the gain %?

aqua_rat__tRnRInRAK0Tc5DIA

The difference between the circumference and the radius of a circle is 37 cm. The area of the circle is: Choices. A) 111 cm2 B) 148cm2 C) 154cm2 D) 259cm2 E) 269cm2

2πr-r=37 or (2π-1)r=37. Or (2* 22/7 -1)r=37 or 37r/7=37 or r=7. Therefore, Area= πr2= (22/7 *7*7)= <gadget id="calculator">(22/7 *7*7)</gadget> <output>154</output> 154 cm2 ANSWER:154cm2 <result>C</result>

C

The difference between the circumference and the radius of a circle is 37 cm. The area of the circle is:

aqua_rat__Ffk7Gxq578vatGx0

A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m? Choose the most appropriate option: A) Rs.3919 B) Rs.3910 C) Rs.3997 D) Rs.3900 E) Rs.3902

Area = (l + b – d) d (80 + 60 – 10)10 =&gt; 1300 m2 1300 * 3 = Rs.3900 Answer:Rs.3900 <result>D</result>

D

A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?

aqua_rat__dOTELA0VL6EH1gsY

There are three prizes to be distributed among nine students. If no students gets more than one prize, then this can be done in? Choose one. A) 10 B) 45 C) 5 D) 84 E) None of these

Explanation : 3 prize among 9 students can be distributed in 9C3 ways = 84 ways. Answer : 84 <result>D</result>

D

There are three prizes to be distributed among nine students. If no students gets more than one prize, then this can be done in?

aqua_rat__jhT6DHlpPz7kMPt4

What percentage of numbers from 1 to 70 have squares that end in the digit 1? Options. A) 90% B) 28% C) 20% D) 23% E) 12%

Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69. Number of such numbers = 14. Required percentage = (14/70 * 100)= <gadget id="calculator">(14/70 * 100)</gadget> <output>20</output> 20% Answer:20% <result>C</result>

C

What percentage of numbers from 1 to 70 have squares that end in the digit 1?

aqua_rat__cwydYeTKCGwDRQJV

Find large number from below question The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder Choices: A) 1234 B) 1265 C) 1350 D) 1467 E) 1647

Let the smaller number be x. Then larger number = (x + 1375). x + 1375 = 6x + 15 5x = 1360 x = 272 Large number = 272+1375= <gadget id="calculator">272+1375</gadget> <output>1_647</output> 1647 1647 <result>E</result>

E

Find large number from below question The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder

aqua_rat__pH8g3nSJue3l6tjB

An ant walks an average of 1000 meters in 30 minutes. A beetle walks 10% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h? Choose the most appropriate option. A) 1.8 B) 1.6 C) 2.775. D) 1.9 E) 3.5.

the ant walks an average of 1000 meters in 30 minutes 1000 meters in 1/2 hours the beetle walks 10% less distance = 1000-10=900 meters in 30 minutes 0.900 km in 30/60 = 1/2 hours speed = 0.900*2= <gadget id="calculator">0.900*2</gadget> <output>1.8</output> 1.8 km/h I guess option 1.8 should be 1.8 <result>A</result>

A

An ant walks an average of 1000 meters in 30 minutes. A beetle walks 10% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h?

aqua_rat__w9K2ZRNxhCNBM31P

A can do a piece of work in 10 days, B in 15 days. They work for 5 days. The rest of work finished by C in 2 days.If they get Rs 1500 for the whole work, the daily wages of B and C are? Choose the correct choice from the following answers: A) 225 B) 276 C) 126 D) 187 E) 1267

Explanation: Let the total work = 30 units. Then capacity of A = 3 units, B = 2 units. Now they worked for 5 days. So they must have completed 25 units. Rest of the work 5 units done by C in 2 days. So C capacity = 5/2= <gadget id="calculator">5/2</gadget> <output>5/2 = around 2.5</output> 2.5 units. Given that toatal wages are Rs.1500 for 30 units. So for 1 unit of work they get Rs.50. Now B and C per day work= (2 + 2.5)= <gadget id="calculator">(2 + 2.5)</gadget> <output>4.5</output> 4.5 units. So their daily wages= 4.5 × 50 = Rs.225 225nswer:225 <result>A</result>

A

A can do a piece of work in 10 days, B in 15 days. They work for 5 days. The rest of work finished by C in 2 days.If they get Rs 1500 for the whole work, the daily wages of B and C are?

aqua_rat__AcvT0KZIwLOcc9Q4

In a nationwide poll, N people were interviewed. If 1/5 of them answered yes to question 1, and of those, 1/3 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions? Pick one: A) N/8 B) 6N/7 C) 4N/15 D) 7N/15 E) 14N/15

The number of people who answered yes to both questions is (1/3)(1/5)N = N/15 The number of people who did not answer yes to both is 1 - N/15 = 14N/15 The answer is 14N/15. <result>E</result>

E

In a nationwide poll, N people were interviewed. If 1/5 of them answered yes to question 1, and of those, 1/3 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions?

aqua_rat__bM6p71WdX1Y2hHWj

Linda bought 3 notebooks at $1.20 each; a box of pencils at $1.50 and a box of pens at $1.70. How much did Linda spend? Choose the correct choice from the following options. A) $6.80 B) $8.40 C) $7.70 D) $4.70 E) $3.90

Linda spent 1.20 ? 3 = $3.60 on notebooks The total amount of money that Linda spent is equal to 3.60 + 1.50 + 1.70= <gadget id="calculator"> 3.60 + 1.50 + 1.70</gadget> <output>6.8</output> $6.80 correct answer $6.80 <result>A</result>

A

Linda bought 3 notebooks at $1.20 each; a box of pencils at $1.50 and a box of pens at $1.70. How much did Linda spend?

aqua_rat__o4ME5GtF2SywlsGm

The present ages of three persons are in proportions 4:7:9.Thirteen years ago, the sum of their ages was 81. Find their present ages. Pick: A) 24, 42 B) 28, 36 C) 35, 45 D) 35, 55 E) of these

Let their present ages be 4x, 7x and 9x years respectively. Then, (4x - 13) + (7x - 13) + (9x - 13) = 81 20x = 120 =&gt; x = 6 Their present ages are 24, 42 and 54 years respectively. 24, 42NSWER:24, 42 <result>A</result>

A

The present ages of three persons are in proportions 4:7:9.Thirteen years ago, the sum of their ages was 81. Find their present ages.

aqua_rat__VolnV3YfnOZ2UjpW

57+58=115. How many such 2 consecutive numbers are there less than 1500 when added gives a sum which is divisible by 5? Choose the correct choice A) 100 B) 200 C) 300 D) 400 E) 500

since 2+3= <gadget id="calculator">2+3</gadget> <output>5</output> 5 &amp; 7+8= <gadget id="calculator">7+8</gadget> <output>15</output> 15 any combination with these no be will give u desirable result... so total no in 100 will be 20 &amp; that's why in 1000,it will be 20X15=300. ANSWER:300 <result>C</result>

C

57+58=115. How many such 2 consecutive numbers are there less than 1500 when added gives a sum which is divisible by 5?

aqua_rat__B2gQs8jQvbsX2umf

The average (arithmetic mean) monthly income of four workers is $1,000. After one worker’s income increases by 50 percent the new average income is $1,200. What was the original income of the worker whose monthly income increased? Choose the correct choice from the following answers. A) $1,800 B) $1,500 C) $1,300 D) $1,600 E) $1,100

Increase in total income was 200*4= <gadget id="calculator">200*4</gadget> <output>800</output> $800, we know that this increase was 50% (1/2) of the workers original income, thus his/her original income was 800*2=$1,600. Answer: $1,600 <result>D</result>

D

The average (arithmetic mean) monthly income of four workers is $1,000. After one worker’s income increases by 50 percent the new average income is $1,200. What was the original income of the worker whose monthly income increased?

aqua_rat__JGRddyKD5rkY8YZO

What is the largest 4 digit number exactly divisible by 35? Choose the correct option A) 4676 B) 4678 C) 9975 D) 9504 E) 9936

Largest 4 digit number = 9999 9999 ÷ 35 = 285, remainder = 24 Hence largest 4 digit number exactly divisible by 88 = 9999 - 24= <gadget id="calculator">9999 - 24</gadget> <output>9_975</output> 9975 answer :9975 <result>C</result>

C

What is the largest 4 digit number exactly divisible by 35?

aqua_rat__Zwpf2yJ8L82YVdvF

The sum of 3 consecutive numbers is definitely Choose the correct choice from the following answers: A) Positive. B) Divisible by 2. C) Divisible by 4. D) Divisible by 3. E) Divisible by 5.

If 1st term is x: x+(x+1)+(x+2)=3x+3---&gt;Always divisible by 3 If 2nd term is x: (x-1)+x+(x+1) +( +1)+( +2)= <gadget id="calculator"> +( +1)+( +2)</gadget> <output>3</output> 3x+3---&gt;Always divisible by 3 If 2nd term is x: (x-1)+x+(x+1)=3x---&gt;Always divisible by 3 If 3rd term is x: (x-2)+(x-1)+x=3x-3---&gt;Always divisible by 3 Answer: Divisible by 3. <result>D</result>

D

The sum of 3 consecutive numbers is definitely

aqua_rat__ngq2XaCkE3jW0cyA

A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in Choose the correct choice A) 5 days B) 6 days C) 7.5 days D) 8.5 days E) None of these

Explanation: B's 5 days work = 110 ∗ 5=12Remaining work =1−12=12A can finish work =15 ∗ 12=7.5days Answer: 7.5 days <result>C</result>

C

A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in

aqua_rat__Eu4O0LBJEpCtULSk

The average of marks obtained by 120 boys was 39. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is? Choose the correct choice from the following choices A) 100 B) 110 C) 120 D) 130 E) 140

Let the number of boys who passed = X. Then, 39 x X + 15 x (120 - X) = 120 x 39 24X = 4680 - 1800 =&gt; X = 2880/24= <gadget id="calculator">2880/24</gadget> <output>120</output> 120. Hence, the number of boys passed= 120. ANSWER:120 <result>C</result>

C

The average of marks obtained by 120 boys was 39. If the average of marks of passed boys was 39 and that of failed boys was 15, the number of boys who passed the examination is?

aqua_rat__VsrTW1b2WhSPzh1b

If the numerator of a fraction T is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent? Choose the correct choice from the following answers: A) 16 1⁄6% B) 25% C) 33 1⁄3% D) 50% E) 66 2⁄3%

This question can be dealt with conceptually or by TESTing VALUES. We're told that the numerator of a fraction T is tripled and the denominator of that same fraction is doubled. We're asked for the resulting increase, in percentage terms, of that fraction. Let's TEST 2/1 If we triple the numerator and double the denominator, we end up with.... (2x3)/(1x2) = 6/2= <gadget id="calculator">6/2</gadget> <output>3</output> 3 Since we're increasing 2 to 3, we're increasing that fraction by (3-2)/2= 1/2 of itself = 50% 50% <result>D</result>

D

If the numerator of a fraction T is tripled, and the denominator of a fraction is doubled, the resulting fraction will reflect an increase of what percent?

aqua_rat__YrhCgshhq59CkoSf

At what rate percent on simple interest will Rs.750 amount to Rs.1125 in 5 years? Options. A) 2 B) 10 C) 4 D) 5 E) 6

375 = (750*5*R)/100 R = 10%.Answer: 10 <result>B</result>

B

At what rate percent on simple interest will Rs.750 amount to Rs.1125 in 5 years?

aqua_rat__cCAfRD2ScFPkAHI2

If 45% of a class averages 95% on a test, 50% of the class averages 78% on the test, and the remainder of the class averages 60% on the test, what is the overall class average? (Round final answer to the nearest percent). Pick: A) 83% B) 84% C) 85% D) 86% E) 87%

This question is a Weighted Average question with a series of dependent variables. The remaining portion of the class represents 100% - 45% - 50% = 5% of the class 85%onverting the portions of the class population to decimal weights, we find: 85%lass Average 100 - 45 - 50= <gadget id="calculator"> 100 - 45 - 50</gadget> <output>5</output> 5% of the class 85%onverting the portions of the class population to decimal weights, we find: 85%lass Average= 0.45x95 + 0.50x78 + 0.05x60 = 84.75 The class average (rounded) is 85% Final Answer 85%) 85% <result>C</result>

C

If 45% of a class averages 95% on a test, 50% of the class averages 78% on the test, and the remainder of the class averages 60% on the test, what is the overall class average? (Round final answer to the nearest percent).

aqua_rat__9vKFcAgwohp7Jo8d

John's Bank's saving amount is decreased 30% due to loan payment and current balance is Rs.7000. Find the actual balance before deduction? Answers: A) 8000 B) 8500 C) 9000 D) 9500 E) 10000

CP* (70/100) = 7000 CP= 100 * 100 =&gt; CP = 10000 Answer:10000 <result>E</result>

E

John's Bank's saving amount is decreased 30% due to loan payment and current balance is Rs.7000. Find the actual balance before deduction?

aqua_rat__GIcgqDZK3co7zzQK

An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+2) will be divisible by 2 ? Choose the correct choice from the following choices: A) 1/9 B) 1/3 C) 1/2 D) 2/3 E) 5/6

n(n+2) to be divisible by 2 either n or n+2 must be a multiples of 2. In each following group of numbers: {1, 2, 3, 4}, {5, 6, 7, 8}, ..., {97, 98, 99, 100} there are EXACTLY 2 numbers out of 4 satisfying the above condition. For example in {1, 2, 3, 4} n can be: 2, or 4. Thus, the overall probability is 2/4 =1/2. Answer: 1/2. <result>C</result>

C

An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+2) will be divisible by 2 ?

aqua_rat__ZgHzUTP3nxdQsLx2

The sequence a1, a2, a3, ... , an, ... is such that an=an−1+an−2/2 for all n≥3n≥3. If a3=4 and a5=20, what is the value of a6 ? Select the correct option: A) 12 B) 16 C) 20 D) 24 E) 28

Since given that an=an−1+an−2/2, then: a5=a4+a3/2 --&gt; 20=a4+4/2 --&gt; a4=36 a6=a5+a4/2 --&gt; a6=20+36/2 --&gt; a5=28 Answer: 28. <result>E</result>

E

The sequence a1, a2, a3, ... , an, ... is such that an=an−1+an−2/2 for all n≥3n≥3. If a3=4 and a5=20, what is the value of a6 ?

aqua_rat__mfbZUSKqu9F01YoQ

The area of a right triangle PCM is 18. Length of smallest side CM is 3 units. Find the length of the other two sides. Choose the correct choice from the following answers A) 12, 9 B) 18, 3 C) 15.16, 6 D) 12, 12.37 E) 12, 15.16

CM=3 AREA=PM*CM/2, thus PM=12 By Pythagorean Theorem, we can now find the value of PC. 12, 12.37 is the correct option. <result>D</result>

D

The area of a right triangle PCM is 18. Length of smallest side CM is 3 units. Find the length of the other two sides.

aqua_rat__SHfNiR0bu4BZl3jY

Find the area of a rhombus whose side is 25 cm and one of the diagonals is 34 cm? Choose the correct choice from the following choices A) 680 sq.cm B) 268 sq.cm C) 618 sq.cm D) 297 sq.cm E) 600 sq.cm

Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus. BE2 + AE2 = AB2 252 = 152 + AE2 AE = √(625 - 225)= <gadget id="calculator">(625 - 225)</gadget> <output>400</output> √400= 20, AC = 20 + 20= <gadget id="calculator">20 + 20</gadget> <output>40</output> 40 cm. Area of a rhombus= 1/2 * d1d2 = 1/2 * 40 * 34= <gadget id="calculator">1/2 * 40 * 34</gadget> <output>680</output> 680 sq.cm. 680 sq.cmnswer:680 sq.cm <result>A</result>

A

Find the area of a rhombus whose side is 25 cm and one of the diagonals is 34 cm?

aqua_rat__B2N4p1ok6WN8JeQI

In a dairy farm, 46 cows eat 46 bags of husk in 46 days. In how many days one cow will eat one bag of husk? Choose the correct choice from the following: A) 1 B) 46 C) 20 D) 26 E) 30

Explanation : One bag of husk = 46 cows per day ⇒ 46 × 1 × 46 = 1 × 46 × x For one cow = 46 days Answer : 46 <result>B</result>

B

In a dairy farm, 46 cows eat 46 bags of husk in 46 days. In how many days one cow will eat one bag of husk?

aqua_rat__Zr847EKngaeWS5bA

A sequence consists of 16 consecutive even integers written in increasing order. The sum of the first 8 of these even integers is 488. What is the sum of the last 8 of the even integers? Choices A) 598 B) 604 C) 610 D) 616 E) 622

The sum of the first 8 numbers is: x + (x+2) +...+ (x+14) = 488 The sum of the next 8 numbers is: (x+16) + (x+2+16) +...+ (x+14+16) = 488 + 8(16) = 488 + 128= <gadget id="calculator">488 + 128</gadget> <output>616</output> 616 The answer is 616. <result>D</result>

D

A sequence consists of 16 consecutive even integers written in increasing order. The sum of the first 8 of these even integers is 488. What is the sum of the last 8 of the even integers?

aqua_rat__XeQKc3n3NTc8Jq8l

A boat travels 40 km downstream in 8 hours and 36 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current. Choose the correct answer A) 8 km/hr, 1 km/hr B) 5 km/hr, 4 km/hr C) 1 km/hr, 6 km/hr D) 2 km/hr, 1 km/hr E) 4 km/hr, 1 km/hr

Downstream speed=40km/8hrs =5kmph upstream speed40 /8= <gadget id="calculator">40 /8</gadget> <output>5</output> 5kmph upstream speed=36km/12hrs =3kmph speed of boat36 /12= <gadget id="calculator">36 /12</gadget> <output>3</output> 3kmph speed of boat=avg of downstream and upstream speeds speed of boat=(5+3)/2= <gadget id="calculator">(5+3)/2</gadget> <output>4</output> 4kmph. current speed=half of the difference of downstream and upstream speeds currend speed=(5-3)/2= <gadget id="calculator">(5-3)/2</gadget> <output>1</output> 1kmph ans is 4km/hr,1km/hr ANSW4 km/hr, 1 km/hrR:4 km/hr, 1 km/hr <result>E</result>

E

A boat travels 40 km downstream in 8 hours and 36 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current.

aqua_rat__NiTuU3JLedZLrGJH

During a given week A programer spends 1/4 of his time preparing flow chart, 3/8 of his time coding and the rest of the time in debugging the programs. If he works 48 hours during the week , how many hours did he spend debugging the program. Select the correct option. A) 15 hours B) 16 hours C) 17 hours D) 18 hours E) 19 hours

1/4 of time for flow charts =48/4= <gadget id="calculator">48/4</gadget> <output>12</output> 12 hours 3/8 time for coding=48*3/8= <gadget id="calculator">48*3/8</gadget> <output>18</output> 18 so remaining time for debugging=48-12-18= <gadget id="calculator">48-12-18</gadget> <output>18</output> 18 hours ANSWER:18 hours <result>D</result>

D

During a given week A programer spends 1/4 of his time preparing flow chart, 3/8 of his time coding and the rest of the time in debugging the programs. If he works 48 hours during the week , how many hours did he spend debugging the program.

aqua_rat__MTHYvrZNUpmEAh4e

Q. How many 6-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5, 5? Choose the correct choice from the following choices: A) 180 B) 240 C) 210 D) 270 E) 300

the number is less than 3000000 so we will have the digit on the left most side to be either 1 or 2 i.e your number can be 1 _ _ _ _ _ _ or 2 _ _ _ _ _ _ case 1 &gt; 1 _ _ _ _ _ _ here the units digit can be either 2 or 6 when the units digit is 2 i.e 1 _ _ _ _ _ 2 number of ways this can be done would be 5! / 2! (as 5 is repeated twice) = 60 when the units digit is 6 i.e. 1 _ _ _ _ _ 6, number of ways would be 5!/(2! * 2!) {both 2 and 5 repeat twice} = 30 case 2 &gt; 2 _ _ _ _ _ _ (here units digit may be 2 or 6) number of ways this can be done would be 5! / (2!) for 2 =60 and 5! / 2! for 6 ... = 60 adding all of these ... gives the answer 180 ... the explanation looks difficult but this technique helps if you are familiar with the concept of permutations when the numbers/alphabets repeat 180 <result>A</result>

A

Q. How many 6-digit even numbers less than 3,000,000 can be formed using the following digits: 1, 2, 2, 3, 5, 5?

aqua_rat__YB8g8wRH7hSLU6Qg

In year Y imported machine tools accounted for 60 percent of total machine-tools sales in the United States, and Japanese imports accounted for 30 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars? Choices: A) 55x/9 B) 50x/9 C) 60x/9 D) 65x/9 E) 75x/9

Sales of imported tools = 60% of the total sales = 0.60*{total} = 3{total}/5; Sales of Japanese tools = 30% of the sales of imported tools = 3/10*3{total}/5 = 9{total}/50. Since the sales of of Japanese tools was x, then 9{total}/50 = x --&gt;9 {total} = 50x {total} = 50x/9 Answer: 50x/9 <result>B</result>

B

In year Y imported machine tools accounted for 60 percent of total machine-tools sales in the United States, and Japanese imports accounted for 30 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?

aqua_rat__v6ZkYfeJARlpCVrI

30% of a number is more than 60% of 150 by 120. Find the number? Choose the correct answer: A) 770 B) 712 C) 720 D) 740 E) 700

(30/100) * X – (60/100) * 650 = 190 2/7 X = 210 X = 700 Answer:700 <result>E</result>

E

30% of a number is more than 60% of 150 by 120. Find the number?

aqua_rat__82tbakccqP26e19O

5,9,17,29,49,__ Choose the most appropriate option: A) 79 B) 80 C) 81 D) 82 E) 83

(9+5) +3= <gadget id="calculator">(9+5) +3</gadget> <output>17</output> 17 (16+9) +4= <gadget id="calculator">(16+9) +4</gadget> <output>29</output> 29 (28+16)+5= <gadget id="calculator">(28+16)+5</gadget> <output>49</output> 49 (48+28)+6= <gadget id="calculator">(48+28)+6</gadget> <output>82</output> 82 ANSWER:82 <result>D</result>

D

5,9,17,29,49,__

aqua_rat__AyGNaPQH9fS2hMvH

If X and Y are positive integers such that (3X + 7Y) is a multiple of 11, then which of the following will be divisible by 11? Options A) 4X + 6Y B) X + Y + 4 C) 9X + 4Y D) 4X - 9Y E) 9X - 4Y

by hit and trail, we put X = 5 and Y = 1 so that (3X + 7Y) = ((3*5) + (7*1))= <gadget id="calculator">((3*5) + (7*1))</gadget> <output>22</output> 22, which is divisible by 11 (4X + 6Y)= 4*5 + 6*1= <gadget id="calculator">4*5 + 6*1</gadget> <output>26</output> 26, which is not divisible by 11 (X + Y + 4)= (5 + 1 + 4)= <gadget id="calculator">(5 + 1 + 4)</gadget> <output>10</output> 10, which is not divisible by 11 (9X + 4Y)= (9*5 + 4*1)= <gadget id="calculator">(9*5 + 4*1)</gadget> <output>49</output> 49 which is not divisible by 11 (4X - 9Y)= (4*5 - 9*1)= <gadget id="calculator">(4*5 - 9*1)</gadget> <output>11</output> 11 which is divisible by 11 (9X - 4Y)= (9*5 - 4*1)= <gadget id="calculator">(9*5 - 4*1)</gadget> <output>41</output> 41 which is not divisible by 11 So the Answer is 4X - 9Y <result>D</result>

D

If X and Y are positive integers such that (3X + 7Y) is a multiple of 11, then which of the following will be divisible by 11?

aqua_rat__RTdVnxRi0stk9FEQ

A man mixes two types of rice (X and Y) and sells the mixture at the rate of Rs. 17 per kg. Find his profit percentage. I. The rate of X is Rs. 20 per kg. II. The rate of Y is Rs. 13 per kg. Choose the correct choice from the following answers: A) I alone sufficient while II alone not sufficient to answer B) II alone sufficient while I alone not sufficient to answer C) Either I or II alone sufficient to answer D) Both I and II are not sufficient to answer E) Both I and II are necessary to answer

EXPLANATION The ratio, in which X and Y are mixed, is not given. So, both I and II together cannot give the answer. answer is (Both I and II are not sufficient to answer). <result>D</result>

D

A man mixes two types of rice (X and Y) and sells the mixture at the rate of Rs. 17 per kg. Find his profit percentage. I. The rate of X is Rs. 20 per kg. II. The rate of Y is Rs. 13 per kg.

aqua_rat__kV0NUH8oW7PYiORM

What percentage of numbers from 1 to 70 have squares that end in the digit 1? Pick: A) 1 B) 14 C) 20 D) 21 E) 22

Clearly, the numbers which have 1 or 9 in the unit's digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69. Number of such numbers = 14. Required percentage = (14/70 * 100)= <gadget id="calculator">(14/70 * 100)</gadget> <output>20</output> 20% ANSWER:20 <result>C</result>

C

What percentage of numbers from 1 to 70 have squares that end in the digit 1?

aqua_rat__hwVBUFjJEnuattWT

A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,056. How much did she invest at 5%? Options. A) $500 B) $400 C) $700 D) $900 E) $950

et x be the portion invested at 5% and Let (1-x) be the rest which is invested at 6% The question states that the return after 1 year is (1056/1000)-1 = 0.053 = 5.3% We want to find the dollar amount invested in X Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%) 0.05x+0.06(1-x)= 0.056 (0.05)x +0.06 - (0.06)x = 0.056 -0.01x = -0.004 x= -0.004/-0.01 = 4/10 = 40% So X = 40% of the 1000 which is 400 ANSWER:$400 <result>B</result>

B

A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,056. How much did she invest at 5%?

aqua_rat__AxZMthsYA00Cibn7

There are 100 apples in a bag of which 98% are green and the rest red. How many green apples do you need to remove so that only 96% of the apples are green? Pick: A) 40 B) 8 C) 15 D) 25 E) 50

98−x/100−x=96100 Or, 9800−100x=9600−96x Or, 200=4x Or, x=50 ANSW50R:50 <result>E</result>

E

There are 100 apples in a bag of which 98% are green and the rest red. How many green apples do you need to remove so that only 96% of the apples are green?

aqua_rat__Uq73f4lZnbEsFIr0

A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is? Choose the correct answer: A) 288 B) 660 C) 500 D) 267 E) 298

Speed = 78 * 5/18 = 65/3 m/sec. Time = 1 min = 60 sec. Let the length of the train be x meters. Then, (800 + x)/60 = 65/3 x = 500 m.Answer: 500 <result>C</result>

C

A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?

aqua_rat__0s2kF1hIiiLfWPqC

Two cars, Car1 and Car2 move towards each other from Z and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Z starting from Y? Choose the correct answer A) 15.5 sec B) 8.4 sec C) 33.6 sec D) 31.11 sec E) 16.8 sec

Z--------------------------------------|----------------------------Y Car A(20mps)-------------------------&gt;P&lt;---------------Car B(15mps) Let 2 cars meet each other at point P in t seconds. Car1 covers distance= 20t. Car2 covers distance=15t. So, total distance ZY= 35t. From P, Car 1 reaches onto Y in 10 secs. So it covers 15t further. so, 15t/20 = 10 So t=40/3 sec and total distance = (35*40)/3 Hence Car2 will cover total distance in (35*40)/(3*15) = 31.11 sec approx. Answer 31.11 sec <result>D</result>

D

Two cars, Car1 and Car2 move towards each other from Z and Y respectively with respective speeds of 20 m/s and 15 m/s. After meeting each other Car1 reaches Y in 10 seconds. In how many seconds does Car 2 reach Z starting from Y?

aqua_rat__8mLrzetJNWej6Im6

A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -. Choose one. A) 7/18 B) 7/19 C) 7/11 D) 7/12 E) 7/15

Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways. Similarly from eight white balls two can be drawn in ways. 7/15 Answer: 7/15 <result>E</result>

E

A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -.

aqua_rat__NbcaXVjGcdvUmXAM

A box contains SEVEN bulbs out of which 3 are defective. If TWO bulbs are chosen at random, find the probability that atleast one bulb is good Choose the correct answer A) 5/6 B) 6/7 C) 7/8 D) 8/9 E) 9/8

Required probability ==1-3C2/7C2= 1 - 1/7 = 6/7. Answer:6/7 <result>B</result>

B

A box contains SEVEN bulbs out of which 3 are defective. If TWO bulbs are chosen at random, find the probability that atleast one bulb is good

aqua_rat__ZM8aVh318ZSCG7mH

The sum of the ages of 4 children born at the intervals of 1 years each is 12 years. what is the age of the youngest child ? Choose the correct option A) 2.5 B) 1.5 C) 1 D) 3.5 E) 4.5

Let x = the youngest child. Each of the other four children will then be x+1, x+2, x+3 We know that the sum of their ages is 12 so, x+(x+1)+(x+2)+(x+3) = 12 therefore The youngest child is 1.5 years old Answer: 1.5 <result>B</result>

B

The sum of the ages of 4 children born at the intervals of 1 years each is 12 years. what is the age of the youngest child ?

aqua_rat__WQBpvHkyIVPYsZYj

In a group of 6 boys&4 girls a Committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 1girl? Choose the correct choice from the following choices. A) 187 B) 190 C) 192 D) 195 E) 213

The committee of 4 persons is to be so formed that it has at least 1 woman The different ways that we can choose to form such a committee are: (i) lw. 3 m in t 6X5X4' x 6C3 = 4x — — 80 3X2X1 x 6c2 =42:: x 26:: = 90 (ii) 2w. 2 m in °C2 (iii) 3w. 1 m in 4C3 x 6C1 = 4 x 6 = 24 (iv) 4w in 6C4 = 1 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least one woman. = 80 + 90 + 24 + 1= <gadget id="calculator">80 + 90 + 24 + 1</gadget> <output>195</output> 195 195 <result>D</result>

D

In a group of 6 boys&4 girls a Committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 1girl?

aqua_rat__PJYRETiUbNH6w5tE

If (7)(x^2) has four different prime factors, at most how many different prime factors does x have? Choose the correct option A) 1 B) 2 C) 3 D) 4 E) 5

x can have at most 4 prime factors, namely the prime factor 7 plus 3 others. If x had more than this number of prime factors, then (7)(x^2) would have more than 4 prime factors. The answer is 4. <result>D</result>

D

If (7)(x^2) has four different prime factors, at most how many different prime factors does x have?

aqua_rat__ThPDbkv91hwE5z1e

How many integers between 324,700 and 436,600 have tens digit 1 and units digit 3? Choose the correct choice from the following options A) 327 B) 645 C) 987 D) 1119 E) 1339

The integers are: 324,713 324,813 etc... 436,513 The number of integers is 4366 - 3247= <gadget id="calculator"> 4366 - 3247</gadget> <output>1_119</output> 1119 The answer is 1119. <result>D</result>

D

How many integers between 324,700 and 436,600 have tens digit 1 and units digit 3?

aqua_rat__h9heGw9jgoQYBQvo

If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 15 degrees? Pick: A) π/3 B) 3π/2 C) 2π D) 5π/2 E) 8π

Area = 16π Radius = 4 Circumference = 2 x 4 x π = 8π Angle forming the arc = 15 degrees. 15/360 = 1/24. Therefore length of arc = 1/24 * 8π = π/3 - π/3nswer choice π/3. <result>A</result>

A

If the area of circle O is 16π, what is the length of an arc on the circle formed by a central angle measuring 15 degrees?

aqua_rat__dZwgypSs32ByJpSS

Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.143 per kg, the price of the third variety per kg will be Choose the correct choice from the following options. A) Rs.165.50 B) Rs.1700 C) Rs. 175.50 D) Rs. 180 E) None

Solution Since first second varieties are mixed in equal proportions, so their average price = Rs.(126+135/2) = Rs.130.50 So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1. We have to find x. x-143/22.50 = 1 =› x - 143 = 22.50 =› x=165.50. Hence, price of the third variety = Rs.165.50 per kg. Rs.165.50nswer Rs.165.50 <result>A</result>

A

Tea worth Rs.126 per kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs.143 per kg, the price of the third variety per kg will be

aqua_rat__ezhRN7vBYKFAlqVQ

Set L is composed of nine numbers, labeled L1 through L9. Set M is also composed of nine numbers, labeled M1 through M9. Set M is defined as follows: M1 = 1 + L1; M2 = 2 + L2; and so on, including M9 = 9 + L9. How much larger is the sum of set M's mean and range than the sum of set L's mean and range? Choose the correct option A) 3 B) 4 C) cannot be determined D) 6 E) 8

Yes, the correct answer is cannot be determined <result>C</result>

C

Set L is composed of nine numbers, labeled L1 through L9. Set M is also composed of nine numbers, labeled M1 through M9. Set M is defined as follows: M1 = 1 + L1; M2 = 2 + L2; and so on, including M9 = 9 + L9. How much larger is the sum of set M's mean and range than the sum of set L's mean and range?

aqua_rat__TxwhjKnDvjoBbujM

If x^3 > y^2 > z, which of the statements could be true? I. x < y = z II. x = z < y III. y < x < z Options A) I only B) III only C) I and II only D) II and III only E) I, II and III

Given : x^3 &gt; y^2 &gt; z I. x &lt; y = z is not true i.e. Answers can not be Options A, C or E II. x = z &lt; y is not true i.e. Answers can not be Options A, C or E III. y &lt; x &lt; z is true for x=4, y=3, z=5 i.e. Answers can only be Options III only Answer: option III only <result>B</result>

B

If x^3 > y^2 > z, which of the statements could be true? I. x < y = z II. x = z < y III. y < x < z

aqua_rat__KmKhS4KTdWMkEuWv

A rectangular tank needs to be coated with insulation. The tank has dimensions of 4 feet, 5 feet, and 2 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation? Choose the correct choice from the following choices: A) $1520 B) $1640 C) $1780 D) $1850 E) $1960

The total surface area is 2(2*4 +4*5 + 2*5) = 76 square feet The total cost is 76*$20 = $1520 The answer is $1520.76* 20= <gadget id="calculator">76* 20</gadget> <output>1_520</output> $1520 The answer is $1520. <result>A</result>

A

A rectangular tank needs to be coated with insulation. The tank has dimensions of 4 feet, 5 feet, and 2 feet. Each square foot of insulation costs $20. How much will it cost to cover the surface of the tank with insulation?

aqua_rat__2ZJvriLjQqW3p59k

A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag? Pick: A) 76 ways B) 65 ways C) 54 ways D) 28 ways E) 30 ways

The word contains five consonants. Three vowels, three consonants can be selected from five consonants in ⁵C₃ ways, two vowels can be selected from three vowels in ³C₂ ways. 3 consonants and 2 vowels can be selected in ⁵C₂ . ³C₂ ways i.e., 10 * 3 = 30 ways. Answer: 30 ways <result>E</result>

E

A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag?

aqua_rat__TNuZ5Y4mnp2RPqC7

A person climbs up to a pole of 88 m high. In every min he climbs 12 m but slips down 8 m...how much time will he take to reach d top? Choose one: A) 20th minute B) 21th minute C) 22th minute D) 24th minute E) 25th minute

in every min person climbs up 12m and slips 8m . hence net displacement becomes 4m. in 19 minutes person would climb (19*4)= <gadget id="calculator"> (19*4)</gadget> <output>76</output> 76m in 20th minute person would climb 12m up.. and it will be on top. hence in 20th minute. person will reach on pole. 20th minuteNSWER:20th minute <result>A</result>

A

A person climbs up to a pole of 88 m high. In every min he climbs 12 m but slips down 8 m...how much time will he take to reach d top?

aqua_rat__N2t7bxxQggij7KpW

If z is a multiple of 7899, what is the remainder when z^2 is divided by 9? Choose the correct choice from the following answers. A) 0 B) 2 C) 3 D) 6 E) 7

The sum of the digits is 7+8+9+9= <gadget id="calculator">7+8+9+9</gadget> <output>33</output> 33. Thus 3 is a factor of 7899, so 3 is a factor of z. Then 3^3= 9 is a factor of z^2. Then the remainder when z^2 is divided by 9 is 0. The answer is 0. <result>A</result>

A

If z is a multiple of 7899, what is the remainder when z^2 is divided by 9?

aqua_rat__ROEg9XH6i2XMX9lb

A bag contains 3 red, 4 green and 4 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball? Pick: A) 6/11 B) 27/55 C) 31/55 D) 91/165 E) 109/165

P(no red balls) = 8/11*7/10*6/9 = 56/165 P(at least one red ball) = 1 - 56/165 = 109/165 The answer is 109/165. <result>E</result>

E

A bag contains 3 red, 4 green and 4 white balls. Three balls are picked up one by one without replacement. What is the probability that there will be at least one red ball?

aqua_rat__YcUOFvGSZpWbjtdJ

In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda? Choose the correct answer: A) 4/7 B) 3/7 C) 35/128 D) 4/28 E) 28/135

using Binomial. theorem n35/128r (p)^r (q)^n-r 735/1284 (1/2)^4 (1/2)^r which is 35/128 Answer is 35/128. <result>C</result>

C

In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 7 consecutive days in Rwanda?

aqua_rat__8WnzxLhtLFg2b8SM

In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 83 more candidates got selected than A. What was the number of candidates appeared from each State? Choose the correct choice. A) 7000 B) 8300 C) 6000 D) 5000 E) 4000

State A and State B had an equal number of candidates appeared. In state A, 6% candidates got selected from the total appeared candidates In state 8300, 7% candidates got selected from the total appeared candidates 8300ut in State 8300, 83 more candidates got selected than State A From these, it is clear that 1% of the total appeared candidates in State 8300 = 83 =&gt; total appeared candidates in State 8300 = 83 x 100 = 8300 =&gt; total appeared candidates in State A = total appeared candidates in State 8300 = 8300 <result>B</result>

B

In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 83 more candidates got selected than A. What was the number of candidates appeared from each State?

aqua_rat__EajSPr5cs54krllF

What is the Mode of the following data set R- {1,2,7,9,6,6,7,7} Choose the correct choice from the following choices: A) 1 B) 2 C) 7 D) 6 E) 9

Mode of a set is the data point that is repeated the most number of times. In the set given, 7 is repeated. Answer: 7 <result>C</result>

C

What is the Mode of the following data set R- {1,2,7,9,6,6,7,7}

aqua_rat__rpCzlzaPegNQksVo

624 people are protesting outside of the White House. If they are standing in a rectangle in which the rows are no less than 6 people and no more than 104, how many different combinations of rectangular shapes are possible? Choices A) 6 B) 7 C) 8 D) 9 E) 10

firstly factors of 624 = 1,2,3,4,6,8,12,13,16,24,26,39,48,52,78,104,156,208,312,624 the question says each row will have people no less than 12 and no more than 52, therefore, we should be interested in the factors between 12 and 52 (inclusive) 12(in each row) * 52(number of columns) =624, similarly 13 * 48 16 * 39 24 * 26 26 * 24 39 * 16 48 * 13 52 * 12 total possibilities = 8 option 8 <result>C</result>

C

624 people are protesting outside of the White House. If they are standing in a rectangle in which the rows are no less than 6 people and no more than 104, how many different combinations of rectangular shapes are possible?

aqua_rat__gNMRciCSUjRlV6qJ

The average age of a group of 10 students was 25. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group? Choose the correct choice from the following options: A) 37 years B) 30 years C) 32 years D) 44 years E) None of these

The total age of 10 students with average 25 = 250 The total age of 12 students with average 27 = 324 The total age of 2 new students = 74 Their average =37 Correct Option 37 years <result>A</result>

A

The average age of a group of 10 students was 25. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?

aqua_rat__pvYPL3dmISIpnS9V

In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 4 ounces of corn syrup, how many ounces of water does it contain? Pick one: A) 45 B) 50 C) 55 D) 60 E) 63

F:C:W 1:12:30 Sport version: F:C 3:12 F:W 1:60 OR 3:180 So C:F:W = 12:3:180 C/W = 12/180 = 3 ounces/x ounces x = 4*180/12= <gadget id="calculator">4*180/12</gadget> <output>60</output> 60 ounces of water 60 <result>D</result>

D

In the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30. In the sport formulation, the ratio of flavoring to corn syrup is three times as great as in the standard formulation, and the ratio of flavoring to water is half that of the standard formulation. If a large bottle of the sport formulation contains 4 ounces of corn syrup, how many ounces of water does it contain?

aqua_rat__uy7FH6tDJ9ELDOtF

A circular rim 14 inches in diameter rotates the same number of inches per second as a circular rim 42 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ? Choose the correct choice from the following options. A) 48pi/x B) 75x C) 48x D) 24x E) 20x

Let's try the explanation. We have two wheels. One with 14pi and the other one with 42pi. They have the same speed. In the smaller wheel it's 14pi*x, which must be equal to the speed of the bigger one (42pi*a number of revolutions).They are asking that number of revolutions (but in minutes, which makes the question even harder). Anyway, we have 14pi*x=42pi*a. (14pi*x)/(42pi). As I said, that's in seconds. So, to convert it to minutes we multiply by 60 and we get the result, 20x. Ans :20x <result>E</result>

E

A circular rim 14 inches in diameter rotates the same number of inches per second as a circular rim 42 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?