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NLP Centre, Faculty of Informatics, Masaryk University 14

aqua_rat__nH2iLtAH9IIDZduy

A train of length 150 metres takes 40.5 seconds to cross a tunnel of length 300 metres. What is the speed of the train in km/hr ? Choose the correct choice from the following choices. A) 13.33 B) 26.67 C) 40 D) 66.67 E) 50

Explanation: Speed = 150+300/40.5m/sec =450/40.5=18/5km/hr = 40 km/hr. ANSWER IS 40 <result>C</result>

C

A train of length 150 metres takes 40.5 seconds to cross a tunnel of length 300 metres. What is the speed of the train in km/hr ?

aqua_rat__vq2n9wKNhPeI76sX

The ratio of the number of boys and girls in a college is 7:8.If the percentage increase in the number of boys and girls be 20% and 10% respectively.What will be the new ratio? Choose the correct option: A) 22:21 B) 19:22 C) 23:22 D) 22:19 E) 21:22

Let the number of boys and girls in the college be 7x and 8x respectively. Their increased number=(120% of 7x) and (110% of 8x) ==[(120/100)*7x] and [(110/100)*8x] =(42x/5) and (44x/5) The required ratio =(42x/5):(44x/5) =21:22 Answer is option 21:22 <result>E</result>

E

The ratio of the number of boys and girls in a college is 7:8.If the percentage increase in the number of boys and girls be 20% and 10% respectively.What will be the new ratio?

aqua_rat__ke5o1GtuxcsUBCC6

Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 3. The numbers are Choose the correct choice from the following answers: A) 12, 24, 30 B) 12, 24, 38 C) 12, 24, 362 D) 3, 6, 9 E) 12, 24, 321

Explanation: Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 3 \inline \fn_jvn \therefore The numbers are 3, 6, 9 Answer: 3, 6, 9) 3, 6, 9 <result>D</result>

D

Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 3. The numbers are

aqua_rat__o906Vxz1onpmzBdr

A miniature roulette wheel is divided into 10 equal sectors, each bearing a distinct integer from 1 to 10, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector. If the wheel is spun two times, approximately what is the probability that the product of the two winning sectors’ integers will be even? Choose the correct choice from the following answers: A) 88% B) 75% C) 67% D) 63% E) 50%

The only way to have an odd product is if both integers are odd. P(odd product) = 1/2*1/2 = 1/4 P(even product) = 1 - 1/4 = 3/4 = 75% The answer is 75%. <result>B</result>

B

A miniature roulette wheel is divided into 10 equal sectors, each bearing a distinct integer from 1 to 10, inclusive. Each time the wheel is spun, a ball randomly determines the winning sector by settling in that sector. If the wheel is spun two times, approximately what is the probability that the product of the two winning sectors’ integers will be even?

aqua_rat__LGINhDUx8jYDWz4T

What is the lowest positive integer that is divisible by each of the integers 1 through 8, inclusive? Choose the correct choice from the following A) 420 B) 560 C) 840 D) 960 E) 1080

The integers are 1 , 2 , 3 , 4 , 5 , 6 , 7 and 8 Lowest positive integer that is is divisible by each of the integers 1 through 8 = 2^3 * 3 * 5 * 7 =8*3 *5 *7 =24 * 35= <gadget id="calculator">24 * 35</gadget> <output>840</output> 840 Answer 840 <result>C</result>

C

What is the lowest positive integer that is divisible by each of the integers 1 through 8, inclusive?

aqua_rat__Kzgh0wKuiFgy3cjP

How many different subsets of the set {0, 1, 2, 3, 4, 5,6,} do not contain 0? Choose the correct answer A) A.66 B) B.57 C) C.31 D) D.32 E) E.58

Number of subset Since we have 6 digits other than 0, we can take any numbers from the set of 6 to make a subset. Also it is a matter of selection and not arrangement.So we will consider combinations. 6c1+6c2+6c3+6c4+6c5+6c6=57 And one set is the NULL set having no elements in it so 57+1= <gadget id="calculator"> 57+1</gadget> <output>58</output> 58. ANSWE.58R E.58. <result>E</result>

E

How many different subsets of the set {0, 1, 2, 3, 4, 5,6,} do not contain 0?

aqua_rat__Hikcaun9IUv2255T

There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one liter every hour in A, it gets filled up like 10, 20, 40, 80, 160 in tank B. (At the end of first hour, B has 10 liters, second hour it has 20, third hour it has 40 and so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely? Select the correct option. A) 22 B) 28 C) 269 D) 26 E) 82

The data related to the first tank A is not necessary. As you can see, the capacity that gets filled in the tank B after each hour is doubled. So If the tank is 1/32nd part is full after 21 hours, it is 1/16th part full after 22 hours, 1/8th part full after 23 hours, 1/4th part full after 24 hours, 1/2 full after 25 hours, completely full after 26 hours. Answer:26 <result>D</result>

D

There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one liter every hour in A, it gets filled up like 10, 20, 40, 80, 160 in tank B. (At the end of first hour, B has 10 liters, second hour it has 20, third hour it has 40 and so on). If tank B is 1/32 filled after 21 hours, what is the total duration required to fill it completely?

aqua_rat__PohxYNE4YEWYWGCQ

Find the sum of first 30 natural numbers Choose the correct choice from the following choices. A) 470 B) 468 C) 465 D) 463 E) 487

Explanation: Sum of n natural numbers =n(n+1) / 2 =30(30+1) / 2=30(31) / 2=465 Option 465 <result>C</result>

C

Find the sum of first 30 natural numbers

aqua_rat__kbyaBVFPFrmv6baD

A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A? Pick one. A) 298 B) 608 C) 279 D) 280 E) 269

80* 7: x* 3 = 1:1 1/2 560: 3x = 2: 3 x = 280 Answer:280 <result>D</result>

D

A and B rent a pasture for 10 months. A put in 80 cows for 7 months. How many can B put in for the remaining 3 months, if he pays half as much again as A?

aqua_rat__SoucudFlOpUeG7qy

If K is the sum of reciprocals of the consecutive integers from 53 to 58, inclusive, then K is closest in value to which of the following? Choose the correct choice from the following options. A) 1/12 B) 1/10 C) 1/8 D) 1/6 E) 1/10

1/53 , 1/54 , 1/55 , 1/56 , 1/57 , 1/58 Hypothetically , assume all 6 Numbers to be 1/53 Hence sum of it would result in = 6/53 ( almost equals 1/7 , or slightly less than 1/7 - ) If all 6 nos were to be 1/58 ... Sum of which would result in 6/58 = 1/10 . Hence answer should lie between 1/7 and 1/10 1/10 i.e 1/10 <result>E</result>

E

If K is the sum of reciprocals of the consecutive integers from 53 to 58, inclusive, then K is closest in value to which of the following?

aqua_rat__1NLS18KB1cX8OVqi

John takes a trip and drives 9 hours from Town X to Town Z at a rate of 60 miles per hour. On his way back, John drives 85 miles per hour and stops in Town Y which is midway between Town X and Town Z. How many hours does it take Scott to drive from Town Z to Town Y? Choose the most appropriate option A) 1.75 B) 1.25 C) 1.45 D) 4.15 E) 3.14

distance from X to Z =9 hr* 60 mph= 540 miles hence distance from Y to Z= 1/2*540= <gadget id="calculator">1/2*540</gadget> <output>270</output> 270 time=270/85=4.15 hrs IMO: 4.15 <result>D</result>

D

John takes a trip and drives 9 hours from Town X to Town Z at a rate of 60 miles per hour. On his way back, John drives 85 miles per hour and stops in Town Y which is midway between Town X and Town Z. How many hours does it take Scott to drive from Town Z to Town Y?

aqua_rat__LMHPwINkg4kfkmvO

A company has 100 employees, 40% of whom are employed part time. If it hires 25 new employees, 40% of whom are employed part time, what will be the percent increase in part time employees? Choose the correct answer: A) 1 2/3 % B) 2 2/3 % C) 4 % D) 25 % E) 9 %

Total employee = 100 Part time Empl = 40 New part time empl = 25 * (40/100)= <gadget id="calculator">25 * (40/100)</gadget> <output>10</output> 10 Total new part time Emp= 10+40= <gadget id="calculator">10+40</gadget> <output>50</output> 50 Old part time Emp= 40 % increase = (new - old)*100/old =10*100/40= <gadget id="calculator">10*100/40</gadget> <output>25</output> 25% Ans-25 % <result>D</result>

D

A company has 100 employees, 40% of whom are employed part time. If it hires 25 new employees, 40% of whom are employed part time, what will be the percent increase in part time employees?

aqua_rat__s8vlLEMfofEJ6U68

In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many girls are there in the class ? Choices: A) 22 B) 32 C) 30 D) 28 E) 11

Let the number of boys and girls participating in sports be 3x and 2x respectively. Then, 3x = 15 or x = 5. So, number of girls participating in sports = 2x = 10. Number of students not participating in sports = 60 - (15 + 10)= <gadget id="calculator">60 - (15 + 10)</gadget> <output>35</output> 35. Let number of boys not participating in sports be y. Then, number of girls not participating in sports= (35 -y). Therefore (35 - y) = y + 5 2y 30 y = 15. So, number of girls not participating in sports = (35 - 15)= <gadget id="calculator">(35 - 15)</gadget> <output>20</output> 20. Hence, total number of girls in the class= (10 + 20)= <gadget id="calculator">(10 + 20)</gadget> <output>30</output> 30. Answer:30 <result>C</result>

C

In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many girls are there in the class ?

aqua_rat__y5imLPT9GOqBZ5Vd

To furnish a room in a model home an interior decorator is to select 4 chairs and 4 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 75 different combinations are possible, how many tables are there in the warehouse? Answers A) A)6 B) B)8 C) C)10 D) D)15 E) E)30

Total number of ways to choose 4 chairs from 5= 5C4=5 Total number of combination=75 That means we need get 15 combinations from the selection of tables.... Screening through the answers.... 6C4=15..... 15*5=75 Answer is 6... 6 <result>A</result>

A

To furnish a room in a model home an interior decorator is to select 4 chairs and 4 tables from the collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 75 different combinations are possible, how many tables are there in the warehouse?

aqua_rat__BM9x06K29n55fBV6

A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? Pick one: A) 66 km/hr B) 72 km/hr C) 78 km/hr D) 81 km/hr E) 85 km/hr

Explanation: 4.5 km/hr =(4.5 x 5/18)m/sec = 5/4m/sec = 1.25 m/sec, and 5.4 km/hr =(5.4 x5/18)m/sec =3/2m/sec = 1.5 m/sec. Let the speed of the train be x m/sec. Then, (x - 1.25) x 8.4 = (x - 1.5) x 8.5 =&gt; 8.4x - 10.5 = 8.5x - 12.75 =&gt; 0.1x = 2.25 =&gt; x = 22.5 Speed of the train =(22.5 x 18/5)km/hr = 81 km/hr. ANSWER IS 81 km/hr <result>D</result>

D

A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

aqua_rat__rNV9sATpDy46Pmfi

160 is what percent of 50 ? Options: A) 5% B) 20% C) 320% D) 200% E) 500%

50*x=160 --&gt; x=3.2 --&gt; 3.2 expressed as percent is 320%. Answer: 320%. <result>C</result>

C

160 is what percent of 50 ?

aqua_rat__Cd35Zr1gY6Qz433H

What will come in place of the x in the following Number series? 46080, 3840, ?, 48, 8, 2, 1 Choose the correct option: A) 1 B) 384 C) 5 D) 7 E) 9

46080 /12= <gadget id="calculator">46080 /12</gadget> <output>3_840</output> 3840 3840 /10= <gadget id="calculator">3840 /10</gadget> <output>384</output> 384 384 /8= <gadget id="calculator">384 /8</gadget> <output>48</output> 48 48 /6= <gadget id="calculator">48 /6</gadget> <output>8</output> 8 8/4= <gadget id="calculator">8/4</gadget> <output>2</output> 2 2 /2= <gadget id="calculator">2 /2</gadget> <output>1</output> 1 384 <result>B</result>

B

What will come in place of the x in the following Number series? 46080, 3840, ?, 48, 8, 2, 1

aqua_rat__qBXv0KGBpaBma1mC

The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area? Select the correct option A) 10% B) 20% C) 25% D) 30% E) 45%

Sol. Required change = (20*100)/(100-20)= <gadget id="calculator">(20*100)/(100-20)</gadget> <output>25</output> 25% 25% <result>C</result>

C

The length of a rectangle is reduced by 20%. By what % would the width have to be increased to maintainthe original area?

aqua_rat__Rxgyc6hgahBGEaeO

Find the average of first 20 natural numbers? Select. A) 5.5 B) 7.2 C) 10.5 D) 12.3 E) 15.5

Sum of first n natural numbers = n(n+1)/2 sum of first 20 natural numbers = 20*21/2= <gadget id="calculator">20*21/2</gadget> <output>210</output> 210 average= 210/20= <gadget id="calculator">210/20</gadget> <output>21/2 = around 10.5</output> 10.5 Answer is 10.5 <result>C</result>

C

Find the average of first 20 natural numbers?

aqua_rat__kwoMXp7iAwuKXobn

The inverse ratio of 4: 2: 1 is? Answers: A) 2:4:8 B) 2:3:9 C) 2:3:2 D) 2:3:6 E) 2:3:1

1/4: 1/2: 1/1 = 2:4:8 2:4:8nswer:2:4:8 <result>A</result>

A

The inverse ratio of 4: 2: 1 is?

aqua_rat__Q5q8HzuYmi11tPup

If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%? Choose the correct choice from the following answers A) 3 B) 8 C) 9 D) 6 E) 4

96% ---- 12 144% ---- ? 96/144 * 12= <gadget id="calculator"> 96/144 * 12</gadget> <output>8</output> 8 Answer: 8 <result>B</result>

B

If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?

aqua_rat__M8y6jQVlon2M9rNk

A password of a computer used two digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero? Options: A) 1/32 B) 1/16 C) 1/8 D) 2/5 E) 1/4

We have two digits can be used for password -0,2,3,5,7. Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9) So, 5/10 * 5/10=1/4(1/4) <result>E</result>

E

A password of a computer used two digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?

aqua_rat__BfMSfqYInam62gLK

Three times the first of three consecutive odd integers is 8 more than twice the third. The third integer is: Choose one: A) 9 B) 11 C) 13 D) 15 E) 20

Let the three integers be x, x + 2 and x+ 4. Then, 3x = 2(x + 4) + 8 x = 16 Third integer = x + 4 = 20. ANSW20R:20 <result>E</result>

E

Three times the first of three consecutive odd integers is 8 more than twice the third. The third integer is:

aqua_rat__8uWk393MHkvW7GW8

NHAI employs 100 men to build a highway of 2km in 50 days working 8 hours a day. If in 25 days they completed 1/3 part of work .than how many more employees should NHAI hire to finish it in time working 10 hours a day? Choose the correct choice from the following options A) 22 B) 60 C) 28 D) 11 E) 218

Here 2km is immaterial. The given problem can be written in a tabular form like below. We can apply chain rule now. Total men required to complete the remaining work = 100×2525×810×2313100×2525×810×2313 = 160 So additional men required = 160 - 100= <gadget id="calculator">160 - 100</gadget> <output>60</output> 60 Answer:60 <result>B</result>

B

NHAI employs 100 men to build a highway of 2km in 50 days working 8 hours a day. If in 25 days they completed 1/3 part of work .than how many more employees should NHAI hire to finish it in time working 10 hours a day?

aqua_rat__yV5inm5TLoZ4HXCF

Two trains 111 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 60 km and the other at the rate of 90 kmph. In what time will they be completely clear of each other from the moment they meet? Pick A) 4.85 B) 7.85 C) 6.85 D) 5.85 E) 6.62

T = (111 + 165)/ (60 + 90) * 18/5 T = 6.62 ANSW6.62R:6.62 <result>E</result>

E

Two trains 111 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 60 km and the other at the rate of 90 kmph. In what time will they be completely clear of each other from the moment they meet?

aqua_rat__cMkzYZJbD6WPwFqO

A train 500 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? Answers: A) 277 m B) 700 m C) 800 m D) 187 m E) 1678 m

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

C

A train 500 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__H8iegkYhr0rsTyHT

The price of a radio was increased by 25 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases? Choose the correct option A) 80% B) 75% C) 65% D) 50% E) 45%

consider base price - $100 25% increase = 1.25*100= <gadget id="calculator">1.25*100</gadget> <output>125</output> $125 another 40% increase on new price= 1.4* 125= <gadget id="calculator">1.4* 125</gadget> <output>175</output> $175 so final price of radio - $175 therefore a 75% increase correct option - 75% <result>B</result>

B

The price of a radio was increased by 25 percent. The new price was then increased by 40 percent. A single increase of what percent is equivalent to these two successive increases?

aqua_rat__xNEFZfwL4Az7SLZy

Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has travelled 100 km more than the second. The distance between P and Q is : Options A) 500 km B) 630 km C) 900 km D) 660 km E) None

Sol. At the time of meeting, let the distane travelled byb the second train be x km. Then, distance covered by the first train is (x + 100) km ∴ x/40 = (x+100)/50 ⇔ 50x = 40x 4000 ⇔ x = 400. So, distance between P and Q = (x+x+100) km = 900 km. Answer 900 km <result>C</result>

C

Two trains start from P and Q respectively and travel towards each other at a speed of 50 km/hr and 40 km/hr respectively. By the time they meet, the first train has travelled 100 km more than the second. The distance between P and Q is :

aqua_rat__IRxJ8sGJvLaCyG9x

What is the investment made if one invests in 15% stock at 50 and earns Rs.2000? Answers: A) 5000 B) 2767 C) 2697 D) 126967 E) 19771

Explanation: To earn Rs.15, investment = Rs.50. Hence, to earn Rs.1500, investment = (1500*50)/15 = Rs.5000 5000NSWER: 5000 <result>A</result>

A

What is the investment made if one invests in 15% stock at 50 and earns Rs.2000?

aqua_rat__dNM2xM2xg4G6Firv

The seating chart of an airplane shows 30 rows of seats. Each row has 3 seats on each side of the center aisle, and one of the seats on each side is a window saet. The view from the window seats in 25 of the rows is obscured by the wings of the airplane. If the first person to be assigned a seat is assigned a window seat and thw window seat is assigned randomly, what is the probability that the person will get a seat with an unobscured view? Choose the most appropriate option. A) 1/6 B) 1/3 C) 2/3 D) 5/6 E) 17/18

priyalr 6 seats per row, think of a boeing 737. We have 30 rows, therefore window 30 seats one one side and 30 window seats on the other, totaling 60 window seats on the whole plane. the view of the window of 25 rows is blocked. two wings, therefore 50 window seats are blocked. Total window seats = 60 Total blocked window seats = 50 Total unblocked seats = 10 We know that a window seat was given, therefore probability for not window seat is 10/60 =1/6 1/6NS 1/6 <result>A</result>

A

The seating chart of an airplane shows 30 rows of seats. Each row has 3 seats on each side of the center aisle, and one of the seats on each side is a window saet. The view from the window seats in 25 of the rows is obscured by the wings of the airplane. If the first person to be assigned a seat is assigned a window seat and thw window seat is assigned randomly, what is the probability that the person will get a seat with an unobscured view?

aqua_rat__lvecONENSf82QLP7

Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. If the gain is proportional to the money invested and the time for which the money is invested and the total gain was Rs. 28000, find the earning of Nandan. Choose the correct option. A) Rs.7000 B) Rs.5000 C) Rs.6000 D) Rs.Rs.4000 E) Rs.6500

3:1 2:1 ------ 6:1 7 ----- Rs.28000 1 ----- ? =&gt; Rs.28,000/7=Rs. 4000 Answer: Rs.Rs.4000 <result>D</result>

D

Krishan and Nandan jointly started a business. Krishan invested three times as Nandan did and invested his money for double time as compared to Nandan. If the gain is proportional to the money invested and the time for which the money is invested and the total gain was Rs. 28000, find the earning of Nandan.

aqua_rat__RwYwkLqbWNMTddDM

A certain bakery sells six different-sized wedding cakes. Each cake costs x dollars more than the next one below it in size, and the price of the largest cake is $24.50. If the sum of the prices of the six different cakes is $109.50, what is the value of x? Select the correct option: A) 1.50 B) 1.75 C) 2.00 D) 2.50 E) 3.00

Since the price of the largest cake (6th) is $24.50, then the price of the smallest cake (1st) is $(24.50-5x). Now, the prices of the cakes are evenly spaced so the sum of the prices is (average price)*(# of cakes)=(first+last)/2*(# of cakes). So, (24.50-5x+24.50)/2*6= 109.50 --&gt; x=2.5. Answer: 2.50. <result>D</result>

D

A certain bakery sells six different-sized wedding cakes. Each cake costs x dollars more than the next one below it in size, and the price of the largest cake is $24.50. If the sum of the prices of the six different cakes is $109.50, what is the value of x?

aqua_rat__eRY0O1Llll0MB69J

Three bells chime at intervals of 18 min., 24 min. and 32 min. respectively. At a certain time they begin together. What length Z of time will elapse before they chime together again? Choose the correct choice from the following options: A) 2 hr. and 24 min. B) 4 hr. and 48 min. C) 1 hr. and 36 min. D) 5 hr. E) 2 hr.

It should be simple. All the three bells will chime again together whenver their time intervals intersect eachother. So the LCM of the three time intervals (18, 24,32) would be the answer. LCM (18, 24, 32) Z= 288 =&gt; 4 hours 48 mins.4 hr. and 48 min. <result>B</result>

B

Three bells chime at intervals of 18 min., 24 min. and 32 min. respectively. At a certain time they begin together. What length Z of time will elapse before they chime together again?

aqua_rat__diIWgzOwuufHj2WD

A man can row downstream at 25 kmph and upstream at 15 kmph. Find the time to reach a destination point at a distance of 50km along the downstream. Choose the correct choice: A) 4 hrs. B) 1 hrs. C) 3 hrs. D) 2 hrs. E) 2 1/2 hrs.

Let the speed of the man in downstream=25 kmph. distance to be covered along the stream=50kmph =&gt;time taken =D/S =50/25= <gadget id="calculator">50/25</gadget> <output>2</output> 2 Hrs. Answer:2 hrs. <result>D</result>

D

A man can row downstream at 25 kmph and upstream at 15 kmph. Find the time to reach a destination point at a distance of 50km along the downstream.

aqua_rat__mXOJu9iiO5IF1PpO

Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters Look at this series: C19, E21, __, I25, K27, ... What number should fill the blank? Choose the correct choice from the following answers: A) D20 B) E21 C) F22 D) G23 E) H24

E21 G23 In this series, the letters progress by 2, and the numbers increase by 2. <result>B</result>

B

Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters Look at this series: C19, E21, __, I25, K27, ... What number should fill the blank?

aqua_rat__WbdoVfJWNRLL2xgm

A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train? Choose the correct choice from the following answers: A) 276m B) 180m C) 286m D) 288m E) 277m

Length of the train be ‘X’ X + 120/15 = X + 180/18 6X + 720 = 5X + 900 X = 180m Answer:180m <result>B</result>

B

A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?

aqua_rat__yD56GKWk1ZciS66h

The ratio of three numbers is 2:3:5 and their sum is 150. The second number of the three numbers is? Choose the correct choice from the following. A) 24 B) 26 C) 27 D) 29 E) 45

2:3:5 Total parts = 10 10 parts --&gt; 150 1 part ----&gt;15 The second number of the three numbers is = 3*15= <gadget id="calculator">3*15</gadget> <output>45</output> 45 Answer : 45 <result>E</result>

E

The ratio of three numbers is 2:3:5 and their sum is 150. The second number of the three numbers is?

aqua_rat__UypcgMwCdgBc6bGS

For any real number x, the operatoris defined as: (x) = x(2 − x) If p + 2 =(p + 2), then p = Options. A) 1 B) 0 C) 1 D) -2 E) 3

(x) = x(2 − x) (p + 2) = (p + 2)(2 - p - 2) = -p(p+1) We are given that p + 2 =(p + 2) Therefore -p(p+2) = (p + 2) Or (p + 2) + p(p+2) = 0 (p + 2)(p+1) = 0 p = -1,p=-2 Option -2 <result>D</result>

D

For any real number x, the operatoris defined as: (x) = x(2 − x) If p + 2 =(p + 2), then p =

aqua_rat__cqUC0eyLt9Riffcv

Calculate the circumference of a circular field whose radius is 5 centimeters. Choose the correct choice A) 2 B) 4 C) 6 D) 8 E) 10

Circumference C is given by C = 2πr = 2π*5 = 10 π cm correct answer 102 *5= <gadget id="calculator">2 *5</gadget> <output>10</output> 10 π cm correct answer 10 <result>E</result>

E

Calculate the circumference of a circular field whose radius is 5 centimeters.

aqua_rat__7vCvYY98UrD3Fjk6

The average age of five persons is 40 years while the average age of some other 10 persons is 25 years. The average age of all the 15 persons is: Pick one A) 27 Years B) 32 Years C) 37 Years D) 30 Years E) 35 Years

x/5==40 x==200 after 10 person x/10==25 x==250 so avg btwn 15 person is,, (250+200) / 15==30 ans ANSWER:30 Years <result>D</result>

D

The average age of five persons is 40 years while the average age of some other 10 persons is 25 years. The average age of all the 15 persons is:

aqua_rat__0PiGAoGZC7KdYiM4

A slot machine in a Las Vegas casino has an average profit of $600 for each 8-hour shift for the five days Sunday through Thursday, inclusive. If the average per-shift profit on Friday and Saturday is 25% greater than on the other days of the week and the slot machine is in operation every hour of every day, what is the total weekly profit that the casino makes from the slot machine? Choose the correct answer. A) a - 4500 B) b - 9000 C) c - 13,500 D) d - 15,500 E) e - 27,000

Correct answer is C - 13500. Total profit per weekday = $600 X 3 (shifts)= $1800 Total profit per week (apart from SaturdaySunday) = $1800 X 5 = $9000 Total profit per shift on weekends = $600 X 125/100 = $750 Total profit on weekends = $750 X 3 (shifts) X 2 (Saturday, Sunday) = $4500. Hence the answer is - $4500 + $9000 = $13,500. (c - 13,500) <result>C</result>

C

A slot machine in a Las Vegas casino has an average profit of $600 for each 8-hour shift for the five days Sunday through Thursday, inclusive. If the average per-shift profit on Friday and Saturday is 25% greater than on the other days of the week and the slot machine is in operation every hour of every day, what is the total weekly profit that the casino makes from the slot machine?

aqua_rat__ZSuVf4TDhmRAJfLa

What is the greatest prime factor of 2^10 - 1? Choose the correct option. A) 17 B) 19 C) 23 D) 29 E) 31

2^10-1 = (2^5-1)(2^5+1) = 31*33 The answer is 31. <result>E</result>

E

What is the greatest prime factor of 2^10 - 1?

aqua_rat__v9NbZd8tUDQ0oFlv

A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train? Choices: A) 81 km/hr B) 88 km/hr C) 62 km/hr D) 46 km/hr E) 34 km/hr

Explanation: Let x is the length of the train in meter and y is its speed in kmph x/8.4 = (y-4.5)(10/36) ---(1) x/8.5 = (y-5.4)(10/36) ---(2) Dividing 1 by 2 8.5/8.4 = (y-4.5)/ (y-5.4) =&gt; 8.4y - 8.4 × 4.5 = 8.5y - 8.5×5.4 .1y = 8.5×5.4 - 8.4×4.5 =&gt; .1y = 45.9-37.8= <gadget id="calculator">45.9-37.8</gadget> <output>8.1</output> 8.1=&gt; y = 81 km/hr 81 km/hrnswer: Option 81 km/hr <result>A</result>

A

A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

aqua_rat__Jr4FqOq7KungMvSi

Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was: Pick one: A) three times as much B) twice as much C) the same D) half as much E) a third as much

Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr. We know that Speed = Distance/Time. Or, Time = Distance/Speed. So, times taken to covered a distance of 50 miles on his first trip = 50/x hr. And times taken to covered a distance of 300 miles on his later trip = 300/3x hr. = 100/x hr. So we can clearly see that his new time compared with the old time was: twice as much. correct answer twice as much <result>B</result>

B

Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was:

aqua_rat__pGxTT16gmLhzHuk6

There are 32 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station? Choose the correct choice from the following: A) 1800 B) 1820 C) 1150 D) 1122 E) 1900

The total number of stations= 34 From 34 Stations we have to choose any two stations and the direction of travel (Ernakulam to Chennai is different from Chennai to Ernakulam) in 34P2 ways. 34P2= 34*33= <gadget id="calculator">34*33</gadget> <output>1_122</output> 1122 ANSWER:1122 <result>D</result>

D

There are 32 stations between Ernakulam and Chennai. How many second class tickets have to be printed, so that a passenger can travel from one station to any other station?

aqua_rat__zPkLFmGgZAKBe17z

There are two buildings P and Q. If 15 persons are sent from P to Q, then the number of persons in each building is the same. If 20 persons are sent from Q to P, then the number of persons in P is double the number of persons in Q. How many persons are there in building P? Select the correct option. A) 110 B) 100 C) 120 D) 140 E) 150

Let the number of persons in building P = p and the number of persons in building Q = q If 15 persons are sent from P to Q, then the number of persons in each building is the same =&gt; p-15 = q+15 =&gt; p - q = 30 ----(Equation 1) If 20 persons are sent from Q to P, then the number of persons in P is double the number of persons in Q =&gt; 2(q - 20) = (p + 20) =&gt; 2q - 40 = p + 20 =&gt; 2q - p = 60 ----(Equation 2) (Equation 1) + (Equation 2)=&gt; q = 90 From Equation 1, p = 30 + q = 30 + 90= <gadget id="calculator">30 + 90</gadget> <output>120</output> 120 i.e., Building P has 120 persons Answer is 120. <result>C</result>

C

There are two buildings P and Q. If 15 persons are sent from P to Q, then the number of persons in each building is the same. If 20 persons are sent from Q to P, then the number of persons in P is double the number of persons in Q. How many persons are there in building P?

aqua_rat__Y0aPs27x0NseoWlU

In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes W of the competition are possible? Choose the correct choice from the following options. A) 18 B) 20 C) 54 D) 84 E) 120

the ways the three teams can be selected is.. i) A is selected, B is also selected, third can be any of the remaining 4.. so total ways 4.. they can be arranged in 4*3!=24 ways.. ii) A is not selected. threee teams can be selected from remaining 5 so total arrangements =5C3*3!=60 total W=84 outcomes 84 <result>D</result>

D

In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes W of the competition are possible?

aqua_rat__pdst0tUTyVdQoXhJ

A man spends 1/5 of his salary on food, 1/10 of his salary on house rent and 3/5 of his salary on clothes. He still has $18000 left with him. Find his salary. Pick A) $180000 B) $280000 C) $380000 D) $480000 E) None

Solution: The expenditure incurred on each item is expressed as part of the total amount (salary), so it is an independent activity. In general for independent activities [1 – (x1/y1 + x2/y2 + x3/y3)] × Total amount = Balance amount [1 – (1/5 + 1/10 + 3/5)] × Total salary = $18000 [1 – 9/10] × Total salary = $18000 Therefore total salary = $18000 × 10 = $180000 $180000nswer $180000 <result>A</result>

A

A man spends 1/5 of his salary on food, 1/10 of his salary on house rent and 3/5 of his salary on clothes. He still has $18000 left with him. Find his salary.

aqua_rat__D41vxIZP9FxrW2xu

A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km? Choose the correct choice: A) 3 B) 5 C) 6 D) 7 E) 9

M = 4 S = 2 US = 4 - 2= <gadget id="calculator">4 - 2</gadget> <output>2</output> 2 D= 6 T = 6/2= <gadget id="calculator">6/2</gadget> <output>3</output> 3 3nswer:3 <result>A</result>

A

A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?

aqua_rat__H1C8wUlEXBpMKIAf

Bradley owns b video game cartridges. If Bradley’s total is one-third the total owned by Andrew and twice the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b? Choices: A) (16/3)b B) (17/4)b C) (13/4)b D) (9/2)b E) (7/12)b

Step 1: Categorize the problem This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices. Step 2: Think like the test maker What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlie’s totals in relation to Bradley’s total rather than giving you Bradley’s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlie’s values in relation to Bradley’s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem. Step 3: Solve the problem b = Bradley’s total 3b = Andrew’s total (1/2)b = Charlie’s total Add each total b + 3b+ (1/2)b = 4b + (1/2)b = (16/4)b + (1/2)b = (9/2)b Therefore,choose (9/2)b. <result>D</result>

D

Bradley owns b video game cartridges. If Bradley’s total is one-third the total owned by Andrew and twice the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?

aqua_rat__Mg40wjmbbbXu2G04

If a - b = 2 and a2 + b2 = 25, find the value of ab. Pick one. A) A)10.5 B) B)12 C) C)15 D) D)18 E) E)20

Explanation: 2ab = (a2 + b2) - (a - b)2 = 25 - 4= <gadget id="calculator">25 - 4</gadget> <output>21</output> 21 ab=10.5 10.5nswer: 10.5 <result>A</result>

A

If a - b = 2 and a2 + b2 = 25, find the value of ab.

aqua_rat__BBQna1MfLCUO2Dh7

3, 7, 15, 31, 63, ? Options: A) 125 B) 112 C) 153 D) 173 E) 127

127 127 127ach number in the series is the preceding number multiplied by 2 and then increased by 1. <result>E</result>

E

3, 7, 15, 31, 63, ?

aqua_rat__GMBIzWXSt5yVZZre

If the complement of a certain angle is two times the measure of that certain angle, then what is the measure of that certain angle? Select the correct option. A) 45° B) 30° C) 22.5° D) 18° E) 15°

Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example. The original angle is x, so the complement is 2x, and together, these add up to 90 degrees. x + 2x = 90 3x = 90 x = 30° Answer = (30°) <result>B</result>

B

If the complement of a certain angle is two times the measure of that certain angle, then what is the measure of that certain angle?

aqua_rat__AJkbELoUJpsatxMZ

If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in Pick: A) 2 days B) 1 day C) 3 days D) 5 days E) 7 days

The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day. 1 day) <result>B</result>

B

If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in

aqua_rat__r6lBJLenxRhDA5j4

If the sum of 1/3 and 22/99 is converted to a decimal, what is the 3000th digit to the right of the decimal place? Options: A) 2 B) 3 C) 5 D) 8 E) 9

1/3 +22/99 = 5/9=0.555555555... hence, the 3000th digit would also be 5 Ans: 5 <result>C</result>

C

If the sum of 1/3 and 22/99 is converted to a decimal, what is the 3000th digit to the right of the decimal place?

aqua_rat__hTqkl0bbJtaFAHck

Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king? Choose the most appropriate option. A) 1/11 B) 2/13 C) 4/13 D) 3/17 E) 3/19

Here, n(S) = 52 There are 13 cards of diamond (including one king) and there are 3 more kings. Let E = event of getting a diamond or a king. Then, n(E) = (13 + 3)= <gadget id="calculator">(13 + 3)</gadget> <output>16</output> 16 P (E)= 16 / 52 = 4/13 4/13 <result>C</result>

C

Three people are playing cards. What is the probability that a card drawn from a pack of 52 cards will be a diamond or a king?

aqua_rat__Axcb2JvLQZh3Ehm2

If x and y are integers such that (x+1)^2 is less than or equal to 16 and (y-1)^2 is less than 64, what is the sum of the maximum possible value of xy and the minimum possible value of xy? Select the correct option: A) -16 B) -10 C) 0 D) 14 E) 16

(x+1)^2 &lt;= 16 x &lt;= 3 x &gt;= -5 (y-1)^2&lt; 64 y &lt; 9 y &gt; -7 Max possible value of xy is -5 × -6 = 30 minimum possible value of xy is -5 × 8 = -40 -40 + 30 = -10 Answer : -10 <result>B</result>

B

If x and y are integers such that (x+1)^2 is less than or equal to 16 and (y-1)^2 is less than 64, what is the sum of the maximum possible value of xy and the minimum possible value of xy?

aqua_rat__pmejPxXrxYicbFnt

If points A and B are (10-5) units apart, which of the following can have only one possible value? I. The area of a square region with side AB II. The circumference of a circle passing through points A and B III. The area of a rectangular region with diagonal AB Choose the correct answer: A) I only B) II only C) III only D) I and II only E) I and III only

I. The area of a square region with side AB --&gt; side=AB=(10-5) or 5 --&gt; the area of a square is 5^2=25, so only one possible value; II. The circumference of a circle passing through points A and B --&gt; circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter; III. The area of a rectangular region with diagonal AB --&gt; consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12). I onlynswer: I only. <result>A</result>

A

If points A and B are (10-5) units apart, which of the following can have only one possible value? I. The area of a square region with side AB II. The circumference of a circle passing through points A and B III. The area of a rectangular region with diagonal AB

aqua_rat__KrF2kll1DVKEgzbx

The banker's discount on a sum of money for 1 1/2 years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is: Choices A) 10% B) 13% C) 12% D) 15% E) 11%

B.D. for 3/2 years = Rs. 558. B.D. for 2 years = Rs.(558 x 2/3 x 2) = Rs. 744 T.D. for 2 years = Rs. 600. Therefore, Sum = B.D. x T.D./B.D. - T.D = Rs. (744 x 600/144 )= Rs. 3100. Thus, Rs. 744 is S.I. on Rs. 3100 for 2 years. Therefore, Rate =(100 x 744/3100 x 2)% = 12% Answer is 12% <result>C</result>

C

The banker's discount on a sum of money for 1 1/2 years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:

aqua_rat__jo5rb80VIGPdgB7i

If two projectiles are launched at the same moment from 1998 km apart and travel directly towards each other at 444 km per hour and 555 km per hour respectively, how many minutes will it take for them to meet? Choose one A) 90 B) 100 C) 110 D) 120 E) 130

The projectiles travel a total of 999 km per hour. The time to meet is 1998/999= <gadget id="calculator"> 1998/999</gadget> <output>2</output> 2 hours= 120 minutes The answer is 120. <result>D</result>

D

If two projectiles are launched at the same moment from 1998 km apart and travel directly towards each other at 444 km per hour and 555 km per hour respectively, how many minutes will it take for them to meet?

aqua_rat__fxPEZsfZcI3RDImA

A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 35 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell? Choose the correct choice from the following choices A) 525. B) 412. C) 432. D) 502. E) 522.

Pastry is divided in 35 customers equally. So,total number of pastry must be a multiple of 35 Only option 525. satisfies the condition, and hence is the answer <result>A</result>

A

A confectioner decides to sell all of his pastry due to the coming holiday. His pastry goods are equally divided among a group of 35 regular customers. If only 49 customers come to the bakery, each one will receive 6 less pastry goods. How much pastry does the confectioner needs to sell?

aqua_rat__SEX8eWRbhMr66KDf

Worker A takes 8 hours to do a job. Worker B takes 6 hours to do the same job. How long it take both A & B, working together but independently, to do the same job? Choices A) 20/9 B) 40/9 C) 50/9 D) 24/7 E) 80/9

one day work of A = 1/8 one day work of B = 1/6 so one day work of A and B together = 1/8 + 1/6 = 7/24 so total days required = 24/7 ANSWER:24/7 <result>D</result>

D

Worker A takes 8 hours to do a job. Worker B takes 6 hours to do the same job. How long it take both A & B, working together but independently, to do the same job?

aqua_rat__pAZqXzfm5BrN009b

One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ? Choices A) Rs. 10000 B) Rs. 5896 C) Rs. 2580 D) Rs. 3697 E) Rs. 60000

Explanation: Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then, 1/3x=1/2(150000-x) x/3+x/2=75000 x=75000*6/5= <gadget id="calculator">75000*6/5</gadget> <output>90_000</output> 90000 Savings in Public Provident Fund= Rs.(150000-90000)=Rs. 60000 Answer:Rs. 60000 <result>E</result>

E

One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?

aqua_rat__Pd5jAubWWaVtDVuL

If the average (arithmetic mean) of (2a+16) and (3a-8) is 84, what is the value of a? Pick one A) 25 B) 30 C) 28 D) 32 E) 42

((2a+16) + (3a-8)) / 2 = (5a+8)/2 = 84 a= 32 The answer is 32. <result>D</result>

D

If the average (arithmetic mean) of (2a+16) and (3a-8) is 84, what is the value of a?

aqua_rat__ohCr9wQMD2MFC3Ml

Consider a quarter of a circle of radius 20. Let r be the radius of the circle inscribed in this quarter of a circle. Find r. Choose one: A) 20*(sqr2 -1) B) 8*(sqr3 -1) C) 4*(sqr7 - 1) D) 12* (sqr7 -1) E) None of these

I got 20/(sqr2 +1) and just forgot to multiply by (sqr2 -1). 20*(sqr2 -1)nswer 20*(sqr2 -1) <result>A</result>

A

Consider a quarter of a circle of radius 20. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.

aqua_rat__cguC58RAhsPccoxd

If k^3 is divisible by 120, what is the least possible value of integer k? Select the correct option: A) 12 B) 30 C) 60 D) 90 E) 120

120 = 2^3*3*5 Therefore k must include at least 2 * 3 * 5= <gadget id="calculator"> 2 * 3 * 5</gadget> <output>30</output> 30. The answer is 30. <result>B</result>

B

If k^3 is divisible by 120, what is the least possible value of integer k?

aqua_rat__J9bfikiKKsgO1IEo

x is the product of each integer from 1 to 25, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x? Choose the correct choice from the following choices A) 5 B) 4 C) 3 D) 6 E) 7

The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula: n5+n52+n53+...+n5k, where k must be chosen such that 5k≤n x = 1*2*3....*25 = 25! No. of trailing zeros in 25! = 25/5 + 25/5^2 = 6 100^k = 10^2k → k = 6/2= <gadget id="calculator">6/2</gadget> <output>3</output> 3 3 <result>C</result>

C

x is the product of each integer from 1 to 25, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x?

aqua_rat__gMQCrojSA1bbAJBg

If n is a positive integer, which of the following expressions must be even? Pick one: A) (n − 1)( n + 1) B) (n − 4)( n + 1) C) (n − 2)( n + 6) D) (n − 5)( n + 1) E) (n − 3)( n + 3)

Whether n is even or odd, (n-4)(n+1) will have one odd factor and one even factor. The product will be even. The answer is (n − 4)( n + 1). <result>B</result>

B

If n is a positive integer, which of the following expressions must be even?

aqua_rat__ArhE8MhmPZa40drZ

30 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 3:2. How many liters of Liquid Q must be added to make the ratio 3:4? Choose the correct choice from the following answers A) 8 B) 10 C) 12 D) 14 E) 16

Let x be the amount of liquid Q to be added. (2/5)*30 + x = (4/7)*(30+x) 420 + 35x = 600 + 20x 15x = 180 x = 12 The answer is 12. <result>C</result>

C

30 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 3:2. How many liters of Liquid Q must be added to make the ratio 3:4?

aqua_rat__aBO5V1bJDhVeoh16

The speed at which a man can row a boat in still water is 21 kmph. If he rows downstream, where the speed of current is 5 kmph, what time will he take to cover 90 metres? Choose the correct choice from the following answers A) 23.46 B) 27.46 C) 28.46 D) 12.46 E) 25.46

Speed of the boat downstream = 21 + 5= <gadget id="calculator">21 + 5</gadget> <output>26</output> 26 kmph= 26 * 5/18 = 7.22 m/s Hence time taken to cover 90 m = 90/7.22 = 12.46 seconds. Answer:12.46 <result>D</result>

D

The speed at which a man can row a boat in still water is 21 kmph. If he rows downstream, where the speed of current is 5 kmph, what time will he take to cover 90 metres?

aqua_rat__asn7SLRGkpoEvQSe

Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $1.28 at the candy store. What is John’s weekly allowance? Choose the correct answer: A) $2.40 B) $3.00 C) $3.20 D) $3.60 E) $4.80

Total allowance=X Amount spent at the arcade=3/5X Amount Remaining=2/5X Amount Spent at the toy store=2/5*1/3X=2/15X Amount Remaining=2/5X-2/15X=4/15X Now, 4/15X=$1.28 Therefore, X=$4.80. Answer $4.80 <result>E</result>

E

Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $1.28 at the candy store. What is John’s weekly allowance?

aqua_rat__dR16IluxJ9tOSPd6

The simple interest at z% for z years will be $z on a sum of Choose the correct choice A) $ (1000)/z B) $(100)z^2 C) $ z D) $ (100)/z E) $ 100z

Principal =$(100*z)/(z*z)=$(100/z). Answer is $ (100)/z <result>D</result>

D

The simple interest at z% for z years will be $z on a sum of

aqua_rat__xjP6Q0REBpS1OFMo

The ratio of two quantities is 3 to 5. If each of the quantities is increased by 6, what is the ratio of these two new quantities? Choose one. A) It cannot be determined from the information given. B) 5/9 C) 12/13 D) 15/14 E) 16/14

let the actual ratio be 3k/5k, increase numerator and denominator by 6 =&gt; 3k+6/5k+6 Until the value of k is unknown we can not determine the actual ratio. OR let the actual be 3/4. After increasing 6 =&gt; 9/10 let the actual be 6/8. After increasing 6 =&gt; 12/14 Therefore without actual quantities we cannot determine the actual ratio. It cannot be determined from the information given.nswer : It cannot be determined from the information given. <result>A</result>

A

The ratio of two quantities is 3 to 5. If each of the quantities is increased by 6, what is the ratio of these two new quantities?

aqua_rat__3iTP6dKjjCZd5dPy

A box contains 4 red chips and 4 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors? Pick one: A) 1/2 B) 4/7 C) 7/12 D) 2/3 E) 7/10

Total selection ways: 8C2=8!/4!4!=28 Selecting one blue chip out of two: 4C1=4!/1!3!=4 Selecting one red chip out of four: 4C1=4!/1!3!=4 Thus, (4C1*4C1)/8C2=(4*4)/28=16/28=4/7=4/7 <result>B</result>

B

A box contains 4 red chips and 4 blue chips. If two chips are selected at random without replacement, what is the probability that the chips are different colors?

aqua_rat__wZ1xoEKT0vGlVhCn

For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.2? Choose the correct answer A) 12.6. B) 14.4. C) 15.8. D) 16.2. E) 16.4.

[6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.2 = 6*0 + 2*7.2 + 8 - 6.2 = 0 +14.4 +1.8 16.2 Answer 16.2. <result>D</result>

D

For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.2?

aqua_rat__OPf9kJOx9qJ8GNHM

the price of a commodity(in rupees per kilogram) is 100+0.1n, on the nthvday of 2007(n=1,2,,,,,100), and then remains constant. On the other hand, the price of another commodity is 89+0.15n on the nth day of 2007(n=1,2,,,,,,365). On which date in 2007, will the price of these twocommodities be equal???? Choose the correct choice from the following options: A) 11th may B) 12th may C) 20th may D) 22th may E) 24th may

price of both the commodity cannot be same within 100days( by puttng n=100 in both the price) price of 1st commodity after 100 days =100+0.1*100= <gadget id="calculator">100+0.1*100</gadget> <output>110</output> 110 day on which 2nd commodity becomes equal to 1st= 89+0.15n=110 n=140 140th day of 2007 is 20th may ANSWER:20th may <result>C</result>

C

the price of a commodity(in rupees per kilogram) is 100+0.1n, on the nthvday of 2007(n=1,2,,,,,100), and then remains constant. On the other hand, the price of another commodity is 89+0.15n on the nth day of 2007(n=1,2,,,,,,365). On which date in 2007, will the price of these twocommodities be equal????

aqua_rat__NUcyA1f4wmmOJFdI

At 3.40, the hour hand and the minute hand of a clock form an angle of Choose the correct choice: A) 120° B) 125° C) 130° D) 135° E) None

Solution Angle traced by hour hand in 17/2 hrs = (360/12x17/2 )° = 255. Angle traced by min hand in 30 min = (360/60x30)° = 180. Required angle = (255 - 180)= <gadget id="calculator">(255 - 180)</gadget> <output>75</output> 75° Answer 125° <result>B</result>

B

At 3.40, the hour hand and the minute hand of a clock form an angle of

aqua_rat__nqGfYjH9FAFVHErN

The average age of 15 students of a class is 14 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is? Choose the correct choice from the following answers. A) 3years B) 4years C) 5years D) 6years E) 7years

Age of the 15th student =[15 * 14 - (14 * 5 + 16 * 9)] = (210 - 214) = 4 years. Answer:4years <result>B</result>

B

The average age of 15 students of a class is 14 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is?

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A train is 320 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length? Choose the correct choice: A) 11 seconds B) 38 seconds C) 40 seconds D) 88 seconds E) 36.8 seconds

Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec Total distance = 320+140= <gadget id="calculator">320+140</gadget> <output>460</output> 460 meter Time= Distance/speed = 460 * (2/25)= <gadget id="calculator">460 * (2/25)</gadget> <output>184/5 = around 36.8</output> 36.8 seconds Answer: 36.8 seconds <result>E</result>

E

A train is 320 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 140 meter length?

aqua_rat__R2HKq0pwiCsY5R2l

The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is? Choose the correct choice from the following options: A) 11 years B) 16 years C) 33 years D) 14 years E) 18 years

Age of the 15th student =[15 * 15 - (14 * 5 + 16 * 9)] = (225 - 214)= <gadget id="calculator">(225 - 214)</gadget> <output>11</output> 11 years. 11 yearsnswer:11 years <result>A</result>

A

The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. Tee age of the 15th student is?

aqua_rat__vyibSuOG1sK18ZWt

A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is: Select: A) 3 : 1 B) 1 : 3 C) 1 : 2 D) 2 : 1 E) None of these

Explanation : Let speed upstream = x Then, speed downstream = 2x Speed in still water = (2x + x)/2 = 3x/2 Speed of the stream = (2x − x)/2 = x/2 Speed in still water : Speed of the stream = (3x/2) (2x/2) = 3 : 1. 3 : 1nswer : Option 3 : 1 <result>A</result>

A

A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:

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Two numbers are in the ratio of 1 : 2. If 6 be added to both, their ratio changes to 3 : 5. The greater number is Choose the correct choice: A) 20 B) 24 C) 28 D) 32 E) 36

Let the ratio be X : Y, Given X/Y = 1/2 , (X + 6)/(Y + 6) = 3/5 =&gt; X = 12 And Y = 24 ANSWER:24 <result>B</result>

B

Two numbers are in the ratio of 1 : 2. If 6 be added to both, their ratio changes to 3 : 5. The greater number is

aqua_rat__RK9XJe41bEp3jQsw

On flipping 3 coins together what is the outcomes for at least two tail? Choose the correct choice from the following: A) 1/7 B) 3/8 C) 3/11 D) 4/13 E) 5/13

Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} Favorable outcomes for at least two heads = favorable outcomes for exactly two heads and favorable outcomes for more than two heads = {TTH, HTT, TTT} 3/8 3/8 <result>B</result>

B

On flipping 3 coins together what is the outcomes for at least two tail?

aqua_rat__WVDbA0zwnxG3Gf6i

If x is 20 percent more than y and y is 60 percent less than z, then x is what percent of z? Choose one A) 500% B) 48% C) 500/3% D) 125% E) 60%

Z = 100 ; Y = 40 so X = 48 X as % of Z = 48/100 * 100= <gadget id="calculator">48/100 * 100</gadget> <output>48</output> &gt; 48% Answer will be (48%) <result>B</result>

B

If x is 20 percent more than y and y is 60 percent less than z, then x is what percent of z?

aqua_rat__tgQsw0oFkG8O8FxH

The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is: Choose the correct choice from the following answers: A) 500 B) 277 C) 222 D) 297 E) 111

Explanation: 110% of S.P. = 616 S.P. = (616 * 100)/110 = Rs. 560 C.P = (110 * 560)/112 = Rs. 500 500nswer:500 <result>A</result>

A

The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is:

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A ladder 18 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 6 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip? Choose the correct option. A) 12.5 B) 15 C) 18 D) 19 E) 25

18^2-6^2=288 it means that the height is equal to 16.9. since the top of the ladder slips down 4 feet, then the height of the wall =16.9-4= <gadget id="calculator">16.9-4</gadget> <output>12.9</output> 12.9 the bottom=sqrt(18^2-12.9^2)=sqrt(324-166.41)=12.5 ans is 12.5 <result>A</result>

A

A ladder 18 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 6 feet from the base of the wall. If the top of the ladder slips down 4 feet, how many feet will the bottom of the ladder slip?

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For her customer feedback score, Jess wants to average at or above an 8.0 rating. For the month of June, she received the following scores: 7, 8, 8, 7, 9, 9, 6, 7, 8 and 7. By what percent did she fall short of her goal? Select the correct option. A) 4% B) 5% C) 8% D) 10% E) 12%

Expected minimum rating = 8 Deviation from the expected minimum rating = (-1 + 0 + 0 - 1 + 1 + 1 - 2 - 1 + 0 - 1)/10 = -4/10 = -0.4 Current rating is 0.4 less than 8. Percentage = (0.4/8)*100= <gadget id="calculator">(0.4/8)*100</gadget> <output>5</output> 5% Answer: 5% <result>B</result>

B

For her customer feedback score, Jess wants to average at or above an 8.0 rating. For the month of June, she received the following scores: 7, 8, 8, 7, 9, 9, 6, 7, 8 and 7. By what percent did she fall short of her goal?

aqua_rat__wnE6PunEE0rBhBYp

he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg. What might be the weight of the new person ? Choose the most appropriate option A) 75 kg B) 95 kg C) 45 kg D) 85 kg E) 25 kg

Explanation: Total weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (75 + 20)= <gadget id="calculator">(75 + 20)</gadget> <output>95</output> 95 kg. Answer: 95 kg <result>B</result>

B

he average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg. What might be the weight of the new person ?

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The value of x is to be randomly selected from the integers from 1 to 11, inclusive, and then substituted into the equation y = x^2 - 4x + 3. What is the probability that the value of y will be negative? Choose the correct choice from the following answers: A) 5/11 B) 4/11 C) 3/11 D) 2/11 E) 1/11

y will only be negative for x=2. (We can check the values from 1 to 11 to be certain.) P(y is negative) = 1/11 The answer is 1/11. <result>E</result>

E

The value of x is to be randomly selected from the integers from 1 to 11, inclusive, and then substituted into the equation y = x^2 - 4x + 3. What is the probability that the value of y will be negative?

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A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? Choose the correct choice from the following choices: A) 287m B) 278m C) 400m D) 228m E) 282m

Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 42 = 50/3 3(x + 300) = 2100 è x = 400m. Answer:400m <result>C</result>

C

A 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?

aqua_rat__d4kvDxZfzBxwnK7l

Water boils at 212°F or 100°C and melts at 32°F or 0°C . If the temperature of the particular day is 35°C , it is equal to Pick one A) 40 B) 80 C) 95 D) 100 E) 120

Let F and C denotes the temparature in Fahrenheit anid Celcsius respectively. Then, (F - 32) /(212 - 32) = (C - 0)/(100 - 0), if c = 35, then F = 95. 95 <result>C</result>

C

Water boils at 212°F or 100°C and melts at 32°F or 0°C . If the temperature of the particular day is 35°C , it is equal to

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One night 40 percent of the female officers on a police force were on duty. If 240 officers were on duty that night and half of these were female officers, how many female officers were on the police force? Choices A) 90 B) 300 C) 270 D) 500 E) 1,000

Let total number of female officers in the police force = F Total number of officers on duty on that night = 240 Number of female officers on duty on that night = 240/2= <gadget id="calculator">240/2</gadget> <output>120</output> 120 (40/100)*F= 120 =&gt;F = 300 Answer 300 <result>B</result>

B

One night 40 percent of the female officers on a police force were on duty. If 240 officers were on duty that night and half of these were female officers, how many female officers were on the police force?

aqua_rat__tFIjbqhTux8t7lmh

If 4/a + 5/a + 6/a is an integer, which of the following must also be an integer? Options: A) 12/a B) 3/a C) 6/a D) 9/a E) 15/a

4/a + 5/a + 6/a =15/a Answer 15/a <result>E</result>

E

If 4/a + 5/a + 6/a is an integer, which of the following must also be an integer?

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A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent? Select the correct option: A) 70% B) 20% C) 60% D) 10% E) 80%

Explanation: 900 ---- 180 100 ---- ? =&gt; 20% Answer: 20% <result>B</result>

B

A cycle is bought for Rs.900 and sold for Rs.1080, find the gain percent?

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The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics? Pick one A) 48 B) 12 C) 75 D) 28 E) 91

Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively. P + C + M = 150 + P C + M = 150 Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 150/2= <gadget id="calculator">150/2</gadget> <output>75</output> 75. Option 75 <result>C</result>

C

The total marks obtained by a student in Physics, Chemistry and Mathematics is 150 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?

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If m and n are positive integers, and m=2n and k=9m, then - Select A) k is a factor of m. B) 2m is a factor of k. C) 3m is a factor of k/2. D) m/2 is a factor of k. E) k is a factor of m/2.

m=2n --&gt; m is even. k=9m --&gt; m is factor of k, thus m/2 = integer must also be a factor of k. Answer: m/2 is a factor of k.. <result>D</result>

D

If m and n are positive integers, and m=2n and k=9m, then -

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The average age of 40 students is 8 years. If the age of teacher is also included , then their average age increases by half a year. What is the age of the teacher? Choose the correct choice from the following choices. A) 45 years B) 48.5 years C) 28.5 years D) 26.5 years E) 27.5 years

Total age of 40 students = 40*8= <gadget id="calculator">40*8</gadget> <output>320</output> 320 Let the age of the the teacher be x, Then (320+x)/41= 8+1/2 =8 ½. 320+x =17/2*41 =697/2= <gadget id="calculator">697/2</gadget> <output>697/2 = around 348.5</output> 348.5, x=348.5-320= <gadget id="calculator">348.5-320</gadget> <output>28.5</output> 28.5 ANSWER:28.5 years <result>C</result>

C

The average age of 40 students is 8 years. If the age of teacher is also included , then their average age increases by half a year. What is the age of the teacher?

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In how many ways can a Chief Minister and a Vice Minister be elected from a team of 11 members? Choices. A) 110 B) 121 C) 132 D) 144 E) 169

There are 11 choices for the Chief Minister. Then there are 10 choices for the Vice Minister. The total number of ways is 11*10= <gadget id="calculator"> 11*10</gadget> <output>110</output> 110. The answer is 110. <result>A</result>

A

In how many ways can a Chief Minister and a Vice Minister be elected from a team of 11 members?

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Two cars namely A and B start simultaneously from a certain place at the speed of 40 kmph and 55 kmph, respectively.The car B reaches the destination 2 hours earlier than A. What is the distance between the starting point and destination? Choose one A) 8 hours 12 minutes B) 6 hours 15 minutes C) 7 hours 20 minutes D) 7 hours 12 minutes E) None

Explanation : Let the time taken by car A to reach destination is T hours So, the time taken by car B to reach destination is (T – 2) hours. S1T1 = S2T2 =&gt; 40(T) = 55 (T – 2) =&gt; 40T = 55T -110 =&gt; 15T = 110 T = 7 hours 20 minutes Answer – 7 hours 20 minutes <result>C</result>

C

Two cars namely A and B start simultaneously from a certain place at the speed of 40 kmph and 55 kmph, respectively.The car B reaches the destination 2 hours earlier than A. What is the distance between the starting point and destination?

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The length of a train and that of a platform are equal. If with a speed of 36 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? Choose the correct choice from the following options. A) 299 B) 300 C) 299 D) 750 E) 261

Speed = [36 * 5/18] m/sec = 10 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 10 =&gt; x = 10 * 60 / 2= <gadget id="calculator">10 * 60 / 2</gadget> <output>300</output> 300 Answer: 300 <result>B</result>

B

The length of a train and that of a platform are equal. If with a speed of 36 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?