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NLP Centre, Faculty of Informatics, Masaryk University 14

aqua_rat__8xXE31jiAUFKP4r3

Find the least number which when divided by 34 and 5 leaves a remainder of 4 in each case. Choose the correct choice from the following A) 170 B) 172 C) 174 D) 176 E) 178

The least number which when divided by different divisors leaving the same remainder in each case = LCM(different divisors) + remainder left in each case. Hence the required least number = LCM(31, 5) + 4 = 174. ANSWER:174 <result>C</result>

C

Find the least number which when divided by 34 and 5 leaves a remainder of 4 in each case.

aqua_rat__9CMyyawrcW2HIGea

A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man? Choose one: A) 5.79 B) 5.77 C) 5.76 D) 5.72 E) 5.71

M = 6 S = 1.2 DS = 7.2 US = 4.8 x/7.2 + x/4.8 = 1 x = 2.88 D = 2.88 * 2 = 5.76.Answer:5.76 <result>C</result>

C

A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?

aqua_rat__IaWoSoHa2g5kG4qc

At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants? Choose the correct choice from the following answers: A) 2 B) 3 C) 4 D) 5 E) 6

39 = 19 + 18 + 12 - 4 - 2x 2x = 19 + 18 + 12 - 4 - 39 = 45 - 39= <gadget id="calculator">45 - 39</gadget> <output>6</output> 6 x= 3 ANSWER:3 <result>B</result>

B

At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 19 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?

aqua_rat__LgAaSUFp0dArub7W

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 red nor green? Options: A) 3/4 B) 1/4 C) 1/3 D) 7/19 E) 1/7

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 red nor green = event that the ball drawn is blue. n(E)=7 P(E)=n(E)/n(S) =7/21 =1/3 The answer should be 1/3 <result>C</result>

C

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 red nor green?

aqua_rat__tnw7Ui1BPJrC4bH0

In how many ways 5 boys and 5 girls can be seated in a row so that boys and girls are alternate? Choose the correct choice from the following answers A) 28400 B) 28500 C) 28600 D) 28700 E) 28800

number of ways = 2*5!*5! = 28800 Answer is 28800 <result>E</result>

E

In how many ways 5 boys and 5 girls can be seated in a row so that boys and girls are alternate?

aqua_rat__V83OaTv80TPm79Cs

For how many integers k is (k^2)+3 = 3+(2^k) ? Select A) None B) 1 C) 2 D) 3 E) 4

(2^2)+3= 3+(2^2) (2^4)+3= 3+(4^2) For k= 2 and 4 the above equality holds true. Answer:Option 2 <result>C</result>

C

For how many integers k is (k^2)+3 = 3+(2^k) ?

aqua_rat__tQQixOUKC7y0es5V

There are two pipes which are functioning simultaneouly to fill a tank in 12 hours, if one pipe fills the tank 10 hours faster than other then how many hours second pipe will take to fill the tank ? Choices A) 30 hours B) 35 hours C) 40 hours D) 42 hours E) 41 hours

Explanation: Lets suppose tank got filled by first pipe in X hours, So, second pipe will fill the tank in X + 10 hours. =&gt;1/X+1/X+10=1/12 =&gt;X=20 30 hoursNSWER IS 30 hours <result>A</result>

A

There are two pipes which are functioning simultaneouly to fill a tank in 12 hours, if one pipe fills the tank 10 hours faster than other then how many hours second pipe will take to fill the tank ?

aqua_rat__Zl6XOOvFbNQSKADd

A train of length 180 metres takes 54 seconds to cross a tunnel of length 270 metres. What is the speed of the train in km/hr? Choose the correct choice from the following answers. A) 50 km/hr. B) 20 km/hr. C) 30 km/hr. D) 40 km/hr. E) None

Sol. Speed = [180 + 270 / 54] m/sec = [450 / 54 * 18/5] km/hr =30 km/hr. Answer 30 km/hr. <result>C</result>

C

A train of length 180 metres takes 54 seconds to cross a tunnel of length 270 metres. What is the speed of the train in km/hr?

aqua_rat__UOB56a4JEf8HfNmn

If 7 ministers are to be seated at a round table conference, then how many different ways can they be seated? Options A) 24 B) 60 C) 720 D) 520 E) 180

Simple formula: There are (n - 1)! ways to arrange n distinct objects in a circle. so its (7-1)= <gadget id="calculator"> (7-1)</gadget> <output>6</output> 6!= 720=720 <result>C</result>

C

If 7 ministers are to be seated at a round table conference, then how many different ways can they be seated?

aqua_rat__QI8MyKUgoNm8D4JD

The number which exceeds 12% of it by 52.8 is: Choices: A) 60 B) 77 C) 269 D) 26 E) 91

Explanation: Let the number be x. Then, x – 12% of x = 52.8 x – (12/100)x = 52.8 x (1– 12/100) = 52.8 (88/100)x = 52.8 x = (100 X 52.8) / 88 = 60 60NSWER: 60 <result>A</result>

A

The number which exceeds 12% of it by 52.8 is:

aqua_rat__LbNCngifFfReK8LA

How many prime numbers are between 15/7 and 131/6? Options A) 3 B) 4 C) 5 D) 6 E) 7

15/7= 3- 131/6= 22- Prime numbers between 3 and 22 are 5, 7, 11, 13, 17, and 19 - sign signifies that the number is marginally less . Answer 6 <result>D</result>

D

How many prime numbers are between 15/7 and 131/6?

aqua_rat__9JBXPIVFa0B0FxUq

A boy has Rs. 320 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? Options. A) 60 B) 110 C) 140 D) 130 E) 120

Let number of notes of each denomination be x. Then x + 5x + 10x = 320 16x = 320 x = 20. Hence, total number of notes = 3x = 60. 60 <result>A</result>

A

A boy has Rs. 320 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

aqua_rat__zzaZ9WQRG2fHUM1U

Find the odd man out. 1, 3, 10, 13, 19, 29 Select the correct option A) 12 B) 9 C) 1 D) 3 E) 10

10 is an even number. All other given numbers are odd Answer : Option 10 <result>E</result>

E

Find the odd man out. 1, 3, 10, 13, 19, 29

aqua_rat__fRamtiOuZ4okTcB4

What is the probability that their sum of two numbers, randomly selected from the set {3,6,9,12,15,18} will be greater than 9? Choose one: A) 7/6 B) 7/9 C) 7/8 D) 7/10 E) 6/7

First7 problem is 6C2 = 12 .. Not 20.. Point 2, you sum should be greater than 9, so these are the following possibilities you have ({3,9},{3,12},{3,15},{3,18},{6,9},{6,12},{6,15},{6,18},{9,12},{9,15},{9,18},{12,15},{12,18},{15,18}) which leads to 14 pairs So the probability is 14 on 12 or 7/6.. 7/6NSWER:7/6 <result>A</result>

A

What is the probability that their sum of two numbers, randomly selected from the set {3,6,9,12,15,18} will be greater than 9?

aqua_rat__zNH3yklhz2Oa7kzG

Two letters from the word KHANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant? Choices: A) 25/28 B) 27/28 C) 30/28 D) 40/28 E) 50/28

There are 6 consonants and 2 vowels in KHANTKAR . probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels) Probability of both vowels = 2C2/8C2 = 1/28 So,Answer is 1 - 1/28 = 27/28 Answer : 27/28 <result>B</result>

B

Two letters from the word KHANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant?

aqua_rat__qC8sEvszsTONNwXs

Working alone, Jim finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Jim alone cleans the entire house in 6 hours. How many hours will it take Nick and Jim to clean the entire house if they work together? Select the correct option. A) 1.5 B) 2 C) 2.4 D) 3 E) 3.6

Answer is 3.6 hours. Jim does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6 answer is 3.6 <result>E</result>

E

Working alone, Jim finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Jim alone cleans the entire house in 6 hours. How many hours will it take Nick and Jim to clean the entire house if they work together?

aqua_rat__gQ3R3NAB8DIyACnn

In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital? Answers A) 11758 B) 11759 C) 11755 D) 11750 E) 11751

200 + 130= <gadget id="calculator">200 + 130</gadget> <output>330</output> 330 800 - 330= <gadget id="calculator">800 - 330</gadget> <output>470</output> 470 200 ---- 5000 470 ---- ?=&gt; 11750 Answer: 11750 <result>D</result>

D

In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.800 is Rs.200 and C's share is Rs.130, what is B's capital?

aqua_rat__PHyw9i4srh2sNeJC

Choose the missing terms out of the given alternatives. CMW, HRB, ?, RBL, WGQ, BLV Choose the correct choice from the following choices: A) MWS B) MWG C) SJE D) HHW E) YSH

MWG MWG The letters move five steps forward. <result>B</result>

B

Choose the missing terms out of the given alternatives. CMW, HRB, ?, RBL, WGQ, BLV

aqua_rat__exc5PTEhQO40kV0N

Which of the following will divide evenly into 407,406,520? Answers. A) 11 B) 21 C) 4 D) 31 E) 41

Rule: 4: Last two digits should be divisible by 4 the last two digits are 00, which are divisible by 4 Answer: 4 <result>C</result>

C

Which of the following will divide evenly into 407,406,520?

aqua_rat__L6IzpqQtZ6DNVryC

Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is Choose the correct answer: A) 30 Km/hr B) 36 Km/hr C) 80 Km/hr D) 90 Km/hr E) None of these

Explanation: Distance covered = 120+120= <gadget id="calculator">120+120</gadget> <output>240</output> 240 m Time= 12 s Let the speed of each train = x. Then relative velocity = x+x = 2x 2x = distance/time = 240/12= <gadget id="calculator">240/12</gadget> <output>20</output> 20 m/s Speed of each train= x = 20/2= <gadget id="calculator">20/2</gadget> <output>10</output> 10 m/s= 10*18/5 km/hr = 36 km/hr Option 36 Km/hr <result>B</result>

B

Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is

aqua_rat__bmUZQNnVQWkXzr5v

A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is? Pick one A) 128 B) 177 C) 199 D) 178 E) 150

Let the length of the train be x meters and its speed be y m/sec. They, x / y = 15 =&gt; y = x/15 x + 100 / 25 = x / 15 x = 150 m. Answer:150 <result>E</result>

E

A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?

aqua_rat__cUcSlEaIhb1zYDw7

Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? Choose one. A) Rs.200 B) Rs.250 C) Rs.300 D) Rs.350 E) Rs.370

Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 550 Rs.250ut x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 550 ⇒ y[12/10 + 1] = 550 ⇒ 22y/10 = 550 ⇒ 22y = 5500 ⇒ y = 5500/22 = 500/2 = Rs.250 Rs.250) <result>B</result>

B

Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?

aqua_rat__lCr8o6fxhWlL2QCZ

The area of playground is 5700 sq. meters. What will be the cost of covering it with grass sheet 1cm deep, if cost of grass sheet is $2.80 per cubic meter. Choose the most appropriate option: A) a) $144 B) b) $150.50 C) c) $159.6 D) d) $158.60 E) e) $160.70

total volume * unit cost = total cost or, 5700 * 0.01 * 2.8 = total cost = 159.6=c) $159.6 <result>C</result>

C

The area of playground is 5700 sq. meters. What will be the cost of covering it with grass sheet 1cm deep, if cost of grass sheet is $2.80 per cubic meter.

aqua_rat__UsFTljRMWjFe26ou

A man has Rs. 400 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? Pick one A) 45 B) 60 C) 75 D) 90 E) 105

Answer : C Let number of notes of each denomination be x. Then, x + 5x + 10x = 400 16x = 400 x = 25. Hence, total number of notes = 3x = 75. <result>C</result>

C

A man has Rs. 400 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

aqua_rat__eT0gc12dlZ86xgCw

An design manager has 10patterns of chairs & 9patterns of tables. In how many ways can he make a pair of table & chair? Choose the most appropriate option: A) 20 B) 40 C) 80 D) 90 E) 100

He has has ten patterns of chairs and eight patterns of tables Hence, A chair can be arranged in 10 ways and A table can be arranged in 9 ways Hence one chair and one table can be arranged in 10 x 9 ways = 90 ways 90 <result>D</result>

D

An design manager has 10patterns of chairs & 9patterns of tables. In how many ways can he make a pair of table & chair?

aqua_rat__xokIrLqG3gbSImzP

The perimeter of a square is 52 m. Find the area of the square. Choose the most appropriate option: A) 161 m². B) 164 m². C) 166 m². D) 169 m². E) 273 m².

Perimeter of square = 52 m But perimeter of square = 4 × side Therefore, 4 × side = 52 m Therefore, side= 52/4= <gadget id="calculator">52/4</gadget> <output>13</output> 13m Now, the area of the square= (side × side) Therefore, area of the square = 13 × 13 m² = 169 m². ANSWER : OPTION 169 m². <result>D</result>

D

The perimeter of a square is 52 m. Find the area of the square.

aqua_rat__bdKlg4c4JDSTIZNd

Find the distance covered by a man walking for 36min at a speed of 10km/hr? Pick one: A) 1km B) 3km C) 6 km D) 5km E) 6km

Distance = 10*36/60= <gadget id="calculator">10*36/60</gadget> <output>6</output> 6 km Answer is 6 km <result>C</result>

C

Find the distance covered by a man walking for 36min at a speed of 10km/hr?

aqua_rat__XYX4l2DbOuP0Or5i

A train 2500 m long can cross an electric pole in 100 sec and then find the speed of the train? Choose the correct choice from the following choices A) 90 B) 60 C) 120 D) 180 E) 360

Length = Speed * time Speed = L/T S = 2500/100= <gadget id="calculator">2500/100</gadget> <output>25</output> 25 M/Sec Speed= 25*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 90 Kmph 90nswer:90 <result>A</result>

A

A train 2500 m long can cross an electric pole in 100 sec and then find the speed of the train?

aqua_rat__jjKUheJfeLWIYMq5

The list price of an article is Rs.70. A customer pays Rs.59.22 for it. He was given two successive discounts, one of them being 10%. The other discount is? Choose the correct choice from the following: A) 8% B) 7% C) 10% D) 12% E) 6%

Option 6% 6%xplanation: 70*(90/100)*((100-x)/100) = 59.22 x = 6% <result>E</result>

E

The list price of an article is Rs.70. A customer pays Rs.59.22 for it. He was given two successive discounts, one of them being 10%. The other discount is?

aqua_rat__3Db23Mv9DMh20sdz

Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science? Choose the correct choice from the following choices: A) 18 B) 68 C) 67 D) 55 E) 56

S:E = 1:3 E:M = 3:5 ------------ S:E:M = 3:9:15 3/27 * 162= <gadget id="calculator">3/27 * 162</gadget> <output>18</output> 18 18nswer:18 <result>A</result>

A

Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science?

aqua_rat__Ef4Bx1wd2UqYQU1u

Kail purchased n items from a catalog for $10 each. Postage and handling charges consisted of $4 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ? Pick one: A) 11n + 2 B) 11n + 4 C) 11n + 3 D) 9n + 3 E) 9n + 4

its 11n + 3 n items for $10 each total price $10n postage and handling of $4 for 1st item and $1 for the rest total postage and handling = $ [4+ (n-1)] = $ n+3 total cost 10n+n+3 = 11n+3 <result>C</result>

C

Kail purchased n items from a catalog for $10 each. Postage and handling charges consisted of $4 for the first item and $1 for each additional item. Which of the following gives the total dollar amount for Kim’s purchase, including postage and handling, in terms of n ?

aqua_rat__Q4ceDEW3MeUh3obg

In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities? Pick one A) A)136 B) B)627 C) C)153 D) D)721 E) E)159

46 + 28 + 10= <gadget id="calculator">46 + 28 + 10</gadget> <output>84</output> 84% 100 – 84= 16% 850 * 16/100= <gadget id="calculator"> 850 * 16/100</gadget> <output>136</output> 136 136nswer:136 <result>A</result>

A

In a school of 850 boys, 46% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?

aqua_rat__lYtfh4MTHPOZP47v

A tank can be filled by pipe A in 5 hours and by pipe B in 8 hours, each pump working on its own. When the tank is full and a drainage hole is open, the water is drained in 20 hours. If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how long does it take for the tank to be filled? Choose the most appropriate option: A) 2.6 hours B) 3.6 hours C) 4.6 hours D) 5.6 hours E) None of these

Let's first find the rates of the pumps and the drainage hole pump A: 1 / 5 , pump B: 1 / 8 , drainage hole: 1 / 20 Let t be the time for the pumps to fill the tank. The pumps ,add water into the tank however the drainage hole drains water out of the tank, hence t ( 1 / 5 + 1 / 8 - 1 / 20) = 1 Solve for t t = 3.6 hours Answer 3.6 hours <result>B</result>

B

A tank can be filled by pipe A in 5 hours and by pipe B in 8 hours, each pump working on its own. When the tank is full and a drainage hole is open, the water is drained in 20 hours. If initially the tank was empty and someone started the two pumps together but left the drainage hole open, how long does it take for the tank to be filled?

aqua_rat__Xi8ks9MZyGnheNqc

A certain company’s profit in 1996 was 15 percent greater than its profit in 1995, and its profit in 1997 was 20 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995? Choose the correct option. A) 5% B) 18% C) 33% D) 35% E) 38%

Soln:- Profit in 1995 - 100 Profit in 1996 - 115 %increase Profit in 1997 in comparison to 1995 = 15 + 115*20%= 38% ANSW38%R:38% <result>E</result>

E

A certain company’s profit in 1996 was 15 percent greater than its profit in 1995, and its profit in 1997 was 20 percent greater than its profit in 1996. The company’s profit in 1997 was what percent greater than its profit in 1995?

aqua_rat__VGYP40vjL2iFsWsU

What is the value of x? Data 1: x - 2y = 7 Data 2: 4x – 28 = 8y Choices: A) 89 B) 10 C) 12 D) 15 E) no solution exists

both are same equations 4X(x-2y=7) is 4x-8y=28 so no solution exists ANSWno solution existsR:no solution exists <result>E</result>

E

What is the value of x? Data 1: x - 2y = 7 Data 2: 4x – 28 = 8y

aqua_rat__yNcGPB4ihjW1j1Gp

The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is Choose one. A) 4/5 B) 7/11 C) 7/13 D) 7/15 E) 8/11

Let the required fraction be x. Then 1 - x = 9 x 20 1 - x2 = 9 x 20 20 - 20x2 = 9x 20x2 + 9x - 20 = 0 20x2 + 25x - 16x - 20 = 0 5x(4x + 5) - 4(4x + 5) = 0 (4x + 5)(5x - 4) = 0 x = 4/5 4/5) <result>A</result>

A

The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is

aqua_rat__CLowsm5TuvRJBMcO

A box contains 8 apples, 7 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n? Pick one: A) 3 B) 4 C) 5 D) 6 E) 7

P(choosing a red apple 5 times in a row) = 7/8*6/7*5/6*4/5*3/4 = 3/8 &lt; 0.5 The answer is 5. <result>C</result>

C

A box contains 8 apples, 7 of which are red. An apple is drawn from the box and its color is noted before it is eaten. This is done a total of n times, and the probability that a red apple is drawn each time is less than 0.5. What is the smallest possible value of n?

aqua_rat__STulqryDacRCoKDF

When not moving on the sidewalk, Maya can walk the length of the sidewalk in 7 minutes. If she stands on the sidewalk as it moves, she can travel the length in 4 minutes. If Maya walks on the sidewalk as it moves, how many minutes will it take her to travel the same distance? Assume she always walks at the same speed, and express your answer as a decimal to the nearest tenth. Pick one. A) 2.9 B) 2.5 C) 2.7 D) 2.1 E) 2.2

Explanation: Assume distance of sidewalk "x" Speed 1 (moving on sidewalk) Speed 2 (moving off sidewalk) Since both the movements are in same direction, we can do speed 1 + speed 2 Speed 1 = x4x4 Speed 2 = x7x7 Speed 1 + speed 2 = 11x2811x28 = = 0.39286x Now new time while moving on sidewalk = x0.39286xx0.39286x = 2.54544 Hence, the answer is 2.5 Answer: 2.5 <result>B</result>

B

When not moving on the sidewalk, Maya can walk the length of the sidewalk in 7 minutes. If she stands on the sidewalk as it moves, she can travel the length in 4 minutes. If Maya walks on the sidewalk as it moves, how many minutes will it take her to travel the same distance? Assume she always walks at the same speed, and express your answer as a decimal to the nearest tenth.

aqua_rat__LEIEpGiNg31uQ1ip

There are 21 balls in a jar: 14 red, 4 blue and 3 green. If a single ball is drawn from the jar, what is the probability of that it is either blue or red? Choose the correct choice from the following answers: A) 1/12 B) 3/4 C) 6/9 D) 6/7 E) 3/4

Blue + Red =18 Total number of balls is 14+4+3= <gadget id="calculator"> 14+4+3</gadget> <output>21</output> 21 So the answer is 18/21=6/7 Answer 6/7 <result>D</result>

D

There are 21 balls in a jar: 14 red, 4 blue and 3 green. If a single ball is drawn from the jar, what is the probability of that it is either blue or red?

aqua_rat__wdgWWBJrsPnbndIt

A train is walking at 6/7 of its usual speed, the train is 20 minutes too late. Find its usual time to cover the journey. Options: A) 1 hour B) 30min C) 3 hours 20 min D) 2 hours 30 min E) 2 hours

new speed = 6/7 of the usual speed new time taken = 7/6 of the usual time taken so, ( 7/6 of the usual time ) - ( usual time ) = 20min 1/6 of the usual time = 20min usual time = 20*6= <gadget id="calculator">20*6</gadget> <output>120</output> 120 min= 2 hours correct option is 2 hours <result>E</result>

E

A train is walking at 6/7 of its usual speed, the train is 20 minutes too late. Find its usual time to cover the journey.

aqua_rat__Nnytc0twqpY986CA

A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt? Answers A) 109 ways B) 908 ways C) 128 ways D) 108 ways E) 104 ways

The boy can select one trouser in nine ways. The boy can select one shirt in 12 ways. The number of ways in which he can select one trouser and one shirt is 9 * 12= <gadget id="calculator"> 9 * 12</gadget> <output>108</output> 108 ways. Answer:108 ways <result>D</result>

D

A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt?

aqua_rat__flkpvkW50zSqQePe

How many meters are there in 770 centimeters? Choose the correct choice from the following: A) 770 meters B) 7.6 meters C) 700 meters D) 6.5 meters E) 7.7 meter

Solution: 1 meter = 100 centimeters Just divide 770 by 100 770 ÷ 100 = 7.7, so there are 7.7 meters in 770 centimeters Option 7.7 meter <result>E</result>

E

How many meters are there in 770 centimeters?

aqua_rat__ZFKEf14oyUOz7vQa

A shopkeeper sold an article at $1800 with 20% profit. Then find its cost price? Choose the correct choice from the following: A) $1000 B) $1500 C) $1850 D) $1600 E) $2000

cost price = selling price *100/(100+profit) C.P. = 1800*100/120= <gadget id="calculator">1800*100/120</gadget> <output>1_500</output> $1500 Answer is $1500 <result>B</result>

B

A shopkeeper sold an article at $1800 with 20% profit. Then find its cost price?

aqua_rat__0yRWYtNed9erd4FI

For what values of k will the pair of equations 3(3x + 4y) = 36 and kx + 12y = 30 does not have a unique solution? Select A) 12 B) 9 C) 3 D) 7.5 E) 2.5

we have 2 equations 1. 3(3x + 4y) = 36 --&gt; 3x + 4y = 12 -- &gt; 9x + 12y = 36 2. kx + 12y = 30 substract 1-2, we get (9-K)x = 6 i.e. x = 6/(9-k) then, by looking at options, we get some value of x except for B. When we put k=9, x becomes 6/0 and hence answer is 9 <result>B</result>

B

For what values of k will the pair of equations 3(3x + 4y) = 36 and kx + 12y = 30 does not have a unique solution?

aqua_rat__Ubev1OSn5rTydEQZ

A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year? Options: A) 32:45 B) 32:47 C) 32:45 D) 32:41 E) 32:42

32:45 : B (8000*4)+(4000*8) : (9000*6)+(6000*6) 64000 : 90000 32 : 45.32:45nswer: 32:45 <result>A</result>

A

A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?

aqua_rat__7xiqTbHiEw724ayZ

Workers decided to raise Rs.3lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25lacs. How many workers were they? Choose the correct choice from the following options: A) 350 B) 400 C) 500 D) 550 E) 590

N * 50 = (325000 - 300000)= <gadget id="calculator">(325000 - 300000)</gadget> <output>25_000</output> 25000 N= 25000 / 50= <gadget id="calculator">25000 / 50</gadget> <output>500</output> 500 500 <result>C</result>

C

Workers decided to raise Rs.3lacs by equal contribution from each. Had they contributed Rs.50 eachextra, the contribution would have been Rs.3.25lacs. How many workers were they?

aqua_rat__jsAyA6bnVMQtBAA0

In how many ways can 12 different gifts be divided among four children such that each child receives exactly three gifts? Select the correct option: A) 16^3 B) (4!)^3 C) 12!/(3!)^4 D) 12!/4! E) 4^12

Total 12 different Gifts, and 4 children. Thus any one child gets 12C3 gifts, then the other child gets 9C3 gifts(12 total - 3 already given), then the third one gets 6C3 gifts, and the last child gets 3C3 gifts. Since order in which each child gets the gift is not imp, thus, ans : 1212!/(3!)^43 * 912!/(3!)^43 * 612!/(3!)^43 * 312!/(3!)^43 = 12! / (3!)^4 Ans : 12!/(3!)^4. <result>C</result>

C

In how many ways can 12 different gifts be divided among four children such that each child receives exactly three gifts?

aqua_rat__WPE2Yox96NTReqey

The sum of three integers A, B and C is 180. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C? Select A) 120 B) 125 C) 105 D) 115 E) 110

A is one third of the sum of B and C.. or A=1/3(B+C)... But A+B+C=180. so 1/3(B+C)+B+C=180 4(B+C)/3= 180 B+C =180*3/4= <gadget id="calculator">180*3/4</gadget> <output>135</output> 135 A=180-135= <gadget id="calculator">180-135</gadget> <output>45</output> 45 2)B is one fifth of the sum of A and C or B=1/5(A+C)... 125ut A+125+C=180 so 1/5(A+C)+A+C=180 A+C=180*5/6= <gadget id="calculator">180*5/6</gadget> <output>150</output> 150 but A=45, so C=150-45= <gadget id="calculator">150-45</gadget> <output>105</output> 105 Answer : 125 <result>B</result>

B

The sum of three integers A, B and C is 180. A is one third of the sum of B and C and B is one fifth of the sum of A and C. What is C?

aqua_rat__hWeb41jaXzOdf9Rn

A man gets a simple interest of Rs.400 on a certain principal at the rate of 5% p.a in eight years. Find the compound interest the man will get on twice the principal in two years at the same rate? Choices: A) s.256.27 B) s.256.29 C) s.205.00 D) s.256.22 E) s.256.25

Let the principal be Rs.P S.I at 5% p.a in 8 years on Rs.P = Rs.400 (P)(8)(5)/100 = 400 P = 1000 s.205.00.I on Rs.2P i.e., Rs.2000 at 5% p.a in two years =2000{ [1 + 5/100]^2 - 1} = = 2000(41/ 400) = Rs.205 Answer:s.205.00 <result>C</result>

C

A man gets a simple interest of Rs.400 on a certain principal at the rate of 5% p.a in eight years. Find the compound interest the man will get on twice the principal in two years at the same rate?

aqua_rat__ALDRlHwe50n53iH1

A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability C that out of the two, one is white and one is blue? Answers. A) 15/56 B) 41/56 C) 13/28 D) 15/28 E) 5/14

The required probability C= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls. Ways to select 6 out of total 8 = 8C6 Ways to select 4 out of 5 white balls = 5C4 Ways to select 2 out of 3 blue balls = 3C2 Thus the required probability = (5C4*3C2)/8C6 = 15/28. 15/28 is thus the correct answer. <result>D</result>

D

A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability C that out of the two, one is white and one is blue?

aqua_rat__FMopeQRpic3Hg6O8

Of 120 applicants for a job, 56 had at least 4 years' experience, 72 had degrees, and 12 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree? Choose the correct choice from the following options A) 10 B) 15 C) 22 D) 20 E) 24

120 - 12= <gadget id="calculator">120 - 12</gadget> <output>108</output> 108 108 - 56 - 72= -20 Then 20 are in the intersection between 4 years experience and degree. Answer : 20 <result>D</result>

D

Of 120 applicants for a job, 56 had at least 4 years' experience, 72 had degrees, and 12 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?

aqua_rat__1Zoc36uFDH2IkSmZ

Eleven books consisting of 5 financial management, 4 marketing management and 2 system management are placed on a shelf at random order. What is the probability that the books of each kind are all together. Choose the correct choice from the following answers. A) 1/1155 B) 1/1255 C) 1/1355 D) 1/1455 E) 1/1555

(Probability of an event) = (Favorable) / (Total) The total number of ways to arrange 11 books in a row is 11!. 3 groups of books: financial management (F), marketing management (M) and system management (S), can be arranged in 3! ways: FMS, FSM, MFS, MSF, SFM, and SMF (this way all the books of each kind will be together). Now, books in F itself can be arranged in 5! ways, in M in 4! ways and in S in 2! ways. Hence, the total number of ways to arrange books so that books of each kind are together is 3!*5!*4!*2!. P = (3!*5!*4!*2!) / 11! = 1/1155. 1/1155nswer: 1/1155 <result>A</result>

A

Eleven books consisting of 5 financial management, 4 marketing management and 2 system management are placed on a shelf at random order. What is the probability that the books of each kind are all together.

aqua_rat__d3EjU04Ck5yeEs1j

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

1/3: 1/2: 1/1 = 2:3:6 Answer: 2:3:6 <result>D</result>

D

The inverse ratio of 3: 2: 1 is?

aqua_rat__CjL0Vgj5SxVvWmnq

Which of the following MUST yield an integer when divided by 11? Select. A) The sum of eleven consecutive positive integers. B) The square of a prime number. C) The sum of two odd integers. D) The product of three consecutive odd numbers. E) The difference between a multiple of 8 and a multiple of 3.

For option A: Let the numbers be (x-5), (x-4), (x-3), (x-2), (x-1), (x), (x+1), (x+2), (x+3), (x+4), (x+5). Now, (x-5)+(x-4)+(x-3)+(x-2)+(x-1) + (x) + (x+1) + (x+2)+(x+3)+(x+4)+(x+5) = 11(x). Hence A is true. No need to check other answers since there can only be one correct answer. So, The sum of eleven consecutive positive integers.ns(The sum of eleven consecutive positive integers.). <result>A</result>

A

Which of the following MUST yield an integer when divided by 11?

aqua_rat__Yl6q3Ybq7ZbHn0kh

A coach must choose five starters from a team of 12 players. How many different ways can the coach choose the starters ? Choose the correct choice from the following choices A) 722 B) 729 C) 278 D) 299 E) 271

Explanation: Choose 5 starters from a team of 12 players. Order is not important. \inline {\color{729lack} 12C_{5}}= 729 Answer: 729) 729 <result>B</result>

B

A coach must choose five starters from a team of 12 players. How many different ways can the coach choose the starters ?

aqua_rat__gXh8X7ahb7FWMovu

Barbata invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 8% of her entire investment? Answers: A) 1200 B) 3000 C) 1000 D) 3600 E) 2400

Let the additional invested amount for 8% interest be x; Equation will be; 2400+0.05*2400+x+0.08x = 2400+x+0.08(2400+x) 0.05*2400+0.08x = 0.06x+0.08*2400 0.02x = 2400(0.08-0.05) x = 2400*0.03/0.02= <gadget id="calculator">2400*0.03/0.02</gadget> <output>3_600</output> 3600 Ans:3600 <result>D</result>

D

Barbata invests $2400 in the National Bank at 5%. How much additional money must she invest at 8% so that the total annual income will be equal to 8% of her entire investment?

aqua_rat__h7OjD1oejOWDiY8J

One side of the bottom layer of a triangular pyramid has 12 balls. How many are there in the whole pyramid?Note that the pyramid is equilateral and solid. Options A) 286 B) 364 C) 504 D) 164 E) 165

As there are 12 balls along one side, it means that there are 12 layers of balls. The top most layer has 1 ball. The second layer has 3 (1+2) balls. The third layer has 6 (1+2+3) balls. The fourth layer has 10 (1+2+3+4) balls. The fifth layer has 15 (1+2+3+4+5) balls. Similarly, there are 21, 28, 36, 45, 55, 66 and 78 balls in the remaining layers. Hence, the total number of balls are = 1 + 3 + 6 + 10 + 15 + 21 +28 + 36 + 45 + 55 + 66 + 78= <gadget id="calculator">1 + 3 + 6 + 10 + 15 + 21 +28 + 36 + 45 + 55 + 66 + 78</gadget> <output>364</output> 364 balls ANSWER:364 <result>B</result>

B

One side of the bottom layer of a triangular pyramid has 12 balls. How many are there in the whole pyramid?Note that the pyramid is equilateral and solid.

aqua_rat__qCv3cfEKesorF66W

Marcella has 25 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left? Choose the correct choice from the following answers: A) 21 B) 20 C) 19 D) 16 E) 15

greatest number of paired shoes means greatest number of lost pairs 9 shoes have 4 pairs and 1 extra shoes of a pair .so a otal of 5 pairs she loses leftover pair=20 ANSWER:20 <result>B</result>

B

Marcella has 25 pairs of shoes. If she loses 9 individual shoes, what is the greatest number of matching pairs she could have left?

aqua_rat__NwmkSTaYC2lD1WIM

A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order Y? (1 cubic meter = 1,000 liters) Choose the correct choice from the following answers A) 92 B) 90 C) 82 D) 78 E) 75

I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5. Y=12.5*6 = 75.75 <result>E</result>

E

A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this order Y? (1 cubic meter = 1,000 liters)

aqua_rat__lhGk1uxaiISYXN2Q

A merchant can buy goods at the rate of Rs. 20 per good. The particular good is part of an overall collection and the value is linked to the number of items that are already on the market. So, the merchant sells the first good for Rs. 2, second one for Rs. 4, third for Rs. 6…and so on. If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell? Options A) 24 B) 18 C) 27 D) 32 E) 34

DETAILED SOLUTION Let us assume he buys n goods. Total CP = 20n Total SP = 2 + 4 + 6 + 8 ….n terms Total SP should be at least 40% more than total CP 2 + 4 + 6 + 8 ….n terms ≥ 1.4 * 20 n 2 (1 + 2 + 3 + ….n terms) ≥ 28n n(n + 1) ≥ 28n n2 + n ≥ 28n n2 - 27n ≥ 0 n ≥ 27 He should sell a minimum of 27 goods. Answer 27hoice (27) <result>C</result>

C

A merchant can buy goods at the rate of Rs. 20 per good. The particular good is part of an overall collection and the value is linked to the number of items that are already on the market. So, the merchant sells the first good for Rs. 2, second one for Rs. 4, third for Rs. 6…and so on. If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?

aqua_rat__6KBAvBLIEwvS8wLz

65% of x = 20% of 747.50. Find the value of x? Select: A) 100 B) 230 C) 150 D) 180 E) 199

65% of x = 20% of 747.50 Then, 65/100 * x = 20/100 * 7475/10 x = 230 Answer is 230 <result>B</result>

B

65% of x = 20% of 747.50. Find the value of x?

aqua_rat__WJ1reICRjwqkaBsW

The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above conditions is: Choices: A) 4 B) 5 C) 6 D) 6 E) 1

Let the required numbers be 33a and 33b. Then, 33a + 33b = 528 =&gt; a + b = 16. Now, co-primes with sum 16 are (1, 15), (3, 13), (5, 11) and (7, 9). Required numbers are (33 * 1, 33 * 15), (33 * 3, 33 * 13), (33 * 5, 33 * 11), (33 * 7, 33 * 9). The number of such pairs is 4. 4nswer:4 <result>A</result>

A

The sum of two numbers is 528 and their H.C.F is 33. The number of pairs of numbers satisfying the above conditions is:

aqua_rat__NFS41KjMd0MkmjIu

The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 200,000 bacteria Choose one: A) 10 B) 12 C) 14 D) 16 E) 18

The question basically asks how many minutes it takes for a population to increase by factor 200 (200,000 / 1,000 = 200). Now you know that every two minutes the population doubles, i.e. is multiplied by 2. So the equation becomes: 2^x &gt;= 200, where x represents the number of times the population doubles. A lot of people remember that 2^10 = 1,024. Hence, 2^8 = 256, i.e. the population has to double 8 times. Since it takes the population 2 minutes to double once it takes 8*2= <gadget id="calculator">8*2</gadget> <output>16</output> 16 minutes to double 8 times. Thus, solution 16= 16 is correct. <result>D</result>

D

The population of a bacteria culture doubles every 2 minutes. Approximately how many minutes will it take for the population to grow from 1,000 to 200,000 bacteria

aqua_rat__cEK75J0OK5mDFRP1

A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 500 m long? Choose the correct choice from the following options: A) 65sec B) 70sec C) 74sec D) 80sec E) 85sec

Speed = 240/24= <gadget id="calculator">240/24</gadget> <output>10</output> 10 m/sec. Required time= (240 + 500)/10= <gadget id="calculator">(240 + 500)/10</gadget> <output>74</output> 74 sec. Answer:74sec <result>C</result>

C

A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 500 m long?

aqua_rat__kzIUAxcBLhkWrGfH

The average temperature of a city in the first four days of a month was 36°. The average for the 2nd, 3rd, 4th and 5th day was 38°. If the temperature of the 1st and 5th day were in the ratio 4 : 5, then what is the temperature on the fifth day ? Choose the correct choice from the following answers: A) 40° B) 49° C) 43° D) 41° E) 42°

Explanation: The temperature for first 4 days = 4 * 36= <gadget id="calculator">4 * 36</gadget> <output>144</output> 144 The temperature for last 4 days= 4 * 38= <gadget id="calculator">4 * 38</gadget> <output>152</output> 152 The difference between the temperatures is (152 – 144)= 8 The ratio of temperature between first and fifth day is 4 : 5 The temperature on fifth day is 5*8= <gadget id="calculator"> 5*8</gadget> <output>40</output> 40 40°NSWER: 40° <result>A</result>

A

The average temperature of a city in the first four days of a month was 36°. The average for the 2nd, 3rd, 4th and 5th day was 38°. If the temperature of the 1st and 5th day were in the ratio 4 : 5, then what is the temperature on the fifth day ?

aqua_rat__MdL4vHfvxUYrAeOK

A bird shooter was asked how many birds he had in the bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds he had in the bag in all? Options A) 9 B) 18 C) 27 D) 36 E) 34

all sparrows bt six i.e. those six can b 3 pigeons and 3 ducks, similarly the other 2 conditions will apply.. 9NSWER:9 <result>A</result>

A

A bird shooter was asked how many birds he had in the bag. He replied that there were all sparrows but six, all pigeons but six, and all ducks but six. How many birds he had in the bag in all?

aqua_rat__I7EwRheQDZexFdAR

Find the number which multiplied by 15 is increased by 196. Pick: A) 14 B) 20 C) 26 D) 28 E) 27

Let the number be x. Then, 15x - x = 196 x = 14 14NSWER:14 <result>A</result>

A

Find the number which multiplied by 15 is increased by 196.

aqua_rat__cyzpP4TyaPKzyLSY

When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy works alone she chops 3 lb. salad in 2 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 80 lb., the salad quantity chopped by Tom is what percent lesser than the quantifying chopped by Tammy?. Choices A) 44% B) 100% C) 105% D) 225% E) 125%

Tom chops 4 lbs in 6 minutes Tammy chops 9 lbs in 6 minutes So in the same amount of time, Tom chops 125% less than Tammy, since 9 is 125% greater than 4. So 125% is the answer. Note that the actual time doesn't matter. If you multiply the time each work by x, you'll multiply the work each does by x, and 9x is still 125% greater than 4x. Ans:125% <result>E</result>

E

When Tom works alone he chops 2 lb. salad in 3 minutes, and when Tammy works alone she chops 3 lb. salad in 2 minutes. They start working together, and after some time finish chopping 65 lb. of salad. Of those 80 lb., the salad quantity chopped by Tom is what percent lesser than the quantifying chopped by Tammy?.

aqua_rat__yzsVtVkgXrW0w531

If a randomly selected non-negative single digit integer is added to {2, 3, 4, 8}. What is the probability that the median of the set will increase but the range still remains the same? Choose the correct choice from the following choices: A) 0.2 B) 0.3 C) 0.4 D) 0.5 E) 0.6

We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes. Hence, the total number of outcomes is 10. We need to find the probability that the median of the set will increase but the range still remains the same. The median of the set is (3 + 4)/2= <gadget id="calculator"> (3 + 4)/2</gadget> <output>7/2 = around 3.5</output> 3.5, thus the number selected must be 4 or greater. For the range to remain the same, the number must be between 2 and 8 inclusive. To satisfy both conditions, the number selected must be 4, 5, 6, 7, or 8. The probability is 5/10= <gadget id="calculator"> 5/10</gadget> <output>1/2 = around 0.5</output> 0.5 The answer is 0.5. <result>D</result>

D

If a randomly selected non-negative single digit integer is added to {2, 3, 4, 8}. What is the probability that the median of the set will increase but the range still remains the same?

aqua_rat__GLUoscnxTf71i0qX

In a survey conducted to find out the readership of three Newspapers A,B and C, it was found that the number of newspaper A is at least 20 and at most 40. The number of people who read newspaper B is at least 50 and at most 70. The number of people who read newspaper C is at least 70 and at most 83. It was also found that 5 people read all three newspapers. Find the minimum number of people who read both A and B but not C. Answers: A) A)1 B) B)2 C) C)3 D) D)0 E) E)5

I wish I could draw a diagram to show you but by giving you number A and B, it might help a little. A and B and C is 5 - that means A and B is at least 5. This seems trivial given the value intervals of A and B but definitely helps to think through how to minimize A and B but not C A and B but not C = |A|-|B| - 5 So i would pick A=25 and B =50 to minimize the value to a 0. (ANS 0) <result>D</result>

D

In a survey conducted to find out the readership of three Newspapers A,B and C, it was found that the number of newspaper A is at least 20 and at most 40. The number of people who read newspaper B is at least 50 and at most 70. The number of people who read newspaper C is at least 70 and at most 83. It was also found that 5 people read all three newspapers. Find the minimum number of people who read both A and B but not C.

aqua_rat__wZ8tRFjaUuIre3gg

6% of customers that enter a store on any given day must not pay tax. If 1000 people shop every day, how many people pay taxes in the store every week Pick: A) 6500 B) 6580 C) 7200 D) 7120 E) 6800

6% of customers do not pay taxes. 6/100 * 1000= <gadget id="calculator">6/100 * 1000</gadget> <output>60</output> 60 Therefore 1000 - 60= <gadget id="calculator">1000 - 60</gadget> <output>940</output> 940 940 * 7= <gadget id="calculator">940 * 7</gadget> <output>6_580</output> 6580 6580) <result>B</result>

B

6% of customers that enter a store on any given day must not pay tax. If 1000 people shop every day, how many people pay taxes in the store every week

aqua_rat__fbLx03JVuVl9APF6

A taxi owner buys diesel at Rs.8.50, Rs. 9 and Rs. 9.50 per litre for three successive years. What approximately is the average cost per litre of diesel if he spends Rs. 5000 each year? Choose the correct choice from the following choices: A) 7.98 B) 8.98 C) 9.98 D) 6.98 E) 8.12

Total Cost = 5000 × 3=15000 Total diesel used = 5000/8.50 + 5000/9 +5000/9.50 =588+555+527= <gadget id="calculator">588+555+527</gadget> <output>1_670</output> 1670 Average cost per litre of diesel=15000/1670 =8.98 ANSWER:8.98 <result>B</result>

B

A taxi owner buys diesel at Rs.8.50, Rs. 9 and Rs. 9.50 per litre for three successive years. What approximately is the average cost per litre of diesel if he spends Rs. 5000 each year?

aqua_rat__JqEZmDhqIWHYBYHt

With the wind, an airplane travels 1120 miles in seven hours. Against the wind, it takes eight hours. Find the rate of the plane in still air and the velocity of the wind. Select the correct option: A) 10 kmph B) 11 kmph C) 12 kmph D) 13 kmph E) 14 kmph

1120 miles in seven hrs that means up speed is 1120/7= <gadget id="calculator"> 1120/7</gadget> <output>160</output> 160. for against the wind 1120 miles in 8 hrs so down speed 1120/8= <gadget id="calculator"> 1120/8</gadget> <output>140</output> 140. now plain speed in still air=1/2(160+140)=150 kmph wind speed=1/2(160-140)=10 kmph 10 kmphNSWER:10 kmph <result>A</result>

A

With the wind, an airplane travels 1120 miles in seven hours. Against the wind, it takes eight hours. Find the rate of the plane in still air and the velocity of the wind.

aqua_rat__A6b2IQ6mT9jOosvF

x = 13.165 y = 7.496 z = 11.557 The number A is obtained by first rounding the values of x, y, and z to the hundredths place and then adding the resulting values. The number B is obtained by first adding the values of x, y, and z and then rounding the sum to the hundredths place. What is the value of A – B? Choose the correct choice: A) 0.01 B) 0.02 C) 0.03 D) 0.1 E) 0.2

Rounding off the values: x = 13.17 y = 7.50 z = 11.56 A = 13.17 + 7.50 + 11.56= <gadget id="calculator">13.17 + 7.50 + 11.56</gadget> <output>32.23</output> 32.23 x + y + z= 13.165 + 7.496 + 11.557 = 32.206 0.02 = 32.21 A - 0.02 = 0.02 Option 0.02 <result>B</result>

B

x = 13.165 y = 7.496 z = 11.557 The number A is obtained by first rounding the values of x, y, and z to the hundredths place and then adding the resulting values. The number B is obtained by first adding the values of x, y, and z and then rounding the sum to the hundredths place. What is the value of A – B?

aqua_rat__zxf6i5nlrfalWPBZ

If a 3-number code is formed of the integers from 1 to 14 inclusively, and each of the numbers in the code is different, how many possible codes are there? Select the correct option: A) 1744 B) 1854 C) 1964 D) 2074 E) 2184

14*13*12= <gadget id="calculator">14*13*12</gadget> <output>2_184</output> 2184 The answer is 2184. <result>E</result>

E

If a 3-number code is formed of the integers from 1 to 14 inclusively, and each of the numbers in the code is different, how many possible codes are there?

aqua_rat__DxQhhflFEd42N1tR

If a car travels a distance of 300 km in 8 hours, partly at a speed of 40 kmh-1 and partly at 30 kmh-1, what is the distance it travelled at the speed of 40 kmh-1? Pick one. A) 200 km B) 210 km C) 220 km D) 240 km E) 250 km

let the distance travelled at 40 kmph=x km distance travelled at 30 kmph =300-x km x/40 + (300-x)/30 = 8 x = 240 ANSWER:240 km <result>D</result>

D

If a car travels a distance of 300 km in 8 hours, partly at a speed of 40 kmh-1 and partly at 30 kmh-1, what is the distance it travelled at the speed of 40 kmh-1?

aqua_rat__pNi7Y0x2NSYfWdqk

If the length of the longest chord of a certain circle is 18, what is the radius of that certain circle? Pick. A) 2.5 B) 9 C) 10 D) 15 E) 20

Longest chord of a circle is the diameter of the circle diameter = 2 * radius If diameter of the circle is given as 18 = 2 * 9 so radius of the circle = 9 correct answer - 9 <result>B</result>

B

If the length of the longest chord of a certain circle is 18, what is the radius of that certain circle?

aqua_rat__HQaS9OMDZzx9H7yp

Nick took a bus from home to market, that travels at 80 kmph. While walking back at 8 kmph, halfway through, he suddenly realized he was getting late and he cycled back the remaining distance in 60 kmph. Find the average speed. Choose the correct answer: A) 49.5 kmph B) 49.0 kmph C) 48.5 kmph D) 48.0 kmph E) none of these

Let the distance be 2x(one way) Time taken by bus = 2x/80, by walking =x/8, by cycling = x/60 hours :. Average speed = Total 48.0 kmphistance/Total time = 8x / x/40 + x/8 + x/60 = 8 *60 / 1.5+7.5+1 = 12.0 ANSWER:48.0 kmph <result>D</result>

D

Nick took a bus from home to market, that travels at 80 kmph. While walking back at 8 kmph, halfway through, he suddenly realized he was getting late and he cycled back the remaining distance in 60 kmph. Find the average speed.

aqua_rat__PKiC3SkDOcv0xq8z

At the faculty of Aerospace Engineering, 310 students study Random-processing methods, 232 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering? Choose the most appropriate option: A) 430 B) 432 C) 440 D) 442 E) 446

310 + 232 - 112 (since 112 is counted twice )= 430 430 is the answer <result>A</result>

A

At the faculty of Aerospace Engineering, 310 students study Random-processing methods, 232 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering?

aqua_rat__tjP2vMhfeP9ktHFg

In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam? Choose the correct choice from the following: A) 52% B) 64% C) 72% D) 76% E) 80%

If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have: 100-------------88----------------------------x And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%. <result>A</result>

A

In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible A score that Lindsey could have received on her midterm exam?

aqua_rat__Zs3J4yB7v7QZjFw0

The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is? Select. A) 176 m B) 189 m C) 245 m D) 189 m E) 197 m

Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==&gt; 2(130 + X) = 750 ==&gt; X = 245 m. Answer:245 m <result>C</result>

C

The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?

aqua_rat__WGJCXYCHOrkqCCs1

The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 40%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged? Pick one. A) 100% decrease B) 50% decrease C) 40% decrease D) 40% increase E) 50% increase

The rate of reaction is invesrsly proportional to the concentration of chemical B present. It used to have B=1 . Now that B is increased by 40%. So the new equation would be 2B=(1/2). In order for the rate of reaction to still be 1, we need to change the concentration of A to yield a 2. It used to be A^2=1, now the new equation should be (sqrt(2)*A)^2=2. The change in the concentration of A can be calculated as (sqrt(2) -1)/1 or approximately 40% increase. Answer 50% decrease. <result>B</result>

B

The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 40%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?

aqua_rat__hcogzudVmibWaYz8

Jill works as a waitress at the local diner where she earns an hourly wage of $8.00 per hour and a standard tip rate of 30% of the cost of the orders she serves. If she worked four 12-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week? Choose the correct choice from the following choices: A) 1120 B) 300 C) 320 D) 350 E) 400

Jill earns 8 dollars/hour and the hourly tip is (3/10)*40. Jill thus earns 8*14+14*12 per day(or 8(14)+12(14)=20(14)=280). Jill has worked for 4 days -&gt; 280*4=1120. This matches answer choice 1120. <result>A</result>

A

Jill works as a waitress at the local diner where she earns an hourly wage of $8.00 per hour and a standard tip rate of 30% of the cost of the orders she serves. If she worked four 12-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?

aqua_rat__boRJigzFRE1w6hMb

Which number is a factor of 20? Choose one A) 3 B) 4 C) 7 D) 18 E) 9

A whole number that divides exactly into another whole number is called a factor 20/5= <gadget id="calculator">20/5</gadget> <output>4</output> 4 answer 4 <result>B</result>

B

Which number is a factor of 20?

aqua_rat__FgbHIPN1uZrko2m0

A and B play a series of 5 games in badminton. A's chance of winning s single game against B is 2/3. Find the chance that A wins exactly 3 games. Select the correct option. A) 64/81 B) 35/128 C) 80/243 D) None of these E) cannot be determined

Explanation : Here, each game is a trial and A's winning the game is a success. All games are independent , so, using the binomial distribution. P(X) = nCx px(1 - p)n-x. Where, x= wins exactly 3 games =&gt; x = 3. p= 2/3, 1-p=1/3, n=5. P(3) = 5C3 (2/3)3(1/3)2 . =&gt; 10 x (2(3)/3(5)). =&gt; 80/243. Answer : 80/243 <result>C</result>

C

A and B play a series of 5 games in badminton. A's chance of winning s single game against B is 2/3. Find the chance that A wins exactly 3 games.

aqua_rat__rMBEhVkxEOQA229o

852.68 − 4.5 + 108.94 = ? − 2132.54 Pick. A) 6078.58 B) 5225.9 C) 6078.54 D) 6088.58 E) None

Option '6078.54' <result>C</result>

C

852.68 − 4.5 + 108.94 = ? − 2132.54

aqua_rat__tCUc0oS9xoyRU5nm

A bag contains 6 red balls, 5 green balls and 6 white balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or green? Choose the correct choice from the following choices: A) 2/5 B) 3/5 C) 11/17 D) 7/15 E) 8/15

Total number of balls = (6 + 5 + 6)= <gadget id="calculator">(6 + 5 + 6)</gadget> <output>17</output> 17. Therefore, n(S)= 17. Let E1 = event of drawing a red ball. and E2 = event of drawing a green ball. Then, E1 n E2 = f. P (E1 n E2) = P(E1) + P(E2) = (6/17 + 5/17) = 11/17. ANSWER:11/17 <result>C</result>

C

A bag contains 6 red balls, 5 green balls and 6 white balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or green?

aqua_rat__aD1HAxGGr9CLLXby

A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long? Answers A) 99 sec B) 89 sec C) 54 sec D) 27 sec E) 22 sec

Speed = 240/24= <gadget id="calculator">240/24</gadget> <output>10</output> 10 m/sec. Required time= (240 + 650)/10= <gadget id="calculator">(240 + 650)/10</gadget> <output>89</output> 89 sec. Answer: 89 sec <result>B</result>

B

A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?

aqua_rat__5oh8BJgW7epADWpU

What will be the cost of building a fence around a square plot with area equal to 49 sq ft, if the price per foot of building the fence is Rs. 58? Select the correct option: A) 3944 B) 1624 C) 2999 D) 2667 E) 2121

Let the side of the square plot be a ft. a2 = 49=&gt; a = 7 Length of the fence = Perimeter of the plot = 4a = 28 ft. Cost of building the fence = 28 * 58 = Rs. 1624. Answer: 1624 <result>B</result>

B

What will be the cost of building a fence around a square plot with area equal to 49 sq ft, if the price per foot of building the fence is Rs. 58?

aqua_rat__aPXtHvxLfsB9VGSj

A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 8 minutes? Choose the correct choice from the following answers: A) 36 B) 54 C) 108 D) 216 E) 432

ON432 Veggiematik machine can chop 36 carrots in 4 minutes So, ON432 Veggiematik machine can chop (1.5)(36) carrots in (1.5)(4) minutes In other words, ON432 Veggiematik machine can chop 54 carrots in8minutes So,SIXVeggiematik machines can chop (8)(54) carrots in6minutes In other words, SIX Veggiematik machines can chop 432 carrots in8minutes <result>E</result>

E

A standard Veggiematik machine can chop 36 carrots in 4 minutes. How many carrots can 6 standard Veggiematik machines chop in 8 minutes?

aqua_rat__Kl4bWcqb53KSOijZ

Two numbers are in the ratio of 5:8. If 30 be subtracted from each, they are in the ratio of 5:9. Find the numbers? Choose the correct choice: A) 122,195 B) 121,199 C) 120,192 D) 102,192 E) 126,109

(5x-30):(8x-30) = 5:9 x = 24=&gt; 120,192 Answer: 120,192 <result>C</result>

C

Two numbers are in the ratio of 5:8. If 30 be subtracted from each, they are in the ratio of 5:9. Find the numbers?

aqua_rat__38Ja5PJ8ZQt3mmvI

A cistern of 475 litres is completely filled using pipes A and B, with Pipe A being open for 5 more hours than pipe B. If we are to interchange the operating hours of the two pipes than pipe A would have pumped half the water as much as pipe B, then find the time for which pipe B was open. Also, given that if the two pipes were open simultaneously the tank would fill in 19 hours. Choose the correct choice from the following options: A) 10 h B) 14 h C) 16 h D) 20 h E) 24 h

DETAILED SOLUTION The 475 litres is filled in 19 hours by the two pipes when they are opened simultaneously. Therefore, rate of water flow by A and B, A + B = 47519 = 25 litres/hour………….(1) Let pipe B was opened for t hours Then, pipe A was opened for t + 5 hours A x (t+5) + B x t = 475 (A + B) x t + 5A = 475 25t + 5A = 475 =) 5t + A = 95 Now, using option analysis a) t = 10 =) 5 x 10 + A = 95 =) A = 45 (not possible from (1)) b) t = 14 =) 5 x 14 + A = 95 =) A = 25 (not possible from (1) as B can’t be zero) c) t = 16 =) 5 x 16 + A = 95 =) A = 15 16 hORRE16 hT ANSWER 16 h <result>C</result>

C

A cistern of 475 litres is completely filled using pipes A and B, with Pipe A being open for 5 more hours than pipe B. If we are to interchange the operating hours of the two pipes than pipe A would have pumped half the water as much as pipe B, then find the time for which pipe B was open. Also, given that if the two pipes were open simultaneously the tank would fill in 19 hours.

aqua_rat__QjB8CwVYmQmMkue1

Ram professes to sell his goods at the cost price but he made use of 800 grms instead of a kg, what is the gain percent? Choose the correct choice from the following choices A) 11 1/7% B) 11 7/7% C) 11 1/9% D) 71 1/9% E) 25%

800 --- 200 100 --- ? =&gt; 25% Answer:25% <result>E</result>

E

Ram professes to sell his goods at the cost price but he made use of 800 grms instead of a kg, what is the gain percent?

aqua_rat__r864lUDeAEhjxf5i

How many three letter words are formed using the letters of the word TIME? Select the correct option. A) 66 B) 57 C) 88 D) 24 E) 21

The number of letters in the given word is four. The number of three letter words that can be formed using these four letters is 4P3 = 4 * 3 * 2= <gadget id="calculator">4 * 3 * 2</gadget> <output>24</output> 24. Answer: 24 <result>D</result>

D

How many three letter words are formed using the letters of the word TIME?

aqua_rat__5a1HfqdvinGeTcQS

A tradesman by means of his false balance defrauds to the extent of 15%? in buying goods as well as by selling the goods. What percent does he gain on his outlay? Choose the correct choice from the following answers: A) 44% B) 48% C) 32% D) 45% E) 34%

g% = 15 + 15 + (15*15)/100 = 32% Answer: 32% <result>C</result>

C

A tradesman by means of his false balance defrauds to the extent of 15%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?

aqua_rat__RkyNoS4YXit9eQkT

Rachel and Sarah started out to visit Grandma. They drove for 50 miles and stopped to rest before driving for 30 more miles. They decided to go back 10 miles to a restaurant they had seen. After leaving the restaurant, they drove 80 more miles to Grandma’s house. How many miles did the girls drive on the way to Grandma’s house? Pick: A) 150 miles B) 160 miles C) 170 miles D) 180 miles E) 200 miles

50 + 30= <gadget id="calculator">50 + 30</gadget> <output>80</output> 80 to turn around 80 + 10= <gadget id="calculator">80 + 10</gadget> <output>90</output> 90 backtrack to restaurant 90 + 80= <gadget id="calculator">90 + 80</gadget> <output>170</output> 170 miles is total distance driven correct answer 170 miles <result>C</result>

C

Rachel and Sarah started out to visit Grandma. They drove for 50 miles and stopped to rest before driving for 30 more miles. They decided to go back 10 miles to a restaurant they had seen. After leaving the restaurant, they drove 80 more miles to Grandma’s house. How many miles did the girls drive on the way to Grandma’s house?

aqua_rat__cZ0Y6TuPzs78il17

20 beavers, working together in a constant pace, can build a dam in 3 hours. How many hours C will it take 12 beavers that work at the same pace, to build the same dam? Choose the correct choice from the following: A) 2. B) 4. C) C=5. D) C=6. E) 8.

C. 5 hrs If there were 10 beavers it qould have taken double C= 6hrs.. so closest to that option is 5. <result>C</result>

C

20 beavers, working together in a constant pace, can build a dam in 3 hours. How many hours C will it take 12 beavers that work at the same pace, to build the same dam?

aqua_rat__UtMMOKriNmPMQoZg

The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue R, in dollars, from the sale of cars priced at $ 15,000? Choose the correct choice: A) 50,000 B) 750,000 C) 850,000 D) 7,500,000 E) R=750,000,000

number of cars sold = x=800000-50y y= 15000 x=800000-750000= <gadget id="calculator">800000-750000</gadget> <output>50_000</output> 50000 revenue from 50000 cars=15000*50000= <gadget id="calculator">15000*50000</gadget> <output>750_000_000</output> 750000000 R=750,000,000 <result>E</result>

E

The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue R, in dollars, from the sale of cars priced at $ 15,000?

aqua_rat__oJHmOAtQFFa2mpBo

In an examination, 300 students appeared. Out of these students; 26 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed. Answers: A) 33 B) 37 C) 54 D) 60 E) 01

The number of students with first division = 26 % of 300 = 26/100 × 300 = 7800/100= <gadget id="calculator">7800/100</gadget> <output>78</output> 78 And, the number of students with second division= 54 % of 300 = 54/100 × 300 =16200/100= <gadget id="calculator">16200/100</gadget> <output>162</output> 162 Therefore, the number of students who just passed= 300 – (78 + 162) = 60 Answer:60 <result>D</result>

D

In an examination, 300 students appeared. Out of these students; 26 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.

aqua_rat__WmLdndTqov9Zc4rc

In a simultaneous throw of a pair of dice, find the probability of getting a total more than 8 Choices: A) 1/2 B) 7/12 C) 3/7 D) 5/12 E) 6/17

Total number of cases = 7*7= <gadget id="calculator">7*7</gadget> <output>49</output> 49 Favourable cases= [(2,7),(3,6),(3,7),(4,5),(4,6),(4,7),(5,4),(5,5),(5,6),(5,7),(6,3),(6,4),(6,5),(6,6),(6,7),(7,2),(7,3),(7,4),(7,5),(7,6),(7,7)] = 21 So Probability = 21/49 = 3/7 Answer is 3/7 <result>C</result>

C

In a simultaneous throw of a pair of dice, find the probability of getting a total more than 8