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NLP Centre, Faculty of Informatics, Masaryk University 14

aqua_rat__jqs6W44dNlavUZzG

A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform? Pick one. A) 44 sec B) 49 sec C) 42 sec D) 47 sec E) None of these

Let the length of the train be x m. When a train crosses an electric pole, the distance covered is its own length. So, x = 12 * 36 * 5 /18= <gadget id="calculator">12 * 36 * 5 /18</gadget> <output>120</output> 120 m. Time taken to cross the platform= (120 +350)/ 36 * 5/18 = 47 min. ANSWER:47 sec <result>D</result>

D

A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?

aqua_rat__EMoS0rJ5vXyZiDG0

A man can row downstream at the rate of 18 Kmph and upstream at 6 Kmph. Find the man’s rate in still water and rate of current? Choose the correct option. A) 8.5 B) 6.0 C) 9.5 D) 9.0 E) 8.25

Rate of still water = 1/2 (down stream + upstream) = 1/2 (18 + 6) = 12 Kmph rate of current = 1/2 (down stream - upstream) = 1/2 (18 - 6) = 1/2 (12) = 6 kmph Answer is 6.0. <result>B</result>

B

A man can row downstream at the rate of 18 Kmph and upstream at 6 Kmph. Find the man’s rate in still water and rate of current?

aqua_rat__yJeJ5HaSbQQBsGhR

A tank is filled by 3 pipes A,B,C in 3 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ? Choose the correct choice: A) 25hr B) 35hr C) 40hr D) 20hr E) 21hr

Suppose pipe A alone take x hours to fill the tank Then pipe B and C will take x/2 and x/4 hours respectively to fill the tank. 1/x + 2/x + 4/x = 1/3 7/x = 1/3 x = 21 hours Answer is 21hr <result>E</result>

E

A tank is filled by 3 pipes A,B,C in 3 hours. Pipe C is twice as fast as B and B is twice as fast as A. How much will pipe A alone take to fill the tank ?

aqua_rat__h5yBspYnkuoKKhGp

An iron cubes of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet are in the ratio 1 : 5 the sides are Choices: A) 10 cm, 50 cm B) 20 cm, 100 cm C) 40 cm, 200 cm D) None of these E) Cannot be determined

Solution Let the sides of the sheet be x and 5x. Then,volume of the sheet= volume of the cube ‹=› x × 5x ×1/2 ‹=› 10×10×10 ‹=› 5x2= 2000 ‹=› x2= 400 ‹=› x = 20. The sides are 20 cm and 100 cm. Answer 20 cm, 100 cm <result>B</result>

B

An iron cubes of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet are in the ratio 1 : 5 the sides are

aqua_rat__S3ws26bhXUwSw89H

Pipe A can fill a tank in 10 hr, pipe B in 20hr and pipe C in 40hr. If all the pipes are open in how many hours will tank be filled? Choose the correct choice: A) 1hr B) 30min C) 15min D) 17min E) 10min

Part filled by (A+B+C) in 1hour = 1/10 + 1/20 + 1/40 = 7/40 All the 3 pipes together will fill the tank in 17min Approximately Answer is 17min <result>D</result>

D

Pipe A can fill a tank in 10 hr, pipe B in 20hr and pipe C in 40hr. If all the pipes are open in how many hours will tank be filled?

aqua_rat__3x4tMPaqGTBMDSr8

If for any number N, f(N) is defined as the least integer that is greater than or equal to N^2, then what is the value of f(-1.5)? Select the correct option: A) -4 B) -3 C) 1 D) 2 E) 3

If N=-1.5, then N^2=2.25. The least integer that is greater than or equal to 2.25 is 3, thus f(-1.5) = 2.25. The answer is 3. <result>E</result>

E

If for any number N, f(N) is defined as the least integer that is greater than or equal to N^2, then what is the value of f(-1.5)?

aqua_rat__ODPvQESsMvvqUMGG

Find the invalid no.from the following series 15 46 63 71 75 77 78 Choose the correct choice: A) 15 B) 46 C) 71 D) 75 E) 78

In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on. 46 46 <result>B</result>

B

Find the invalid no.from the following series 15 46 63 71 75 77 78

aqua_rat__VZcSkWedIAjG9nDN

The function f(x) is defined for all positive integers x as the number of even factors of x and the function g(x) is defined for all positive integers x as the number of odd factors of x. For positive integers a and b if f(b)*g(a) = 0 and f(a) = 1, which of the following could be the least common multiple of a and b? Choose the correct answer. A) 12 B) 16 C) 20 D) 30 E) 36

f(b)∗g(a)=0 : any positive integer has at least one odd factor: 1. Thus, g(a) cannot be 0, which implies that f(b) = 0. This on the other hand means that b is an odd integer (odd integers does not have even factors). f(a)=1f(a)=1: aa has 1 even factor. This means that aa must be 2 (the only positive integer which has only 1 even factor is 2). The least common multiple of a=2a=2 and b=odd is 2∗odd. Only option D can be represented this way: 30=2∗1530=2∗15. Answer: 30 <result>D</result>

D

The function f(x) is defined for all positive integers x as the number of even factors of x and the function g(x) is defined for all positive integers x as the number of odd factors of x. For positive integers a and b if f(b)*g(a) = 0 and f(a) = 1, which of the following could be the least common multiple of a and b?

aqua_rat__aG6T7Y9oWUpyZiHW

The profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448. What should be the sale price for making 55% profit? Choose the correct choice from the following: A) $480 B) $450 C) $992 D) $870 E) $660

C Let C.P. = $ x. Then, 832 - x = x - 448 2x = 1280 =&gt; x = 640 Required S.P. = 155% of $ 640 = 150/100 * 640 = $ 992. <result>C</result>

C

The profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448. What should be the sale price for making 55% profit?

aqua_rat__JpWUEXeMnPJt1gDJ

In filling a room with gas 100 m * 10 m * 10 m the volumes of gas will be? Choose the correct answer: A) 100 cu.m B) 1000 cu.m C) 10000 cu.m D) 100000 cu.m E) 10000000 cu.m

100 * 10 * 10= <gadget id="calculator">100 * 10 * 10</gadget> <output>10_000</output> 10000 ANSWER:10000 cu.m <result>C</result>

C

In filling a room with gas 100 m * 10 m * 10 m the volumes of gas will be?

aqua_rat__RMBcKANTJwsqEfxm

Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is r, what is the difference between the probability that r is even and the probability that r is odd? Choose the correct choice from the following. A) 1/9 B) 1/6 C) 2/9 D) 1/4 E) 1/2

1/9ge of Boys r:4, 6, 7 Sum of ages taken 2 at a time: 10,13,11 1/9ges of Girls:5, 8, 9 Sum of ages taken 2 at a time: 13,17,14 9 Combinations of sum between sets(10,12,11)(13,17,14) =23,27,24- 16,30,17- 24,28,25 Prob(Even)= 5/9 Prob(Odd) =4/9 1/9nswer=5/9 - 4/9 = 1/9 <result>A</result>

A

Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is r, what is the difference between the probability that r is even and the probability that r is odd?

aqua_rat__D0BiVuIWNWamjSjm

A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? Pick. A) 3.6 sec B) 18 sec C) 36 sec D) 72 sec E) None

Speed of train relative to jogger = 45 - 9= <gadget id="calculator">45 - 9</gadget> <output>36</output> 36 km/hr.= 36 * 5/18= <gadget id="calculator">36 * 5/18</gadget> <output>10</output> 10 m/sec. Distance to be covered= 240 + 120= <gadget id="calculator">240 + 120</gadget> <output>360</output> 360 m. Time taken= 360/10= <gadget id="calculator">360/10</gadget> <output>36</output> 36 sec ANSWER:36 sec <result>C</result>

C

A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?

aqua_rat__ihbyOoOqQXfMVtge

A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is: Options A) 1/26 B) 1/52 C) 2/62 D) 2/26 E) 3/26

Here, n(S) = 52. Let E = event of getting a queen of club or a king of heart. Then, n(E) = 2. P(E) = n(E)/n(S) = 2/52 = 1/26 1/26nswer should be 1/26 <result>A</result>

A

A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:

aqua_rat__55z4rzrDOP8w3ain

Today Chris ate 15 jellybeans. Bella ate 2/3 of the jellybeans Chris did, Frances ate 5 more jellybeans than Bella did , and Sandhya ate 20% more than Frances. How many jellybeans did Sandhya eat? Choose the correct choice from the following A) 18 B) 20 C) 13 D) 25 E) 15

A 13 Chris ate 15 jellybeans Bella ate 2/3 of the jellybeans Chris did. Bella= 2/3 x 15 =10 Frances ate 5 more jellybeans than Bella. Frances= 10+5 jellybeans. =15 Sandhya ate 20% more jellybeans than Frances. Sandhya = 15 + 15 × 20% = 15 + 15 × 0.20 = 15 + 3= <gadget id="calculator">15 + 3</gadget> <output>18</output> 18 Sandhya ate 18 jellybeans. The correct answer is 18. <result>A</result>

A

Today Chris ate 15 jellybeans. Bella ate 2/3 of the jellybeans Chris did, Frances ate 5 more jellybeans than Bella did , and Sandhya ate 20% more than Frances. How many jellybeans did Sandhya eat?

aqua_rat__Rp7Zd64dBU0jYb5C

In a shop 40% of the articles are sold at a profit of 20% and the remaining at a loss of 10%.what is the overall profit/loss? Choose the correct choice from the following answers. A) 6% loss B) 4% loss C) 2% profit D) 10% loss E) none

40*1.2+60*0.9/100=1.02 ANSWER:2% profit <result>C</result>

C

In a shop 40% of the articles are sold at a profit of 20% and the remaining at a loss of 10%.what is the overall profit/loss?

aqua_rat__NAsPfVZ96q3eIbhB

Vijay bought 160 shirts at the rate of Rs. 205 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%? Choose the correct choice from the following: A) s.225 B) s.288 C) s.485 D) s.261 E) s.282

Total CP per shirt = 205 + 1400/160 + 1.75 + 320/160 = Rs. 217.5 SP = CP[(100 + profit%)/100] = 217.5 * [(100 + 20)/100] = Rs.261. Answer:s.261 <result>D</result>

D

Vijay bought 160 shirts at the rate of Rs. 205 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?

aqua_rat__hYgcLH6WD7W14ieh

A number is increased by 10% and then decreased by 10%, the final value of the number is ? Choose the most appropriate option A) decreases by 1% B) decreases by 2% C) decreases by 3% D) decreases by 4% E) none of the above

Here, x = 10 and y = - 10 Therefore, the net % change in value = ( x + y + xy/100)% = [10 - 10 + (10 * -10)/100]% or - 1% Since the sign is negative, there is a decrease in value by 1%. decreases by 1%NSWER:decreases by 1% <result>A</result>

A

A number is increased by 10% and then decreased by 10%, the final value of the number is ?

aqua_rat__IbN23ZUL4qyQ6aad

Mangala completes a piece of work in 9 days, Raju completes the same work in 21 days. If both of them work together, then the number of days required to complete the work is Pick one. A) 6 days B) 7 days C) 8 days D) 9 days E) 11 days

If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days. That is, the required No. of days = 9 × 21/30 = 6 days. 6 days <result>A</result>

A

Mangala completes a piece of work in 9 days, Raju completes the same work in 21 days. If both of them work together, then the number of days required to complete the work is

aqua_rat__QmgqR6uFd54bfY5Y

What is the probability of getting a sum 9 from two throws of a dice? Options: A) 1/6 B) 1/8 C) 1/9 D) 1/12 E) None of these

In two throws of a dice, n(S) = (6 x 6) = 36. Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}. P(E) =n(E)/n(S)=4/36=1/9 . Answer:1/9 <result>C</result>

C

What is the probability of getting a sum 9 from two throws of a dice?

aqua_rat__qsx2wTBmipYHqVwk

In a covering a certain distance the speed of A and B are in the ratio of 6: 9, A takes 20 min more, than B to reach the destination. The time taken by A to reach the destination is: Choose the correct option: A) 1 Hour B) 2 Hours C) 1.5 Hours D) 2.5 Hours E) 3 Hours

Let the speed of 1 Hour and B are 6x Kmph and 9x Kmph respectively, Let the total distance to travel = y Km y/6x - y/9x = 1/3 y/x(1/18 = 1/3 y = 6x Required time = 6x/6x = 1 hour 1 Hournswer 1 Hour.6 /6= <gadget id="calculator">6 /6</gadget> <output>1</output> 1 hour 1 Hournswer 1 Hour. <result>A</result>

A

In a covering a certain distance the speed of A and B are in the ratio of 6: 9, A takes 20 min more, than B to reach the destination. The time taken by A to reach the destination is:

aqua_rat__NzYq5U6mcieA5hyo

In a renowned city, the average birth rate is 7 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day. Choose the correct choice from the following answers A) 215,000 B) 216,000 C) 217,000 D) 218,000 E) 219,000

This question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds. For this particular question : Increase in the population every 2 seconds = 7-2= <gadget id="calculator">7-2</gadget> <output>5</output> 5 people. Total 2 second interval in a day= 24*60*60/2 = 43,200 Population increase = 43,200 * 5 = 216,000. Hence 216,000. <result>B</result>

B

In a renowned city, the average birth rate is 7 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day.

aqua_rat__K2mKerJVjoQoH1bz

9 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond? Pick one: A) 40587 B) 60451 C) 16152 D) 24325 E) 40320

it is like a circular arrangement. total ways for n people to arrange in a circle is = factorial (n-1) in this case n= 9 hence ans = 8 factorial = 40320 hence 40320 <result>E</result>

E

9 baseball players each stand at different corners of a baseball diamond. The sides of the diamond are all of equal length. Two arrangements of baseball players are considered different only when the relative positions of the players differ. How many different ways can the baseball players arrange themselves around the diamond?

aqua_rat__PW554sO0Iwa19aJ8

A is twice as fast as B. If B alone can do a piece of work in 24 days, in what time can A and B together complete the work? Choose the correct answer A) 10 B) 12 C) 6 D) 2 E) 8

A can do the work in 24/2 i.e., 12 days. A and B's one day's work = 1/12+ 1/24 = (2 + 1)/24 = 1/8 So A and B together can do the work in 8 days. Answer: 8 <result>E</result>

E

A is twice as fast as B. If B alone can do a piece of work in 24 days, in what time can A and B together complete the work?

aqua_rat__zBBPbd7jFJq4TlY6

The expression (5x-2)/(x+3) is equivalent to which of the following? Choose the correct choice from the following choices. A) (5-2)/3 B) 5 – (2/3) C) 5 – (x)/(x+3) D) 5 – (17)/(x+3) E) 5 + (17)/(x+3

iven asked to find the value of (5x-2)/(x+3)... Now take X as 1 then we get 3/4... From the options check which one gets the same 3/4. From option D = 5 – (17)/(x+3) =&gt; 5 - (17)/(1+3) =&gt; 3/4.. All other options will result in some other value.. Answer: 5 – (17)/(x+3) is the correct option <result>D</result>

D

The expression (5x-2)/(x+3) is equivalent to which of the following?

aqua_rat__OcxZWIl90ncA7owp

From a group of 7 women and 6 men, five persons are to be selected to form a committee so that at least 3 women are there in the committee. In how many ways can it be done? Choices A) A)650 B) B)656 C) C)696 D) D)724 E) E)756

From a group of 7 women and 6 men, five persons are to be selected with at least 3 men. Hence we have the following 3 options. We can select 5 women ...(option 1) Number of ways to do this = 7C5 We can select 4 men and 1 man ...(option 2) Number of ways to do this = 7C4 × 6C1 We can select 3 women and 2 men ...(option 3) Number of ways to do this = 7C3 × 6C2 Total number of ways = 7C5 + (7C4 × 6C1) + (7C3 × 6C2) = 7C2 + (7C3 × 6C1) + (7C3 × 6C2)[∵ nCr = nC(n - r) ] = 7 × 6 2 × 1 + 7 × 6 × 5 3 × 2 × 1 × 6 =7×62×1+7×6×53×2×1×6 + 7 × 6 × 5 3 × 2 × 1 × 6 × 5 2 × 1 +7×6×53×2×1×6×52×1 = 21 + 210 + 525 = 756 =21+210+525= <gadget id="calculator">21+210+525</gadget> <output>756</output> 756 756) <result>E</result>

E

From a group of 7 women and 6 men, five persons are to be selected to form a committee so that at least 3 women are there in the committee. In how many ways can it be done?

aqua_rat__EI966crXqyKLofZi

There are 9 color balls at a row. From that how many ways can 9 different color balls be arranged in a row so that black, white, red and green are never together? Choose the correct choice from the following answers: A) 223600 B) 214600 C) 566600 D) 786789 E) 345600

Total number of ways in which 9 different colour balls can be arranged in a row =9! ⋯(A) Now we will find out total number of ways in which 9 different colour balls can be arranged in a row so that black, white, red and green balls are always together. We have total 9 balls. Since black, white, red and green balls are always together, group these 4 balls together and consider as a single ball. Hence we can take total number of balls as 6. These 6 balls can be arranged in 6! ways. We had grouped 4 balls together. These 4 balls can be arranged among themselves in 4! ways. Hence, total number of ways in which 9 different colour balls be arranged in a row so that black, white, red and green balls are always together =6!×4! ⋯(B) From (A) and (B), Total number of ways in which 9 different colour balls can be arranged in a row so that black, white, red and green balls are never together =9!–6!×4!=6!×7×8×9−6!×4!=6!(7×8×9–4!)=6!(504–24)=6!×480=720×480=345600 345600 <result>E</result>

E

There are 9 color balls at a row. From that how many ways can 9 different color balls be arranged in a row so that black, white, red and green are never together?

aqua_rat__qyQpCWkW8ogYb4Ur

The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is? Pick. A) 76 B) 21 C) 26 D) 28 E) 11

Explanation: Lot the total number of workers be v Then, 8OOOv = (12000 * 7) + 6000 (v - 7) &lt;=&gt; 2000v = 42000 &lt;=&gt; v = 21. Answer: 21 <result>B</result>

B

The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is?

aqua_rat__bImYpycg029cF1KS

The area of a triangle is with base 4m and height 8m? Pick A) 11 B) 10 C) 787 D) 16 E) 12

1/2 * 4 * 8= <gadget id="calculator">1/2 * 4 * 8</gadget> <output>16</output> 16 m2 Answer: 16 <result>D</result>

D

The area of a triangle is with base 4m and height 8m?

aqua_rat__0yoHaA8lMEUaHiQi

A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 400 revolutions. How many revolutions does the second wheel make in covering d feet? Choose the most appropriate option: A) 400xy B) 400y - x C) 400x - y D) 400x/y E) 400y/x

First Wheel with diameter x inches ----&gt; So the circumference = x*pi --------- (1) Second Wheel with diameter y inches ----&gt; So the circumference = y*pi --------- (2) Revolutions = distance/circumference So, from equation (1) 400 = d/(x*pi) d = 100 * x * pi ---------- (3) From equation (2) Revolutions = d/(y*pi) = (400 * x * pi) / (y*pi) = 400x/y Answer (400x/y) <result>D</result>

D

A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 400 revolutions. How many revolutions does the second wheel make in covering d feet?

aqua_rat__C6UrlAJYPisfDBBu

A pupil's marks were wrongly entered as 73 instead of 45. Due to that the average marks for the class got increased by half. The number of pupils in the class is : Choose the correct choice A) 56 B) 80 C) 20 D) 25 E) 26

Let there be x pupils in the class. Total increase in marks = (X*1/2) = X/2. X/2 = (73 - 45) =&gt; X/2 = 28 =&gt; X = 56. 56NSWER:56 <result>A</result>

A

A pupil's marks were wrongly entered as 73 instead of 45. Due to that the average marks for the class got increased by half. The number of pupils in the class is :

aqua_rat__ZwAQQDa84mdhiRWP

Sixty men can stitch 200 shirts in 30 days working 8 hours a day. In how many days can 45 men stitch 300 shirts working 6 hours a day? Choose the correct choice from the following options. A) 20 B) 90 C) 10 D) 80 E) 70

80 80 We have M1 801 H1 / W1 = M2 802 H2 / W2 (Variation rule) (60 * 30 * 8)/ 200 = (45 * 802 * 6) / 300 802 = (60 * 30 * 8 * 300) / (200 * 45 * 6) =&gt; 802 = 80. <result>D</result>

D

Sixty men can stitch 200 shirts in 30 days working 8 hours a day. In how many days can 45 men stitch 300 shirts working 6 hours a day?

aqua_rat__f6HH96x5zEkO8Fw2

The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 180,000. What was the percent increase in the cost of the home? Choose the correct choice from the following options. A) 60% B) 50% C) 55% D) 40% E) 33.3%

Percentage Increase = Increase in price / original price *100= (180000-120000)/120000*100= <gadget id="calculator">(180000-120000)/120000*100</gadget> <output>50</output> 50% Answer: 50% <result>B</result>

B

The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 180,000. What was the percent increase in the cost of the home?

aqua_rat__81p2A1Dhk2ztr2D2

a boy average marks in five subject is 60.he score 90 in math,in physics he scores 95.in rest three in how much maximum subject he can score more than or equal to 95. Answers. A) 1 B) 2 C) 3 D) 0 E) 4

addition of marks of all five subject=300. math+physics=185 sum of three subject marks=300-185= <gadget id="calculator">300-185</gadget> <output>115</output> 115 here it is clearly visible that he can only score more than 95 in one subject if he will score more than 95 in two then it will exceed 115 because marks are not in negative. answer 1 <result>A</result>

A

a boy average marks in five subject is 60.he score 90 in math,in physics he scores 95.in rest three in how much maximum subject he can score more than or equal to 95.

aqua_rat__5VQWkYuMwVnaZp5Z

In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is? Answers: A) 75 B) 78 C) 80 D) 82 E) 86

Divisor = (6 * 3) + 2= <gadget id="calculator">(6 * 3) + 2</gadget> <output>20</output> 20 5 * Quotient= 20 Quotient = 4. Dividend = (Divisor * Quotient) + Remainder Dividend = (20 * 4) + 6= <gadget id="calculator">(20 * 4) + 6</gadget> <output>86</output> 86 86) <result>E</result>

E

In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is?

aqua_rat__ualovC09bpkHRR3r

A and B entered into a partnership investing Rs. 16000 and Rs. 12000 respectively. After 3 months, A withdrew Rs. 5000 while B invested Rs. 5000 more. After 3 more months C joins the business with a capital of Rs. 21000. The share of B exceeds that of C, out of a total profit of Rs. 26400 after one year by Pick: A) Rs. 3200 B) Rs. 3400 C) Rs. 3600 D) Rs. 3800 E) None of these

Explanation: A:B: C = 16000*3 + 11000*9:12000*3 + 17000*9:21000*6 = 147:189:126 = 7:9:6 Difference of B and C’s shares = Rs. [26400 * (9/22) — 26400 * (6/22)) = Rs. 3600 Option Rs. 3600 <result>C</result>

C

A and B entered into a partnership investing Rs. 16000 and Rs. 12000 respectively. After 3 months, A withdrew Rs. 5000 while B invested Rs. 5000 more. After 3 more months C joins the business with a capital of Rs. 21000. The share of B exceeds that of C, out of a total profit of Rs. 26400 after one year by

aqua_rat__FTsEzaVyvSW9vRc4

The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 500? Pick A) 4 B) 6 C) 8 D) 10 E) 12

To maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^8 = 256 &lt; 500, then the greatest possible length of integer z is 8. The answer is 8. <result>C</result>

C

The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 500?

aqua_rat__kWJKlIndV49xJHf9

X and Y are two points respectively on sides AB and AC of triangle ABC such that XY is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium XYCB is 25:144 and BC=13 cm, then find the length of XY. Choose the correct option A) 12 B) 13 C) 14 D) 11 E) 5

ABC and AXY are similar triangles. So (side of ABC/side of AXY)^2=169/25 side of ABC/side of AXY = 13/5 So the length of XY = 5 Answer - 5 <result>E</result>

E

X and Y are two points respectively on sides AB and AC of triangle ABC such that XY is parallel to BC. If the ratio of area of triangle ADE to that of the trapezium XYCB is 25:144 and BC=13 cm, then find the length of XY.

aqua_rat__L2LqmnYaj2htNrhs

Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $6.30? Answers A) 426 B) 430 C) 443 D) 410 E) 486

I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money: -the 100 pack costs 1.5$, meaning 0.015$ per envelope -the 50 pack costs 1$, meaning 0.02$ per envelope -the single envelope costs 0.03$ per envelope Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones. Having 6.3$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 0.3 $ left. so we buy 10 individual envelopes. If we add up the numbers, we get 400+10= <gadget id="calculator"> 400+10</gadget> <output>410</output> 410 envelopes. Answer 410 <result>D</result>

D

Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $6.30?

aqua_rat__YQQIw1TdsgdnJxgj

A taxi leaves Point A 5 hours after a bus left the same spot. The bus is traveling 20 mph slower than the taxi. Find the speed of the taxi, if it overtakes the bus in three hours. Options: A) 34 B) 32 C) 36 D) 38 E) 40

Let the speed of bus be v - 20, speed of taxi be v The bus travelled a total of 8 hrs and taxi a total of 3 hrs. Hence 8 * (v-20) = 3v 8v - 160 = 3v 5v = 160 v = 32 mph 32 <result>B</result>

B

A taxi leaves Point A 5 hours after a bus left the same spot. The bus is traveling 20 mph slower than the taxi. Find the speed of the taxi, if it overtakes the bus in three hours.

aqua_rat__kuflz1sTF7sApPH1

The average temperature from Tuesday to Friday is 48°C and from Wednesday to Saturday is 52°C. If the temperature on Tuesday is 42°C, what was it on Saturday? Options. A) 52°C B) 55°C C) 58°C D) 51°C E) 53°C

Temperature on Tuesday + Wednesday + Thursday + Friday = 4 x 48°58°C = 192°58°C Temperature on Tuesday = 42°58°C Thus, Wednesday + Thursday + Friday = (192°58°C - 42°58°C) = 150°58°C Temperature on Wednesday + Thursday + Friday + Saturday = 4 × 52°58°C = 208°58°C Thus, Saturday’s temperature = 208 - 150°58°C = 58°58°C ANSWER:58°C <result>C</result>

C

The average temperature from Tuesday to Friday is 48°C and from Wednesday to Saturday is 52°C. If the temperature on Tuesday is 42°C, what was it on Saturday?

aqua_rat__ugk83fIZYw5XbBnm

In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 5.5), (8, 0), (0, -5.5), (-8, 0)? Choose the correct answer A) 56 B) 88 C) 112 D) 116 E) 120

Ares of rhombus= 1/2* D1 *D2 Length of 1st diagonal = 8+8= <gadget id="calculator">8+8</gadget> <output>16</output> 16 Length of 2nd diagonal= 5.5+5.5= <gadget id="calculator">5.5+5.5</gadget> <output>11</output> 11 Area= 1/2*16*11= <gadget id="calculator">1/2*16*11</gadget> <output>88</output> 88 88 is the answer <result>B</result>

B

In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 5.5), (8, 0), (0, -5.5), (-8, 0)?

aqua_rat__Q4x3eGSypKiMbgJD

A man engaged a servant on the condition that he would pay him Rs.600 and a uniform after one year service. He served only for 9 months and received uniform and Rs.400, find the price of the uniform? Pick: A) s.80 B) s.85 C) s.90 D) s.100 E) s.200

9/12 = 3/4 * 600= <gadget id="calculator">3/4 * 600</gadget> <output>450</output> 450 400 ------------- 50 1/4 -------- 50 1 --------- ?=&gt; Rs.200 ANSWs.200R:s.200 <result>E</result>

E

A man engaged a servant on the condition that he would pay him Rs.600 and a uniform after one year service. He served only for 9 months and received uniform and Rs.400, find the price of the uniform?

aqua_rat__9pLd8U1Osk1UeyYl

If a young child was 17 months old one year ago, how old was the child, in months, x months ago? Pick one: A) x − 29 B) x − 12 C) 17 − x D) 24 − x E) 29 − x

The child's age today is 17 months + 12 months = 29 months x months ago, the child's age was (29 - x) months old. The answer is 29 − x. <result>E</result>

E

If a young child was 17 months old one year ago, how old was the child, in months, x months ago?

aqua_rat__ksTzDTm67ifOODuw

When positive integer N is divided by positive integer J, the remainder is 11. If N/J = 724.04, what is value of J? Choose the correct choice from the following. A) 140 B) 150 C) 260 D) 275 E) 280

When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder So, Dividend/Divisor = Quotient + Remainder/Divisor Given that N/J = 724.04 Here 724 is the quotient. Given that Remainder = 11 So, 724.04 = 724 + 11/J So, J = 275 <result>D</result>

D

When positive integer N is divided by positive integer J, the remainder is 11. If N/J = 724.04, what is value of J?

aqua_rat__y3hxq0Ynu5oIJUxx

Find the side of the largest possible square slabs which can be paved on the floor of a room 2 m 50 cm long and 1 m 50 cm broad. Also find the number of such slabs to pave the floor. Options. A) 25, 20 B) 30, 15 C) 50, 15 D) None of these E) 75,35

Explanation: H50, 15F (250, 150) = 50 cm The number slabs = 250 *150/ 50*50 =15 Answer: 50, 15 <result>C</result>

C

Find the side of the largest possible square slabs which can be paved on the floor of a room 2 m 50 cm long and 1 m 50 cm broad. Also find the number of such slabs to pave the floor.

aqua_rat__V7Dj8hrDyFfhlMmg

A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required? Choose the correct option. A) 34 B) 40 C) 68 D) 88 E) 98

Explanation: We have: l = 20 ft and lb = 680 sq. ft. So, b = 34 ft. Length of fencing = (l + 2b) = (20 + 68)= <gadget id="calculator">(20 + 68)</gadget> <output>88</output> 88 ft. Answer: 88 <result>D</result>

D

A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?

aqua_rat__4o69MCEXY2TpUdUB

A farmer brought 76 cows, the price of each cow being the same and then sold 20 cows at a profit of 15%, 40 cows at a profit of 19% and the remainder at a profit of 25% making a total profit of Rs.26,280. What is the cost price of each cow? Select the correct option: A) Rs.1000 B) Rs.1800 C) Rs.1500 D) Rs.1400 E) Rs.2500

Let cost price of each Cow is x. Total Cost of 76 Cows = 76x. SP of 20 Cows = 20x + 15% of 20x SP of 20 Cows = 20x + 3x = 23x SP of 40 Cows 20 + 3= <gadget id="calculator">20 + 3</gadget> <output>23</output> 23x SP of 40 Cows= 40x + 19% of 40x = 47.6x SP of remaining cows (16 cows) = 16x + 25% of 16x = 20x Total selling price of 76 cows = 23x + 47.6x + 20x = 90.6x. Total Profit 23 + 47.6 + 20= <gadget id="calculator">23 + 47.6 + 20</gadget> <output>90.6</output> 90.6x. Total Profit= Rs. 26280 Total SP - Total CP = Total Profit 90.6x - 76x = 26280 14.6x = 26280 x = 1800. CP of each Cow is Rs. 1800. ANSWER :OPTION Rs.1800 <result>B</result>

B

A farmer brought 76 cows, the price of each cow being the same and then sold 20 cows at a profit of 15%, 40 cows at a profit of 19% and the remainder at a profit of 25% making a total profit of Rs.26,280. What is the cost price of each cow?

aqua_rat__qzbAIdIpaTdZEosp

Bus 1 and Bus 2 run between cities A and B. Bus 1 leaves city A at the same time Bus 2 leaves city B, each at a constant rate of speed. Their first meeting is 60 miles from city A. After reaching their respective destinations and immediately turning around, their second meeting is 30 miles from city B. What is the distance in miles between city A and city B? Choose one A) 90 B) 120 C) 125 D) 150 E) 180

let d=distance between cities A and B bus 1 distance to first meeting=60 miles bus 1 distance from first to second meeting=(d-60)+30=d-30 miles bus 2 distance to first meeting=d-60 miles bus 2 distance from first to second meeting=60+(d-30)=d+30 miles because both buses take the same time for the pre-meeting leg, and the same time for the inter-meeting leg, and their speeds remain constant, their ratios between pre-meeting distance and inter-meeting distance should be the same therefore, 60/(d-30)=(d-60)/(d+30) d^2=150d d=150 miles 150 <result>D</result>

D

Bus 1 and Bus 2 run between cities A and B. Bus 1 leaves city A at the same time Bus 2 leaves city B, each at a constant rate of speed. Their first meeting is 60 miles from city A. After reaching their respective destinations and immediately turning around, their second meeting is 30 miles from city B. What is the distance in miles between city A and city B?

aqua_rat__mWJAprycFJS0XgA3

If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is? Choose the correct choice from the following answers: A) 87 B) 40 C) 37 D) 28 E) 26

A.M. of 75 numbers = 35 Sum of 75 numbers = 75 * 35= <gadget id="calculator">75 * 35</gadget> <output>2_625</output> 2625 Total increase= 75 * 5= <gadget id="calculator">75 * 5</gadget> <output>375</output> 375 Increased sum= 2625 + 375= <gadget id="calculator">2625 + 375</gadget> <output>3_000</output> 3000 Increased average= 3000/75= <gadget id="calculator">3000/75</gadget> <output>40</output> 40. Answer:40 <result>B</result>

B

If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is?

aqua_rat__jLV5e1hGXdDPTm7M

A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 1300. How many workers were part of the latter production run? Choose the correct choice from the following answers: A) A)6 B) B)10 C) C)9 D) D)15 E) E)23.5

The daily average production is given by 5n + 20- given In the first k days, 500 units are produced = (5n+20)K =500 k = 500/5n+20...................................1 5 workers were added = 5(n+5)+20 = 5n +45 cumulative is 1300 .. thus for the current period = 1300 -500= <gadget id="calculator">1300 -500</gadget> <output>800</output> 800 (5n+45)K= 800 k = 800/5n+45........................................2 equate 1 and 2 500/5n+20 = 800 /5n+45 500(5n+45) = 800(5n+20) 25n + 225 = 40n + 160 -15n = -65 n = 4 thus n+5 = 9 hence 9 <result>C</result>

C

A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 1300. How many workers were part of the latter production run?

aqua_rat__GB9dIvMV3mb7Zca7

A car started running at a speed of 36 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey. Choose the correct choice A) 45 km B) 76 km C) 25 km D) 15 km E) 30 km

45 km 45 km The total distance covered by the car in the first 10 hours = 36 + 38 + 40 + 42 + 44 + 46 + 48+ 50 + 52 + 54= sum of 10 terms in 45 kmP whose first term is 36 and last term is 54 = 10/2 [36 + 54] = 450 km. <result>A</result>

A

A car started running at a speed of 36 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey.

aqua_rat__84ldeV4WFAS8NfVH

In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples? Choose the correct choice from the following options A) 5/26 B) 5/78 C) 5/21 D) 5/56 E) 5/12

Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁) As remaining person can be any one among three couples left. Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅ = (10 * 6)/252 = 5/21 5/26nswer:5/26 <result>A</result>

A

In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?

aqua_rat__hkpIkF0Zr6iNu3YY

Kristy, Amy, and Blair are going on a cross-country road trip from Washington to Maine. The total driving time is 48 hours. Each driver will drive 6 hours daily and in the remaining hours of the day the group will sight-see and explore. They will sleep in the car when they are not driving. They all have driver's licenses, but Amy is scared of driving in unfamiliar places and would prefer not to take the wheel. How much sooner would the group arrive in Maine, in hours, if Amy chose to drive, compared to just Kristy and Blair? Choose the correct choice from the following answers A) 12 B) 24.76 C) 31.92 D) 36.92 E) 24

All three girls calculation: 3 girls x 6 hours = 18 hours of driving per day, 6 nondriving hours/day 48 total trip hours divided by 18 daily driving hours = 2.67 days / driving rotations 2.67 x 24 (hours in one day) = 64.08 total hours for road trip 2 girls calculation: 2 girls x 6 hours = 12 hours of driving per day, 12 nondriving hours/day 48 total trip hours divided by 12 daily driving hours = 4 days / driving rotations 4 x 24 (hours in one day) = 96 total hours for road trip FINAL ANSWER: 96 hours (2 girls total) minus 64.08 (3 girls total) = ANSWER 31.92: The group would arrive in Maine 31.92 hours sooner if all three drove. <result>C</result>

C

Kristy, Amy, and Blair are going on a cross-country road trip from Washington to Maine. The total driving time is 48 hours. Each driver will drive 6 hours daily and in the remaining hours of the day the group will sight-see and explore. They will sleep in the car when they are not driving. They all have driver's licenses, but Amy is scared of driving in unfamiliar places and would prefer not to take the wheel. How much sooner would the group arrive in Maine, in hours, if Amy chose to drive, compared to just Kristy and Blair?

aqua_rat__RAtqBGtHvrU8uwYL

P, Q and R can do a work in 10 , 12 and 15 days respectively. What is the share ratio of P, Q and R respectively? Answers A) 6 : 5 : 7 B) 6 : 5 : 4 C) 6 : 5 : 3 D) 6 : 4 : 5 E) 4 : 5 : 6

The ratio of their working rates = 1/10 : 1/12 : 1/15 = 6 : 5 : 4. Answer: 6 : 5 : 4 <result>B</result>

B

P, Q and R can do a work in 10 , 12 and 15 days respectively. What is the share ratio of P, Q and R respectively?

aqua_rat__qNZWJnUk6yXBKC22

A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 30 percent, what is the discount rate on mysteries? Choose the correct choice from the following choices: A) 17.18% B) 12% C) 13% D) 14% E) 15%

Let B be the discount on biographies and M be the discount on mysteries So., B + M = 0.30 -----(1) 17.18%nd (20*5 + 12*3) - (20*5*(1-B) + 12*3*(1-M)) = 19 --&gt; 100(1-(1-B)) + 36(1-(1-M) = 19 100B + 36M = 19 ------(2) Solving 12., we get M = 0.1718 = 17.18 17.18% <result>A</result>

A

A bookstore has a shelf that contains biographies which normally sell for $20 each and mysteries that normally sell for $12 each. During a sale, the biographies and mysteries are discounted at different rates so that a customer saves a total of $19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries. If the sum of the discount rates for the two types of books is 30 percent, what is the discount rate on mysteries?

aqua_rat__DIh126Ft15MOIrSm

Amar started a business investing Rs. 34000/-. After 3 months, Vamsi joined him with a capital of Rs. 40000/-. At the end of the year, they make a profit of Rs. 17040/-. What will be Amar’s share in the profit? Choose the correct choice A) Rs. 9025/- B) Rs. 9052.5/- C) Rs. 9503.5/- D) Rs. 9504.5/- E) None of these

Explanation: Amar : Vamsi = (34000 * 12 : 40000 * 9) = 408000 : 360000 = 408 : 300 = 51 : 45 Amar’s share = 17040 * 51/91 = 177.5 * 51 = Rs. 9052.5/- Answer: Option Rs. 9052.5/- <result>B</result>

B

Amar started a business investing Rs. 34000/-. After 3 months, Vamsi joined him with a capital of Rs. 40000/-. At the end of the year, they make a profit of Rs. 17040/-. What will be Amar’s share in the profit?

aqua_rat__VtSLeEhg7nLDYTgV

A bag contains ten marbles of the same size: 3 are identical green marbles, 2 are identical red marbles, and the other 5 are five distinct colors. If 5 marbles are selected at random, how many distinct combinations Q of five marbles could be drawn? Choices. A) 41 B) 51 C) 62 D) 72 E) 82

there will be different cases, which we will take one by one.. 1)case 1 when all five colours are different-7c5=21.. 2)case 2 when three different colours and 2 of same type=6c3*2=30.. 3)case 3 when two different colours and 3 of same type=6c2=15.. 4)case 4 when one different colours and 2 of two different colors=5c1*4!/2!2!=15... 5)case 4 when 3 of one type and 2 of other colour=1... total Q-82 ans 82 <result>E</result>

E

A bag contains ten marbles of the same size: 3 are identical green marbles, 2 are identical red marbles, and the other 5 are five distinct colors. If 5 marbles are selected at random, how many distinct combinations Q of five marbles could be drawn?

aqua_rat__TCh9lX6RnMXObxaT

If the greatest common divisor of (n+2)!, (n-1)!, and (n+4)! is 120, what is the value of n? Choose the correct choice from the following: A) 4 B) 5 C) 6 D) 7 E) 3

Notice that: 1! = 1 2! = 2 3! = 6 4! = 24 5! = 120 So, the smallest factorial must be 5! for the GCD to be 120 The smallest of the three factorials is (n-1)! So, we need (n-1)! to equal 5! This means that n = 6 If n = 6, then (n+2)!, (n-1)!, and (n+4)! become 8!, 5! and 10! Let's CONFIRM this conclusion 8! = (1)(2)(3)(4)(5)(6)(7)(8) = (120)(6)(7)(8) 5! = (1)(2)(3)(4)(5) = 120 10! = (1)(2)(3)(4)(5)(6)(7)(8)(9)(10) = (120)(6)(7)(8)(9)(10) As you can see, 120 is a divisor of all three factorials. In fact, 120 is the GREATEST COMMON divisor of all three factorials. Answer: 6 <result>C</result>

C

If the greatest common divisor of (n+2)!, (n-1)!, and (n+4)! is 120, what is the value of n?

aqua_rat__Hwgo8X5En2Z70Z9Y

The bus that travels from St. Louis to Chicago and back comes to St. Louis every 3 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 6 hours. If at 12:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again? Pick. A) 16:00. B) 18:00 C) 20:00 D) 22:00. E) 24:00.

Time taken by bus to travel from St. Louis to Chicago and back comes to St. Louis = 3 hours Time taken by bus to travel from St. Louis to Springfield and back comes to St. Louis = 6 hours Time taken by both buses to meet again in St. Louis will be LCM of 3 and 6 = 6 If the buses start at 12:00 o'clock from St. Louis , they will meet again in St. Louis at 18:00 hours Answer 18:00 <result>B</result>

B

The bus that travels from St. Louis to Chicago and back comes to St. Louis every 3 hours while the bus that travels from St. Louis to Springfield and back comes to St. Louis every 6 hours. If at 12:00 o'clock both bused arrived at St. Louis, at what time will they meet in St. Louis again?

aqua_rat__Nu1z25U0VCGr0qRq

A man bets on no.16 on a roulette wheel 14times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and istherefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what r the odds of winning on the bet that he takes? Answers A) 35:1 B) Either ;35:1 C) Either 70;35:1 D) Either 55;45:1 E) Either 65;35:5

Each of the span is an independent event and the outcome of the 15th span will not depend on the outcome of the earlier spans. Either ;35:1 Either ;35:1) <result>B</result>

B

A man bets on no.16 on a roulette wheel 14times and losses each time. On the 15th span he does a quick calculation and finds out that the no. 12 had appeared twice in the 14 spans and istherefore, unable to decide whether to bet on 16 or 12 in the 15th span. Which will give him the best chance and what r the odds of winning on the bet that he takes?

aqua_rat__bhWNsiPruvDhaURs

Let A be the event that a randomly selected two digit number is divisible by 2 and let B be the event that a randomly selected two digit number is divisible by 10. What is P(A and B)? Choose the correct choice from the following: A) 1/20 B) 1/15 C) 1/12 D) 1/8 E) 1/2

P(1/20 and B) = 1/2*1/10 = 1/20 The answer is 1/20. <result>A</result>

A

Let A be the event that a randomly selected two digit number is divisible by 2 and let B be the event that a randomly selected two digit number is divisible by 10. What is P(A and B)?

aqua_rat__vhwc7ALldrajfzaU

A train 280 m long, running with a speed of 63 km/hr will pass a tree in? Select: A) 65 sec B) 16 sec C) 18 sec D) 13 sec E) 76 sec

Speed = 63 * 5/18 = 35/2 m/sec Time taken = 280 * 2/35= <gadget id="calculator">280 * 2/35</gadget> <output>16</output> 16 sec Answer:16 sec <result>B</result>

B

A train 280 m long, running with a speed of 63 km/hr will pass a tree in?

aqua_rat__lSrMv6rtFIpTO2xJ

Shaun is starting a new diet plan that offers him the choice of fruit or yogurt for breakfast, 6 different entrees for lunch, and 9 different entrees for dinner. If Shaun chooses an Italian entree for lunch, he always chooses an Italian entree for dinner. If Shaun chooses a Chinese entree for lunch, he never chooses a Chinese entree for dinner. If there are 2 Italian entrees and 2 Chinese entrees among the lunch choices, and 3 Italian entrees and 3 Chinese entrees among the dinner choices, from how many different daily menus can Shaun choose? Choose the correct choice: A) 24 B) 36 C) 72 D) 90 E) 108

Let the Breakfast set be {F , Y} Lunch be {I ,I , C,C , L1,L2} Dinner be {I,I,I , C,C,C, D1,D2,D3} There are only 2 restrictions, Italian Lunch has to go with Italian Dinner and Chinese Lunch cannot go with Chinese dinner. So the set of Breakfast, Lunch and Dinner will {Any BF, Italian Lunch, Italian Dinner } = 2 * 2 * 2 {Any BF, Chinese Lunch, Not Chinese Dinner} = 2 * 2 * 6 {Any BF, Not Italian or Chinese Lunch, Any Dinner} = 2 * 2 * 9 Adding all these gives 72. Answer is 72 <result>C</result>

C

Shaun is starting a new diet plan that offers him the choice of fruit or yogurt for breakfast, 6 different entrees for lunch, and 9 different entrees for dinner. If Shaun chooses an Italian entree for lunch, he always chooses an Italian entree for dinner. If Shaun chooses a Chinese entree for lunch, he never chooses a Chinese entree for dinner. If there are 2 Italian entrees and 2 Chinese entrees among the lunch choices, and 3 Italian entrees and 3 Chinese entrees among the dinner choices, from how many different daily menus can Shaun choose?

aqua_rat__2mM7YABWWwHdedAi

If 3/p=6 & 3/q=18 then p-q=? Select the correct option: A) 5/24 B) 6/24 C) 7/24 D) 8/24 E) 1/3

p=3/6 , q=3/18=&gt;q=1/6 therefore p-q=(1/2)-(1/6)=1/3 ANSW1/3R:1/3 <result>E</result>

E

If 3/p=6 & 3/q=18 then p-q=?

aqua_rat__Ea2sVYZt63JSvCJi

What is the smallest no. which must be added to 532869 so as to obtain a sum which is divisible by 9? Choose the correct choice from the following options: A) 9 B) 2 C) 1 D) 3 E) 6

For 532869 , 5+3+2+8+6+9=33 3 must be added to 532869 to make it divisible by 9. Now ,5+3+2+8+7+2=27=&gt; 27 is a multiple of 9 and hence 532869 is also divisible by 9 3 <result>D</result>

D

What is the smallest no. which must be added to 532869 so as to obtain a sum which is divisible by 9?

aqua_rat__lUAAwVBfPYiMm5UR

In a division sum, the remainder is 8 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder. The dividend is: Choose the correct choice from the following A) 200 B) 251 C) 250 D) 262 E) 254

Diver = (8*3)+3= <gadget id="calculator">(8*3)+3</gadget> <output>27</output> 27 3* Quotient= 27 Quotient = 9 Dividend = (Divisor * Quotient) + Remainder Dividend = (27 * 9) + 8= <gadget id="calculator">(27 * 9) + 8</gadget> <output>251</output> 251 251 <result>B</result>

B

In a division sum, the remainder is 8 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder. The dividend is:

aqua_rat__Pngn2AeKjpnBBYoC

Six bells commence tolling together and toll at intervals of 2,4,6,8,10 and 12 seconds respectively. in 30 m9nutes,how many times do they toll together ? Choices: A) 4 B) 10 C) 15 D) 16 E) 17

Solution L.C.M. of 2,4,6,8,10,12 is 120. So, the bells will toll together after every 120 seconds, i.e., 2 minutes In 30 minutes, they will toll together left [ ( 30/2 )+ 1= <gadget id="calculator"> ( 30/2 )+ 1</gadget> <output>16</output> 16 times. Answer 16 <result>D</result>

D

Six bells commence tolling together and toll at intervals of 2,4,6,8,10 and 12 seconds respectively. in 30 m9nutes,how many times do they toll together ?

aqua_rat__a7F0IfRCxrMWpAH1

The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum? Choose the correct option: A) 33772 B) 26782 C) 26788 D) 13500 E) 27761

P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)] P = 13500 Answer: 13500 <result>D</result>

D

The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?

aqua_rat__rpM5p8oaYnhjESQS

What annual payment will discharge a debt of Rs. 1125 due in 2 years at the rate of 5% compound interest? Choose the correct choice from the following answers: A) 993.2 B) 551.25 C) 534.33 D) 605.03 E) 646.33

Explanation: Let each installment be Rs. x. Then, x/(1 + 5/100) + x/(1 + 5/100)2 = 1125 820x + 1125 * 441 x = 605.03 So, value of each installment = Rs. 605.03 Answer: Option 605.03 <result>D</result>

D

What annual payment will discharge a debt of Rs. 1125 due in 2 years at the rate of 5% compound interest?

aqua_rat__Zkj43RQHlpkRcJKc

If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 8400 ? Choose the correct choice from the following answers A) Rs.12 B) Rs.16 C) Rs.14 D) Rs.10 E) Rs.18

Required difference = [3 ½ % of Rs.8400] – [3 1/3 % of Rs.8400] = [(7/20-(10/3)]% of Rs.8400 =1/6 % of Rs.8400 = Rs. [(1/6)8(1/100)*8400] = Rs. 14. Answer is Rs.14. <result>C</result>

C

If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 8400 ?

aqua_rat__ebBHPQ9aYvCxCBIQ

If 0.5% of A =80 paise, then the value of A is ? Options: A) Rs. 170 B) Rs. 160 C) Rs. 1.70 D) Rs. 4.25 E) None

Answer ∵ 0.5/100 of A = 80/100 ∴ A = Rs. (80 / 0.5) = Rs. 160 Correct Option: Rs. 160 <result>B</result>

B

If 0.5% of A =80 paise, then the value of A is ?

aqua_rat__3U0k3rZ6aAgWqhkq

In the Biotechnology class of 2000, there were X graduates. 32 of the graduates found a job, 45 continued on to their second degree and 13 did both. If only 9 people didn't do both, What is X equal to? Pick: A) 69. B) 71 C) 73 D) 75 E) 76

Graduates got job = 32 Graduates continued to second degree = 45 Graduates got job and continued to second degree = 13 Graduates didn't get job and didn't continue to second degree = 9 Job No Job Total Second Degree 13 32 45 No Second Degree 19 9 28 Total 32 41 X Therefore X = 73 Answer 73 <result>C</result>

C

In the Biotechnology class of 2000, there were X graduates. 32 of the graduates found a job, 45 continued on to their second degree and 13 did both. If only 9 people didn't do both, What is X equal to?

aqua_rat__0romVjNe1BYU4mv0

The original price of a car was $30,000. Because the car owner thought he could get more money for the car, he set a new price by increasing the original price of the car by 5%. After a week, the car had not sold, so the owner discounted the new price by 5%, and the car was finally sold. What price was the car sold for? Options: A) $29,915 B) $29,925 C) $29,935 D) $29,945 E) $29,955

The car was sold for (0.95)(1.05)($30,000)=$29,925. The answer is $29,925. <result>B</result>

B

The original price of a car was $30,000. Because the car owner thought he could get more money for the car, he set a new price by increasing the original price of the car by 5%. After a week, the car had not sold, so the owner discounted the new price by 5%, and the car was finally sold. What price was the car sold for?

aqua_rat__I8WH8XRT2Z41jZ4u

Due to construction, the speed limit along an 9-mile section of highway is reduced from 55 miles per hour to 30 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? Pick A) A) 5.61 B) B) 8 C) C) 10 D) D) 15 E) E) 8.19

Old time in minutes to cross 9 miles stretch = 9*60/55 = 9*12/11 = 9.81 New time in minutes to cross 9 miles stretch = 9*60/30 = 9*2/1= <gadget id="calculator">9*2/1</gadget> <output>18</output> 18 Time difference= 8.19 Ans:8.19 <result>E</result>

E

Due to construction, the speed limit along an 9-mile section of highway is reduced from 55 miles per hour to 30 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?

aqua_rat__pig202uQxdM9XJci

Points M(7,2) and N(5,14) lie on the xy - plane. What is the midpoint of line segment MN? Choose the correct option: A) (5,0) B) (6,8) C) (0, (136^(1/2))/2) D) (3/2,0) E) (1,5)

The midpoint of a segment is exactly halfway between its endpoints and it's location can be found using the Midpoint Theorem, which states: • The x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints. • Likewise, the y-coordinate is the average of the y-coordinates of the endpoints. So, x=(7+5)/2= <gadget id="calculator">(7+5)/2</gadget> <output>6</output> 6 and y=(2+14)/2= <gadget id="calculator">(2+14)/2</gadget> <output>8</output> 8 --&gt; coordinates of the midpoint are (6, 8). Answer: (6,8). <result>B</result>

B

Points M(7,2) and N(5,14) lie on the xy - plane. What is the midpoint of line segment MN?

aqua_rat__zi7LxAK0erzmJiyB

When x is multiplied by 3, the result is 26 more than the result of subtracting x from 62. What is the value of x? Select: A) -4 B) -2 C) 11 D) 13 E) 22

The equation that can be formed is: 3x-26=62-x or, 4x=88 or, x=22. Answer : 22 <result>E</result>

E

When x is multiplied by 3, the result is 26 more than the result of subtracting x from 62. What is the value of x?

aqua_rat__s8N1AAJJVITJ7b17

What is remainder of the division (1425*1427*1429)/12? Select A) 5 B) 0 C) 1 D) 2 E) 3

remainder will be number/ 100 here as the divisor is two digit number = 12. hence checking for the last two digits = 5*7*9 = 15 Thus remainder = 3. Answer : 3 <result>E</result>

E

What is remainder of the division (1425*1427*1429)/12?

aqua_rat__D31yT4ecxE4IdYAG

Missing number in the series 4 9 20 43 90 185 376? Choose the correct choice from the following options: A) 175 B) 185 C) 759 D) 195 E) 180

4*2+1= <gadget id="calculator">4*2+1</gadget> <output>9</output> 9 9*2+2= <gadget id="calculator">9*2+2</gadget> <output>20</output> 20 20*2+3= <gadget id="calculator">20*2+3</gadget> <output>43</output> 43 43*2+4= <gadget id="calculator">43*2+4</gadget> <output>90</output> 90 90*2+5= <gadget id="calculator">90*2+5</gadget> <output>185</output> 185 185*2+6= <gadget id="calculator">185*2+6</gadget> <output>376</output> 376 376*2+7= <gadget id="calculator">376*2+7</gadget> <output>759</output> 759 ANSWER:759 <result>C</result>

C

Missing number in the series 4 9 20 43 90 185 376?

aqua_rat__dVXbqGdZVQO8UQli

The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 1024 feet squared, what is the difference between the length and the width of the roof? Pick one. A) 38. B) 40. C) 42. D) 48. E) 46.

Let the width= x x*4x=1024 x^2= 256 x= 16 Length= 4*16= <gadget id="calculator">4*16</gadget> <output>64</output> 64 difference= 64-16= <gadget id="calculator">64-16</gadget> <output>48</output> 48 48. is the answer <result>D</result>

D

The roof of an apartment building is rectangular and its length is 4 times longer than its width. If the area of the roof is 1024 feet squared, what is the difference between the length and the width of the roof?

aqua_rat__HQG4RE1QhuSa2LPz

At present the age of the father is 3 times that of the age of the son. Three years hence the father's age would be 2 times that of his son. Find the present age of the father? Choose the correct choice from the following answers: A) 18years B) 12years C) 20years D) 16years E) 25years

18yearsge of the son = (3-1)*3 / (3-2)= <gadget id="calculator">(3-1)*3 / (3-2)</gadget> <output>6</output> 6 years 18yearsge of the father= 6*3= <gadget id="calculator">6*3</gadget> <output>18</output> 18 years 18yearsnswer is 18years <result>A</result>

A

At present the age of the father is 3 times that of the age of the son. Three years hence the father's age would be 2 times that of his son. Find the present age of the father?

aqua_rat__zZBR242s6tD938pT

Pat and Cara begin running at the same time and they start at the same place on a straight path. Pat runs at 9 miles per hour, and Cara runs at 5 miles per hour. After 10 minutes, Pat stops to stretch. If it takes Pat 20 minutes to stretch and Cara continues to run during this time, how many minutes will it take Pat to catch up to Cara? Answers. A) 12 B) 15 C) 18 D) 21 E) 24

In 10 minutes, Pat runs 1.5 miles. In 30 minutes, Cara runs 2.5 miles. Pat can catch Cara at a rate of 4 miles per hour. Since Cara is ahead by 1 mile, it will take Pat 1 / 4= <gadget id="calculator">1 / 4</gadget> <output>1/4 = around 0.25</output> 0.25 hours= 15 minutes to catch Cara. the answer is 15. <result>B</result>

B

Pat and Cara begin running at the same time and they start at the same place on a straight path. Pat runs at 9 miles per hour, and Cara runs at 5 miles per hour. After 10 minutes, Pat stops to stretch. If it takes Pat 20 minutes to stretch and Cara continues to run during this time, how many minutes will it take Pat to catch up to Cara?

aqua_rat__BXkwcqGaz28vUUd2

Tomy's age 16 years hence will be thrice his age four years ago. Find Tomy's present age? Pick: A) 12 years B) 13 years C) 15 years D) 14 years E) 18 years

Let MTomy's present age be 'x' years. x+ 16 = 3(x- 4) =&gt; 2x = 28 =&gt; x = 14 years. 14 years <result>D</result>

D

Tomy's age 16 years hence will be thrice his age four years ago. Find Tomy's present age?

aqua_rat__yaougb6xRz6u906G

Suppose son name is 120,his brother name is 150 and his mother name is 190.find out his father's name??? Choose the correct choice from the following answers A) 220 B) 210 C) 230 D) 240 E) 250

since difference between all name is =30 so father's name will be 190+30= <gadget id="calculator"> 190+30</gadget> <output>220</output> 220. 220NSWER:220 <result>A</result>

A

Suppose son name is 120,his brother name is 150 and his mother name is 190.find out his father's name???

aqua_rat__PVFt9KQtrAyCIcoo

A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey? Choose the correct choice from the following. A) 19 kmph B) 24 kmph C) 17 kmph D) 12 kmph E) 16 kmph

Distance from A and B be 'd' Average Speed = total distance/total time Average Speed = (2d)/[(d/20) + (d/30)] = (2d)/[5d/60) =&gt; 24 kmph. Answer:24 kmph <result>B</result>

B

A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?

aqua_rat__1LB4ccnUaR09htpv

Tommy has a lot of Lego blocks, but only green and red blocks. There are four times as many green blocks as there are red blocks. If Tommy has Y Lego blocks, how many red blocks are there, in terms of Y. Answers. A) 3*Y B) Y/3 C) Y/5 D) Y/4 E) Y/6

Since Y equals the number of blocks, then Y = Green + Red Since there are four times green blocks as red blocks, then Green = 4*Red Thus Y = 4*Red + Red, which simplifies to Y=5*Red Therefore the Red = Y/5 Answer: Y/5 <result>C</result>

C

Tommy has a lot of Lego blocks, but only green and red blocks. There are four times as many green blocks as there are red blocks. If Tommy has Y Lego blocks, how many red blocks are there, in terms of Y.

aqua_rat__1IM9oZFDk13AgHCj

Milk contains 5% water.What quantity of pure milk should be added to 10 litres of milk to reduce this to 2% ? Options A) 5 litres B) 7 litres C) 15 litres D) Cannot be determined E) None of these

Here required quantity of pure milk = 10×(5−2)/2 = 10×3/2 = 15 litres. Answer 15 litres <result>C</result>

C

Milk contains 5% water.What quantity of pure milk should be added to 10 litres of milk to reduce this to 2% ?

aqua_rat__3j11NF74STlylO4Z

How many three letter words are formed using the letters of the word BREAK? Answers: A) A)240 B) B)360 C) C)720 D) D)120 E) E)480

The number of letters in the given word is five. The number of three letter words that can be formed using these four letters is 5P4 = 5 * 4 * 3*2= <gadget id="calculator">5 * 4 * 3*2</gadget> <output>120</output> 120. Answer:120 <result>D</result>

D

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

aqua_rat__5yQpRBwT1VlZNJRe

According to the formula F=9/5 (C) +32, if the temperature in degrees Farenheit (F) increases by 26, by how much does the temperature in degrees Celsius (C) increase? Select the correct option. A) 9 B) 14.44 C) 47 D) 48 3/5 E) 59

You can plug in values. C = 5/9*(F-32) F=32 --&gt; C=0; F=32+26= <gadget id="calculator">32+26</gadget> <output>58</output> 58 --&gt; C=5/9*26=14.44. Increase = 14.44 degrees. Answer: 14.44. <result>B</result>

B

According to the formula F=9/5 (C) +32, if the temperature in degrees Farenheit (F) increases by 26, by how much does the temperature in degrees Celsius (C) increase?

aqua_rat__b8CPrnKTrYRdoCEg

The center of a circle is (5, -2). (5, 7) is outside the circle, and (2, -2) is inside the circle. If the radius, r, is an integer, how many possible values are there for r? Select: A) 4 B) 2 C) 2 D) 10 E) 12

r must be greater than 3 and smaller than 9, hence r=4,5,6,7 or 8. 4nswer 4 <result>A</result>

A

The center of a circle is (5, -2). (5, 7) is outside the circle, and (2, -2) is inside the circle. If the radius, r, is an integer, how many possible values are there for r?

aqua_rat__UlgoX0CtYwPGcFQw

When 100 is divided by positive integer x, the remainder is 3. What is the remainder when 197 is divided by x? Select: A) 2 B) 3 C) 4 D) 6 E) 8

if100/x leaves a reminder 3 then (100-3) i.e. 97 is divisible by x So (100+97)/x leaves a reminder rem(100/x)+rem(97/x)=&gt; 3+0= <gadget id="calculator">3+0</gadget> <output>3</output> 3 Answer :3 <result>B</result>

B

When 100 is divided by positive integer x, the remainder is 3. What is the remainder when 197 is divided by x?

aqua_rat__jJYFTzvN7rtXXDre

The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 50/kg. how much did a kg of coffee cost in june ? Choose the correct choice from the following answers: A) 50 B) 60 C) 80 D) 100 E) 120

Let the price of tea and coffee be x per kg in June. Price of tea in July = 1.2x Price of coffee in July = 0.8x . In July the price of 1/2 kg (500gm) of tea and 1/2 kg (500gm) of coffee (equal quantities) = 50 1.2x(1/2) + 0.8x(1/2) = 50 =&gt; x =50 Thus proved...option 50. <result>A</result>

A

The prices of tea and coffee per kg were the same in june. In july the price of coffee shot up by 20% and that of tea dropped by 20%. if in july , a mixture containing equal quantities of tea and coffee costs 50/kg. how much did a kg of coffee cost in june ?

aqua_rat__0JSCPEuDEkbrO2gI

A train passes a station platform in 38 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? Choose the correct choice from the following. A) 200 B) 220 C) 240 D) 250 E) 270

Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20)= <gadget id="calculator">(15 * 20)</gadget> <output>300</output> 300 m. Let the length of the platform be x meters. Then, x + 300 / 38= 15 x + 300 = 570 x = 270 m. Answer: Option 270 <result>E</result>

E

A train passes a station platform in 38 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

aqua_rat__DjbRhF4r0JICHLXx

What two-digit number is less than the sum of the square of its digits by 13 and exceeds their doubled product by 5? Select. A) 95 B) 99 C) 26 D) 73 E) None of the Above

Let the digits be x and y. The number would be 10x + y. We are given that 2xy + 5 = 10x +y = x^2 y^2 -13 Thus 2xy +5 = x^2 + y^2 - 13 x^2 + y^2 -2xy = 16 (x-y)^2 = 16 (x-y) = 4 or -4 Substituting the values of (x-y) in the equation 2xy +5 = 10x + y x comes out to be 1 or 9... thus the two numbers can be 15 or 99 Thus the answer is 99 <result>B</result>

B

What two-digit number is less than the sum of the square of its digits by 13 and exceeds their doubled product by 5?

aqua_rat__io7RyNBeYePlQQJg

The length of the room is 4m and width is 5m. Find the cost of paving the floor by slabs at the rate of Rs.200 per sq meter? Pick. A) 1000 B) 2000 C) 4000 D) 3000 E) 6000

l=4m w=5m area of the floor = 4 x 5 = 20 sq m cost of paving = 200 x 20= Rs. 4000 Answer: 4000 <result>C</result>

C

The length of the room is 4m and width is 5m. Find the cost of paving the floor by slabs at the rate of Rs.200 per sq meter?

aqua_rat__nprxS240fUKusM53

Nina has exactly enough money to purchase 5 widgets. If the cost of each widget were reduced by $1.25, then Nina would have exactly enough money to purchase 8 widgets. How much money does Nina have? Select the correct option. A) $16.7 B) $24 C) $30 D) $36 E) $40

A its is. Let price = X (x-1.25)8 = 5X X= 10/3 hence total money = 5*10/3= 16.7 <result>A</result>

A

Nina has exactly enough money to purchase 5 widgets. If the cost of each widget were reduced by $1.25, then Nina would have exactly enough money to purchase 8 widgets. How much money does Nina have?

aqua_rat__j3tuD88UeoIRLGbv

At the beginning of the year, the ratio of boys to girls in high school X was 3 to 4. During the year, 10 boys and twice as many girls transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of boys to girls was 4 to 5, how many boys were there in high school X at the beginning of the year? Choose the correct choice from the following options: A) 70 B) 120 C) 100 D) 90 E) 110

let the total number of boys and girls at the beginning of the year be 3x and 4x respectively. now 10 boys and 20 girls are transferred to another school. thus no. of boys and girls students left in the school X are 3x-10 and 4x-20 respectively. the ratio of these boys and girls students = 4/5 thus we have (3x-10)/(4x-20) = 4/5 15x-50= 16x-80 x=30 thus total no. of boys at the beginning of the year =4(30)= 120 Answer is option 120 <result>B</result>

B

At the beginning of the year, the ratio of boys to girls in high school X was 3 to 4. During the year, 10 boys and twice as many girls transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of boys to girls was 4 to 5, how many boys were there in high school X at the beginning of the year?

aqua_rat__zK12U0NPsVfOG77g

If |m+n|=|m-n|, then m*n must be equal to: Choose one A) -3 B) 0 C) -2 D) -4 E) -5

Solution 1: Distance perspective |m-n| = |m+n| ==&gt; The distance of m and n is equal to the distance of m and -n. &lt;=======(-n)=======0=======(n)======&gt; Only 0 is the value that has a distance equal to n and -n. Solution 2: |m-n| = |m+n| (square both) m^2 -2mn + n^2 = m^2 + 2mn + n^2 4mn = 0 mn = 0 Answer: 0 <result>B</result>

B

If |m+n|=|m-n|, then m*n must be equal to:

aqua_rat__z65YfGIo8Rkpkv6p

City A to city B, Andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip? Options: A) 56 B) 57.5 C) 58.9 D) 61.4 E) 62

The total distance is 1×50+3×60=2301×50+3×60=230. And the total time is 4 hours. Hence, Average Speed=(Total DistanceTotal Time)=2304=57.5 57.5 <result>B</result>

B

City A to city B, Andrew drove for 1 hour at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?

aqua_rat__uaVLN3HzMc2HDeGi

In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line before each of Frederick, Gale, and Harold? Choose the correct choice from the following choices A) 1,008 B) 1,296 C) 1,512 D) 2,016 E) 2,268

We want A, B, and C to be before F, G and H. Let's deal with this constraint first: consider A, B, and C as one unit {ABC} and F, G and H also as one unit {FGH}. According to the condition we need them to be arranged as {ABC}{FGH}. A, B, and C, within their unit can be arranged in 3! ways, similarly F, G and H , within their unit can also be arranged in 3! ways. So, we have a line with 6 people XXXXXX. D can take any place in the line so D has 7 options: *X*X*X*X*X*X*. Now, we have a line with 7 people and E can take any place there, so E has 8 options: *X*X*X*X*X*X*X*. Total = 3!*3!*7*8 = 2,016. Answer: 2,016. <result>D</result>

D

In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line before each of Frederick, Gale, and Harold?

aqua_rat__Ie33pDsNfKoat1Ac

In a zoo, the ratio of the number of cheetahs to the number of pandas is 1 : 3 and was the same five years ago. If the increase in the number of cheetahs in the zoo since then is 1, then what is the increase in the number of pandas? Choose the correct choice from the following answers: A) 2 B) 4 C) 5 D) 10 E) 3

One short cut to solve the problem is c:p = 1:3 c increased to 2 =&gt; 1:3 = 2:x =&gt; x = 6 =&gt;p increased by 3 3 is the answer <result>E</result>

E

In a zoo, the ratio of the number of cheetahs to the number of pandas is 1 : 3 and was the same five years ago. If the increase in the number of cheetahs in the zoo since then is 1, then what is the increase in the number of pandas?