MU-NLPC/Calc-aqua_rat huggingface dataset:
At an upscale fast-food restaurant, Shin can buy 3 burgers, 7 shakes, and one cola for $120. At the same place it would cost $164.50 for 4 burgers, 10 shakes, and one cola. How much would it cost for a meal of one burger, one shake, and one cola?
Choose the correct choice from the following choices:
A) $21  B) $27  C) $31  D) $41  E) It cannot be determined

Solution: let's suppose that the price of a burger is BB, of a shake - SS and that of a cola is CC. We can then construct these equations:   3B+7S+C=120   4B+10S+C=164.5   Subtracting the first equation from the second gives us B+3S=44.5   Now if we subtract the new equation two times from first or 3 times from second we will get B+S+C=31. In any case, there is no necessity to know each item's price, just the sum.   Answer: $31
Answer: C
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 :
Choose the correct choice from the following options:
A) 4  B) 6  C) 8  D) 12  E) 15

Solution: Explanation:   Let the required numbers be 33a and 33b.   Then, 33a + 33b = 528.   => a + b= 16.   Now, co-primes with sum 16 are (1, 15), (3, 13), (5, 11) and (7, 9).   âˆ´   Required numbers are   (33 * 1, 33 * 15), (33 * 3, 33 * 13), (33 * 5, 33 * 11),(33 x 7, 33 x 9).   The number of such pairs is 4.   4NSWER IS 4
Answer: A
The area of the GiftBox is 40 m2 that of a longer side 10 m2 and of the shorter side 4 m2, find the edge of the new cube?
Select
A) 40 m3 B) 10 m2 C) 60 m3 D) 80 m3 E) 50 m3

Solution: lb = 40 ; lh = 10 ; fh = 4   (lbh)2 = 40 * 10 * 4 => lbh = 40 m3   40 m3NSWER:40 m3
Answer: A
For all positive integers n and m, the function A(n) equals the following product:
(1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/4 + 4^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is  Choose the correct option:
A) 1/4 B) 1/5 C) 1/6 D) 1/7 E) 1/8

Solution: For all positive integers n and m,   A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number,   note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2)   B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive.   A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...}   A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2)   The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ...   missing numbers are 1/8, 1/13, 1/16, ....   B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25)   here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values   The largest reciprocal that present in B(25) but not in A(5) is 1/7   Answer 1/7
Answer: D
what is the sum of the first 15 odd natural numbers	Options.
A) 300 B) 400 C) 500 D) 600 E) 225

Solution: sum of first n odd natural nuber is = n^2   so sum of the first 15 odd natural numbers=(15)^2=225   ans 225   ANSW225R:225
Answer: E
The simple interest at x% for x years will be $x on a sum of Choose the correct option:
A) $ (1000)/x
B) $(100)x^2
C) $ x
D) $ (100)/x
E) $ 100x

Solution: Principal =$(100*x)/(x*x)=$(100/x).   Answer is $ (100)/x
Answer: D
How many times the keys of a writter haveto be pressedin order to write first 400 counting no.'s?
Choices
A) 998 B) 1000 C) 1092 D) 1100 E) 1200

Solution: 1 to 9 = 9 * 1= 
9 * 1 = 9
9   10 to 99= 90 * 2= 
90 * 2 = 180
180   100 to 400= 301 * 3= 
301 * 3 = 903
903   -----------   1092   1092
Answer: C
Celeste worked for h hours each day for d consecutive days. If she earns $9.50 per hour, what is the total amount she earned?  Answers:
A) 9.50/d + h	B) 9.50 + d + h	C) 9.50 + dh	D) 9.50h + d	E) 9.50dh

Solution: H hours for d days.   Income each day = 9.5*h   Total income = 9.5*h*d   Correct option: 9.50dh
Answer: E
A shopkeeper fixes the marked price of an item 35% above its cost price. The percentage of discount allowed to gain 8% is
Choose the correct answer: A) 20% B) 27% C) 31% D) 43% E) None

Solution: Solution   Let C.P	=Rs.100   Then, marked price	=Rs.135,   S.P	=Rs.108.   Discount %	=(27/135×100)%   = 20%   20%nswer 20%
Answer: A
Ketchup, Mustard and Mayo bottles at a hot dog stand are in the ratio of 3: 3: 2. If there are 6 Ketchup bottles, the number of Mayo bottles at the hot dog stand is: Choices: A) 12 B) 6 C) 3 D) 1 E) 4

Solution: Explanation :   Let Ketchup = 3x, Mustard = 3x & Mayo = 2x. Now, 3x = 6 hence x = 2.   Number of Mayo Bottles = 2x which is 4.   Answer : 4
Answer: E
The ratio of the volumes of two cubes is 2197 : 1331. What is the ratio of their total surface areas?
Select:
A) 169 : 121 B) 169 : 127 C) 169 : 191 D) 121 : 169 E) 121 : 182

Solution: Explanation:   Ratio of the sides = ³√2197 : ³√1331 = 13 : 11   Ratio of surface areas = 13^2 : 11^2 = 169 : 121   169 : 121nswer: Option 169 : 121
Answer: A
In how many different ways can the letters of the word â€˜EXTENTâ€™ be arranged?  Select the correct option
A) 250
B) 180
C) 300
D) 310
E) 360

Solution: Number of ways = 6!/2!2! = 6X5X4X3X2X1/2X1X2X1 = 180   180
Answer: B
In April's entire movie collection she has only 4 movies she likes, even though she has 13 movies. If she picks 2 movies randomly and simultaneously from her collection, what is the probability that exactly 1 of the movies will be one that she likes?	Choose the correct option.
A) 4/13
B) 21/36
C) 1/12
D) 6/13
E) 9/26

Solution: The probability is equal to the number of desired choices divided by the total number of possibilities.   Probability = Favorable/Total   Total = 13C2 = 13*12/2= 
13*12/2 = 78
78   Favorable:   Pick 1 out of 4 movies she likes   AND   Pick 1 out of 9 movies she doesn't like   4C1*9C1= 4*9= 
4*9 = 36
36   P= 36/78 = 6/13   When you use combination method, it is picking all possible cases and the order doesn't matter. Whereas, upon choosing probability method to solve, order matters.   Thus,   Total Probability:   Probability of choosing a movie she likes first AN6/13 Probability of choosing a movie she doesn't like   OR   Probability of choosing a movie she doesn't like first AN6/13 Probability of choosing a movie she likes
Answer: D
When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder S when N is divided by 30?  Choices:
A) (a) 4	B) (b) 7	C) (c) 11	D) (d) 13	E) (e) 17

Solution: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder S when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.(c) 11
Answer: C
Joseph has a bag with 2 red balls and 3 blue balls. If he pulls out two at random and simultaneously, what is the probability of him pulling one red and one blue ball?	Choices: A) 3/5 B) 2/3 C) 8/15 D) 4/12 E) 7/18

Solution: The probability is equal to the number of desired choices divided by the total number of possibilities.   Probability = Favorable/Total   Total = 5C2 = 5*4/2= 
5*4/2 = 10
10   Favorable:   Pick 1 red ball out of 2 red balls   AND   Pick 1 blue ball out of 3 blue balls   2C1*3C1= 2*3= 
2*3 = 6
6   P=6/10=3/5   When you use combination method, it is picking all possible cases and the order doesn't matter. Whereas, upon choosing probability method to solve, order matters.   Thus,   Total Probability:   Probability of choosing a red ball first 3/5ND Probability of choosing a blue ball   OR   Probability of choosing a blue ball first 3/5ND Probability of choosing a red ball   3/5nswer: 3/5
Answer: A
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years. The present age of the husband is	Choices:
A) 35 years  B) 40 years  C) 45 years  D) 50 years  E) NOne

Solution: Sol.   Sum of the present ages ofH husband, wife and child   = (27 × 3 + 3 × 3)years = 90 years.   Sum of present ages of wife and child = (20 × 2 + 5 × 2) = 50 years.   ∴ Husband's present age = (90 - 50)= 
(90 - 50) = 40
40 years.   Answer 40 years
Answer: B
A man, a woman and a boy can together complete a piece of work in 3 days. If a man alone can do it in 6 days and a boy alone in 12 days, how long will a woman take to complete the work? Choose the correct choice:
A) 12days B) 10days C) 9days D) 8days E) 11days

Solution: Explanation:   (1 Man + 1 woman + 1 boy)’s 1day’s work = 1/3   1 man’s 1 day work = 1/6   1boy’s 1 day’s work = 1/1   (1 Man + 1 boy) ‘s 1 day’s work = 1/6 + 1/12 = 1/4   Therefore, 1 woman’s 1 day’s work = 1/3 – 1/4 = 1/12   Therefore, the woman alone can finish the work in 12days.   12daysnswer: Option 12days
Answer: A
Set A: 3, r, 8, 10
Set B: 4, y, 9, 11
The terms of each set above are given in ascending order. If the median of Set A is equal to the median of Set B, what is the value of y – r?
Choose one.
A) -2
B) -1
C) 0
D) 1
E) 2

Solution: So we have even no. of elements in the Set   So median is the average of Middle two numbers   (r+8)/2= (y+9)/2   y - r= -1   Answer -1
Answer: B
A cylinder is 6 cms in diameter and 6 cms in height. If spheres of the same size are made from the material obtained, what is the diameter of each sphere? Choose the correct answer: A) 5 cms B) 2 cms C) 3 cms D) 4 cms E) 6 cms

Solution: since the sphere is made out of the cylinder material their volume will be same   volume of cylinder = pi * 3^2 * 6   volume of one sphere = 4/3 * pi * r ^3 (where r is radius of sphere)   so if there are N such sphere's   equating the volumes,   pi*r^2*h = N*(4/3)*pi*R^3   N is the number of spheres,   substituting the, r and h   9*6 = N*(4/3)*(D/2)^3   D is the diameter of a sphere,   N = (9*6*3*8)/(4*D^3)   N = 324/D^3   now substitute the given answers for D and find the values for N, since a N has to be an integer only value fit for D is 3,   ANSWER:3 cms
Answer: C
What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?  Choose the correct choice from the following options:  A) 20%  B) 80%  C) 20%  D) 27%  E) 50%

Solution: SP2 = 2/3 SP1   CP = 100   SP2 = 80   2/3 SP1 = 80   SP1 = 120   100 --- 20 => 20%   20%nswer: 20%
Answer: A
What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular 7-sided polygon)?	Choose the correct option:
A) 1/2 B) 1/3 C) 1/4 D) 1/6 E) 1/7

Solution: From any vertex, there are two vertices on sides, which do not make a diagonal but a side.   So the remaining n-3 vertices make diagonals.   There are 2 of these diagonals which are the shortest.   The probability of choosing one of the shortest diagonals is 2/4 = 1/2.   The answer is 1/2.
Answer: A
In a triangle, one side is 6 Cm and another side is 6 Cm. which of the following can be the perimeter of the triangle?
Answers
A) 18.  B) 25.  C) 20.  D) 32.  E) 34.

Solution: Given : one side is 6 Cm and another side is 9 Cm. So the 3rd side will be > 3 and < 15. Thus the perimeter will be : 18 < perimeter < 30. Only option satisfying this condition is 20. Hence 20..
Answer: C
A, B and C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 105, how much must C pay as his share of rent?	Choose the most appropriate option:	A) 27	B) 50	C) 55	D) 65	E) none

Solution: Sol.   A : B : C = 10 * 7 : 12 * 5 : 15 * 3 = 70 : 60 : 45 = 14 : 12 : 9.   âˆ´ Câ€™s rent = Rs. [105 * 9/35] = Rs. 27.   27nswer 27
Answer: A
Find the value of X, Y by solving the below equations
2X - Y = 16
X - Y = -5 Options.
A) 15, 18 B) 15, 13 C) 13, 28 D) 21, 26 E) 25, 24

Solution: 2X - Y = 16 ----(I)   X - Y = -5 -----(II) by Subtract (II) From (I)   ------------   X = 21   By Replacing the value of X in (I) we get 2*21 - Y = 16 ==>   -Y = 16 - 42 = -26 ===> Y = 26.   So, X = 21, Y = 26   Answer 21, 26) 21, 26
Answer: D
when a number is divided by 13,the remainder is 11.When the same number is divided by 17,the remainder is 9.What is the number ?	Choose the correct answer
A) 389  B) 356  C) 380  D) 350  E) 349

Solution: x=13p+11 and x=17q+9   13q+11=17q+9   17q-13q=2   q=2+13q/17   The least value of p for which q=2+13q/17 is a whole number is p=26   x=(13*26*11)=(338+11)= 
(338+11) = 349
349.   Answer is 349
Answer: E
If, for all integers n ≥ 1, xnxn is the probability of selecting at random an integer with an odd number of unique positive factors from among the positive integers less than or equal to n^2, then the sum of the first 5 values of xnxn is	Select
A) less than 1
B) between 1 and 2
C) between 2 and 3
D) between 3 and 4
E) greater than 4

Solution: x1 : 1/1   x2 : 1,4 of 1,2,3,4 ----2/4   x3 : 1,4,9 of 1,2...9 ----3/9   x4 : 1,4,9,16----------4/16   x5 : 1,4,9,16,25--------5/25   Total 1+2/4+3/9+4/16+5/25 = 2.3   between 2 and 3 is the right answer
Answer: C
The population of a town is 176400. If it increase at the rate of 5% per annum. What was its population 6 years ago?
Select the correct option
A) 152460	B) 214560	C) 131632	D) 210000	E) 200000

Solution: population 2 years ago = 176400/(1 + 5/100)^6   Answer is 131632
Answer: C
At 6′o a clock ticks 6 times. The time between first and last ticks is 35 seconds. How long does it tick at 12′o clock
Select: A) 77 B) 76 C) 28 D) 66 E) 11

Solution: Explanation:   For ticking 6 times, there are 5 intervals.   Each interval has time duration of   35/5= 
  35/5 = 7
7 secs   At 12 o'clock, there are 11 intervals,   So total time for 11 intervals= 11 × 7 = 77 secs.   77nswer: 77
Answer: A
A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?  Choose the correct choice from the following
A) 24 km  B) 76 km  C) 99 km  D) 77 km  E) 20 km

Solution: Let the distance between A and B be x km.   Total time = x/(9 + 1) + x/(9 - 1) = 4.5   => x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.   Answer: 20 km
Answer: E
A can do a piece of work in 80 days. He works at it for 10 days & then B alone
finishes the remaining work in 42 days. In how much time will A and B, working
together, finish the work? Choose the correct choice from the following choices
A) 122days	B) 41days	C) 80days	D) 42days	E) 30days

Solution: Work done by A in 10 days=10/80=1/8   Remaining work=(1-(1/8))=7/8   Now, work will be done by B in 42 days.   Whole work will be done by B in   (42*8/7)= 
  (42*8/7) = 48
48 days   Therefore, A's one day's work=1/80   B’s one day's work=1/48   (A+B)'s one day's work=1/80+1/48=8/240=1/30   Hence, both will finish the work in 30 days.   answer 30days 30days
Answer: E
A square mirror has exactly half the area of the rectangular wall on which it is hung. If each side of the mirror is 21 inches and the width of the wall is 28 inches, what is the length of the wall, in inches?  Choose the correct choice from the following.
A) 21.5
B) 31.5
C) 41.5
D) 61.5
E) 71.5

Solution: Since the mirror is 42 inches in all sides, it must be a square. Area of a square is A=a^2; 21^2=441.Area of rectangle is double of that 2 *441= 
2 *441 = 882
882.Now A=lw and we need find w so A/l=w ; 882/28= 
882/28 = 63/2 = around 31.5
31.5 Answer!   Answer is 31.5
Answer: B
At Veridux Corporation, there are 215 employees. Of these, 90 are female, and the rest are males. There are a total of 40 managers, and the rest of the employees are associates. If there are a total of 135 male associates, how many female managers are there? Choose the correct choice from the following options
A) 50
B) 20
C) 25
D) 30
E) 35

Solution: Well, first letâ€™s take care of the â€œtotalsâ€. The numbers in the â€œtotalsâ€ row must add up. If 90 are females, the other 215 â€“ 90 = 125 must be males. Similarly, the numbers in the â€œtotalsâ€ column must add up. If 40 are managers, then the other 215 â€“ 40 = 175 must be associates.   Now, in the â€œassociateâ€ row, 135 + E = 175, which means E = 40â€” the other 40 associates must be female.   Now, to find B, which is what the question is asking, we need only look at the sum in the â€œfemaleâ€ column: B + 40 = 90, which means B = 50. There are fifteen female managers in this company. Thus, the answer = 50(50).
Answer: A
The ratio of toddlers to infants at a day care center is 7 to 3. If twelve more infants join the day care to change the ratio to 7 to 5, how many toddlers are there at this day care center?  Choose one:
A) 24
B) 36
C) 42
D) 72
E) 120

Solution: 5x - 3x = 12   So, 2x = 6   hence no of toddlers is 6*7= 
6*7 = 42
42   Answer will be (42) 42
Answer: C
For integers U and V, when U is divided by V, the remainder is odd. Which of the following must be true?
Choose the correct choice from the following answers:
A) At least one of U and V is odd
B) The sum U + V is odd
C) U and V share no common factors other than 1
D) UV is odd.
E) U is odd

Solution: At least one of U and V is oddt least one of U and V is odd   At least one of U and V is odd
Answer: A
The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is? Select the correct option.
A) 4/5
B) 4/7
C) 5
D) 5/7
E) None

Solution: 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   Option 4/5
Answer: A
In a certain mathematical activity, we start with seven cards, each with a different prime number written on it. These seven cards are randomly put into three boxes in the following way: one box must get four cards, one must get two, and one gets only one. Then, for each box, we find the product of all the cards in the box, and that’s the “number” of the box. Then, we put those three numbers in order, from lowest to highest, and that is our set. How many different sets T can be created from this process?  Pick one.
A) 35  B) 105  C) 210  D) 420  E) 630

Solution: T=7C4 * 3C2 = 105 Answer B.   7C4 ways to choose 4 numbers for Box 1   3C2 ways to choose 2 numbers for Box2   1 way for Box 3 .   every combination will give a different product and can be arranged least to highest only in one way .105
Answer: B
If the volume of a cube is x^3 cubic units, what is the number of square units in the surface area of the cube? Choose the correct choice:
A) x^2  B) x^3  C) x^6  D) 6x^2  E) 6x^3

Solution: The question basically asks you to calculate the surface area of the cube.   Volume of the cube = x^3   This means each side of the cube = x   Hence area of each side = x^2   Total surfaces in a cube = 6   Total surface area = 6*x2   Correct Option: 6x^2
Answer: D
If x is a positive integer, which of the following must be odd?
Choose the correct choice from the following answers:
A) x+1 B) x^2+x C) x^2+x+9 D) x^2−1 E) 3x^2−3

Solution: A. X+1 = can be odd or even. Since O + O =E or E + O = O   B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]   C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 9 = ODD   Hence x^2+x+9.
Answer: C
The total marks obtained by a student in Mathematics and Physics is 60 and his score in Chemistry is 10 marks more than that in Physics. Find the average marks scored in Mathamatics and Chemistry together. Choose the most appropriate option
A) 35	B) 30	C) 25	D) Data inadequate	E) None of these.

Solution: Let the marks obtained by the student in Mathematics, Physics and Chemistry be M, P and C respectively.   Given , M + C = 60 and C - P = 10 M + C / 2 = [(M + P) + (C - P)] / 2 = (60 + 10) / 2= 
(60 + 10) / 2 = 35
35.   35NSWER:35
Answer: A
A train 325 m long passed a pole in 25 sec. How long will it take to pass a platform 900 m long? Answers:  A) 76 sec  B) 94 sec  C) 87 sec  D) 75 sec  E) 96 sec

Solution: Speed = 325/25= 
325/25 = 13
13 m/sec.   Required time= (325 + 900)/13   = 94 sec.   Answer:94 sec
Answer: B
48% of respondents to a survey consisted of those who used both M and N and those who used neither M nor N. 41% of respondents did not use M. 38% used N. What percent of respondents used only N? Choose one:
A) 19.5%
B) 21.5%
C) 20%
D) 15.5%
E) 17.5%

Solution: From the question, we can summarize the information as follows:   N Not N   M X   Not M Ans y 41   38 100   Then we can set a system of 3 equations 3 unknowns described below:   X + Y = 48   X + Ans = 38   Y + Ans = 41   Sum up all three equations to get 2X + 2Y + 2Ans = 127   15.5%ivide both sides by 2 to get X + Y + Ans = 63.5   Replace X + Y with 48 to get 48 + Ans = 63.5   Substract 48 from both sides to get Ans = 63.5 - 48= 
63.5 - 48 = 15.5
15.5   The answer must be 15.5%.
Answer: D
A player holds 13 cards of four suits, of which seven are black and six are red. There are twice as many diamonds as spades and twice as many hearts as diamonds. How many clubs does he hold ?	Choices.
A) 4 B) 5 C) 6 D) 7 E) 8

Solution: D=2S   H=2D =4S   6+S+2S+4S=13;6+7S=13   2S+4S=6S 2 +4= 
2 +4 = 6
6S=6   S=1   6=6   ANSWER:6
Answer: C
Mangala completes a piece of work in 10 days, Raju completes the same work in 12 days. If both of them work together, then the number of days required to complete the work is?	Choose the correct choice from the following choices.
A) 5.5 days  B) 6.5 days  C) 7.5 days  D) 8.5 days  E) 9.5 days

Solution: 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 = 10 Ã— 12/22 = 5.5 days.   5.5 days)
Answer: A
Two bullet trains of equal lengths take 8 seconds and 15 seconds respectively to cross a telegraph post. If the length of each bullet train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?  Pick one
A) 13 sec. B) 10.4 sec. C) 12 sec. D) 17 sec. E) 19 sec.

Solution: Speed of the first bullet train = 120/8 m/sec = 15 m/sec.   Speed of the second bullet train = 120/15 m/sec = 8 m/sec.   Relative speed = (15 + 8)= 
(15 + 8) = 23
23 m/sec.   Required time= (120 + 120)/23 sec = 10.4 sec.   10.4 sec.
Answer: B
Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 30 items in the same time Machine Z produces 38 items. If machine Y takes 19 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?
Select:  A) 6  B) 9  C) 9 1/2  D) 15  E) 13 1/2

Solution: rate z/rate y=38/30   time z/time y=30/38   30/38*19= 
30/38*19 = 15
15 minutes   15
Answer: D
If the annual increase in the population of a town is 10% and the present number of people is 15000, what will the population be in 2 years?  Choose the correct choice from the following options:	A) 12100	B) 15240	C) 18150	D) 18452	E) 19002

Solution: The required population is = 15000 (1 + 10/100)^2   = 15000 * 11/10 * 11/10= 
15000 * 11/10 * 11/10 = 18_150
18150   Answer is 18150
Answer: C
Machine A and machine B are each used to manufacture 550 sprockets. It takes machine A 10 hours longer to produce 550 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?	Select the correct option.
A) 6
B) 5
C) 7
D) 8
E) 9

Solution: Machine 5: Takes x hours to produce 550 sprockets   Machine A: Takes (x+10) hours to produce 550 sprockets   Machine 5: In 1 hour, 5 makes 550/x sprockets   Machine A: In 1 hour, A makes 550/(x+10) sprockets   Equating:   1.1(550/(x+10)) = 550/x   605/(x+10) = 550/x   605x = 550x+5500   55x = 5500   x = 100   A makes   550/(110)= 
  550/(110) = 5
5 sprockets per hour   Answer : 5
Answer: B