MU-NLPC/Calc-aqua_rat huggingface dataset:
In a company with 48 employees, some part-time and some full-time, exactly (1/3) of the part-time employees and (1/4) of the full-time employees take the subway to work. What is the greatest possible number H of employees who take the subway to work?	Pick:
A) 12	B) 13	C) 14	D) 15	E) 16

Solution: P/3 + F/4 = P/3 + (48-P)/4 = 12 + P/2   P/3 + F/3 = (P+F)/3 = 48/3= 
48/3 = 16
16   P/4 + F/4= 12   P/3 + F/3 > P/3 + F/4 > P/4 + F/4   --> 16> 12 + P/12 > 12   GREATEST Possible H: 12 + p/12 = 15 --> p = 36 ( integer --> good)   15 or 15 is the answer
Answer: D
Mary is expected to pay back a total sum of $819200 to her bank as mortgage. If she is expected to make a payment which is double of the previous months amount, how long will it take her to fully repay the loan if her initial payment was $400.	Pick one
A) 13  B) 15  C) 12  D) 10  E) 11

Solution: First payment--$400   Total amount to be repaid--$819200   First month payment--$400   Second month payment--$400*2=$800   Third month payment--$800*2  -- 400*2= 
  -- 400*2 = 800
$800   Third month payment--$800*2=$1600   Fourth month payment--$1600*2 -- 800*2= 
 -- 800*2 = 1_600
$1600   Fourth month payment--$1600*2=$3200   Fifth month payment--$3200*2  -- 1600*2= 
  -- 1600*2 = 3_200
$3200   Fifth month payment--$3200*2=$6400   Sixth month payment--$6400*2 -- 3200*2= 
 -- 3200*2 = 6_400
$6400   Sixth month payment--$6400*2=$12800   Seventh month payment--$25600*2 -- 6400*2= 
 -- 6400*2 = 12_800
$12800   Seventh month payment--$25600*2=$51200   11ight month payment--$51200*2-- 25600*2= 
-- 25600*2 = 51_200
$51200   11ight month payment--$51200*2=$102400   Ninth month payment--$102400*2-- 51200*2= 
-- 51200*2 = 102_400
$102400   Ninth month payment--$102400*2=$204800   Tenth month payment--$204800*2 -- 102400*2= 
 -- 102400*2 = 204_800
$204800   Tenth month payment--$204800*2=$409600   11leventh month payment--$409600*2 -- 204800*2= 
 -- 204800*2 = 409_600
$409600   11leventh month payment--$409600*2=$819200   Answer is 11-- 409600*2= 
-- 409600*2 = 819_200
$819200   Answer is 11
Answer: E
What will $500 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually?	Choose the correct choice from the following options:
A) $788	B) $812	C) $864	D) $878	E) $912

Solution: After one year: 1.2 * $500   After two years: (1.2)^2 * $500   After three years: (1.2)^3 * $500 = $864   The answer is $864.
Answer: C
The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?	Pick.
A) 18/35
B) 18/18
C) 18/19
D) 18/17
E) 18/12

Solution: If both agree stating the same fact, either both of them speak truth of both speak false.   Probability = 3/5 * 4/7 + 2/5 * 3/7   = 12/35 + 6/35 = 18/35   18/35nswer:18/35
Answer: A
If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is  Choices:	A) 54.48	B) 54.68	C) 54.6	D) 54.58	E) None of these

Solution: Explanation:   (55×50)+(60×55)+(45×60) / 55+60+45   8750 / 160=54.68   Option 54.68
Answer: B
How many numbers amongst the numbers 7 to 56 are there which are exactly divisible by 8 but not by 6?  Select the correct option:
A) Nil	B) 1	C) 2	D) 3	E) More than 3

Solution: 8,16,24,32,40,48,56 are divisible by 8.   24,48 are divisible by 6 also.   So there are 5 numbers exactly divisible by 8 but not by 6   ANSWMore than 3R:More than 3
Answer: E
The ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm. Find the ratio of the breadth and the area of the rectangle?	Pick one.
A) 1:96  B) 1:92  C) 1:98  D) 1:94  E) 1:99

Solution: Let the length and the breadth of the rectangle be 4x cm and 3x respectively.   (4x)(3x) = 6912   12x2 = 6912   x2 = 576 = 4 * 144 = 22 * 122 (x > 0)   => x = 2 * 12= 
2 * 12 = 24
24   Ratio of the breadth and the areas= 3x : 12x2 = 1 : 4x   = 1:96.   1:96nswer:1:96
Answer: A
The speed of a boat in upstream is 80 kmph and the speed of the boat downstream is 100 kmph. Find the speed of the boat in still water and the speed of the stream?
Choose the correct choice from the following choices
A) 90, 10 kmph	B) 35, 27 kmph	C) 50, 60 kmph	D) 45, 55 kmph	E) 45, 65 kmph

Solution: Speed of the boat in still water = (80+100)/2= 
(80+100)/2 = 90
90 kmph. Speed of the stream= (100-80)/2= 
(100-80)/2 = 10
10 kmph   90, 10 kmphNSWER:90, 10 kmph
Answer: A
The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it? Choose the most appropriate option:	A) 20%	B) 18%	C) 15%	D) 12%	E) 14%

Solution: 100 * 100= 
100 * 100 = 10_000
10000   80 * 110= 
80 * 110 = 8_800
8800   10000------- 1200   100 ------- ?= 12%   ANSWER:12%
Answer: D
The ratio of numbers is 3:4 and their H.C.F is 8. Their L.C.M is:  Choose one
A) 12  B) 96  C) 24  D) 48  E) 98

Solution: Let the numbers be 3x and 4x.   Then their H.C.F = x. So, x = 8.   So, the numbers are 24 and 32.   L.C.M of 24 and 32 = 96.   ANSWER:96
Answer: B
If set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={12,12,12...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ? Pick.
A) a) k(n+m+mn)+ k
B) b) (1+n+m+mn)(k+1)
C) c) k^2(mn+n/m)
D) d) kmn(k+m+n)
E) e) None of the above.

Solution: a) how many 2's are included?   b) how many 3's are included?   and   c) how many 11's are included?   For the number of 2, we could have zero 2's, or one 2, or two 2's, all the way up to n 2's. That's (n + 1) possibilities for the 2's. Similarly, (m + 1) possibilities for the 3's and (k + 1) possibilities for the 11's. We simply multiply these three numbers.   NOTICE that one set, the set that includes no 2's, no 3's, and no 11's, is included. This is known in mathematics as thenull set, sometimes called the empty set, a set with no members. Technically, this is a subset of every possible set, but that's a technical detail of set theory that goes well beyond what the GMAT would expect students to know. Even the the calculation is not that difficult, some of the technical aspects of this question are not in line with the GMAT's expectations.   The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together:   (mn + m + n + 1)(k + 1).   Mike   c) k^2(mn+n/m)
Answer: C
A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?
Choose the correct choice:
A) 220  B) 277  C) 298  D) 100  E) 271

Solution: A can give B (5 min - 4 1/2 min) = 30 sec start.   The distance covered by B in 5 min = 1000 m.   Distance covered in 30 sec = (1000 * 30)/300= 
(1000 * 30)/300 = 100
100 m.   A can give B 100m start.   Answer:100
Answer: D
A password of a computer used four digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero?
Options.
A) 1/32
B) 1/16
C) 1/8
D) 2/5
E) 1/2

Solution: We have four digits can be used for password -0,2,3,5,7.   Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)   So, 5/10 * 5/10 * 5/10 * 5/10 =1/16 (1/16)
Answer: B
If x is an even integer and y is an odd integer, which of the following is an even integer?  Select
A) x+y	B) x+2y	C) 3x+y	D) x+y^2	E) x+y+2

Solution: Plug in an even integer for x; in this case 2   Plug in an odd integer for y; in this case 1   2+1= 
2+1 = 3
3 Odd    2+(2*1)= 
 2+(2*1) = 4
4 Even   (3*2)+1= 6 + 1= 
6 + 1 = 7
7 Odd   2+(1^2)= 2 + 1= 
2 + 1 = 3
3 Odd    2+1+2= 
 2+1+2 = 5
5 Odd   Answer: x+2y
Answer: B
The sum of the present age of Henry and Jill is 48. What is their present ages if 9 years ago Henry was twice the age of Jill?
Options.
A) and 27 B) and 24 C) and 22 D) and 29 E) of these

Solution: Let the age of Jill 9 years ago be x, age of Henry be 2x   x+9 + 2x+9 = 48   x = 10   Present ages will be 19 and 29   Answer : and 29
Answer: D
Which number can we add to 722425 to get a number exactly divisible by 456?  Pick one.
A) 312	B) 335	C) 347	D) 361	E) 383

Solution: 722425 / 456 = 1584 with a remainder of 121.   We need to add 456 - 121= 
456 - 121 = 335
335   The answer is 335.
Answer: B
The mean of four integers L will not change if all the integers are multiplied by any constant. What is always true about this set of numbers?
I. The mean of the set is 0
II. The sum of the largest member and the smallest member of the set is 0
III. The set contains both positive and negative integers Choose the correct choice.
A) I only B) II only C) III only D) I and II only E) I, II, and III

Solution: If we consider a set {1,2,3,4}, when multiplied with a constant we take that constant as 1 and multiply resulting set will contain the same numbers as the original. so how can the answer be I only.....I only
Answer: A
In a class there are 10 boys and 25 girls. In how many ways can a boy and a girl be selected?
Choose the correct choice:
A) 400
B) 250
C) 600
D) 530
E) 630

Solution: Explanation:   We can select one boy from 10 boys in 10 ways.   We select one girl from 25 girls in 25 ways   We select a boy and girl in 10 * 25 ways i.e., = 250 ways.   Answer: Option 250
Answer: B
On a certain transatlantic crossing, 15 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?
Choices.
A) 33 1/3%
B) 40%
C) 37.5%
D) 60%
E) 66 2/3%

Solution: On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?   Solution: Let total number of passengers be 100   According to Q stem 40% of passengers who had round-trip tics have taken cars - let number of passengers with round trip be X then   40% of X = 15 => X= 37.5.   Answer 37.5%
Answer: C
Look at this series: 5.2, 4.8, 4.4, 4, ... What number should come next?
Select
A) 4.1	B) 3.6	C) 2.6	D) 5.0	E) 5.5

Solution: 3.6   3.6   In this simple subtraction series, each number decreases by 0.4.
Answer: B
If n is an integer, what is the greatest possible value for n that would still make the following statement true: 11*10^n < 1/10 ?
Choose the correct answer.
A) –4 B) –3 C) –2 D) –1 E) 0

Solution: Just putting values, the LHS becomes   n=0 --> 11   n=-1 --> 11/10   n=-2 --> 11/100   n=-3 --> 11/1000   Anything lower will be smaller than 11/1000. n=-2, equality doesnt hold but it does for n=-3.   Answer is –3.
Answer: B
The area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 3 per metre approximately	Choose the correct choice from the following answers
A) 4457	B) 4567	C) 4235	D) 4547	E) 4675

Solution: Explanation:   Area = (17.56 x 10000) m2= 175600 m2.   ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.   Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.   Cost of fencing = Rs. (1485.78 x 3) = Rs. 4457.   4457nswer: Option 4457
Answer: A
The population of a town is 8000. It decreases annually at the rate of 20% p.a. What will be its population after 2 years?	Select the correct option:	A) 5100	B) 5120	C) 5130	D) 5140	E) 5160

Solution: Formula :   ( After =100 denominator   Ago = 100 numerator)   8000 × 80/100 × 80/100 = 5120   5120
Answer: B
Statement: "In order to bring punctuality in our office, we must provide conveyance allowance to our employees."
Assumptions:
1)Conveyance allowance will not help in bringing punctuality.
2)Discipline and reward should always go hand in hand.  Pick:
A) Only assumption I is implicit
B) Only assumption II is implicit
C) Either I or II is implicit
D) Neither I nor II is implicit
E) Both I and II are implicit

Solution: Assumption I goes against the statement. So, it is not implicit. The allowance will serve as a reward to the employees and shall provoke them to come on time. So, II is implicit.   Only assumption II is implicit)
Answer: B
Steel company has four empty trucks that will head out in the morning, all four to the same destination. The clerk has four different boxes to ship to that same destination. All four boxes could go on any one of the trucks, or the boxes could be split up into any groupings and given to the trucks in any combinations (ie. two to one truck, one to another, and one to another). In how many different ways could the boxes be put on the four trucks?  Choose the correct choice
A) 16	B) 64	C) 256	D) 576	E) 4096

Solution: MAGOOSHOFFICIAL SOLUTION:   Steel company has four empty trucks that will head out in the morning, all four to the same destination.Where we put one box has absolutely no bearing on where we put any of the other boxes. The placement of the four boxes is completely independent of one another. For each box, we have four choices.   N = 4*4*4*4 = 16*16= 
16*16 = 256
256   Answer= (256)
Answer: C
If the tens digit x and the units digit y of a positive integer n are reversed, the resulting integer is 18 more than n. What is y in terms of x ?	Choose the correct choice from the following answers
A) 20 - x B) 18 - x C) x + 18 D) x + 2 E) x - 2

Solution: Original Digits=xy i.e. Number=10x+y   After reversing the digits:   Digits=yx i.e. Number=10y+x   10y+x is 9 more than 10x+y   10x+y+18=10y+x   10x-x+18=10y-y   9x+18=9y   x+2=y   OR   y=x+2   Ans:x + 2
Answer: D
The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 15, how many more dollars, in terms of x, will it cost per person? Answers.
A) x/6	B) x/16	C) x/40	D) 3x/40	E) 3x/80

Solution: Choose x as a multiple of 16, I chose 64:   So for 10 people, that's 6.4 each and for 16 people it's 4 USD each... Pick one of the options that gives you 6.4 - 4 = 2.4... The answer is 3x/40.
Answer: D
Reb normally drives to work in 45 minutes at an average speed of 40 miles per hour. This week, however, she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20% . If Reb averages between 12 and 16 miles per hour when biking, how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives? Pick one:
A) 135	B) 105	C) 95	D) 75	E) 45

Solution: Reb normally drives to work in 45 minutes at an average speed of 40 miles per hour.   Use formula 75 = RT   Car:   T1: 45 min   R1: 40 mph   751: [(40*45)/60= 
(40*45)/60 = 30
30 miles   Bike:   T1:?   R2: 12 - 16 mph   752: 08*751= 24 miles   T1: [(24*60)/12= 
(24*60)/12 = 120
120 min (Only 12 mph speed yields an answer given in the choices)   Therefore, 75eb has to leave 120 min - 45 min= 75 min early   ANSWER: 75
Answer: D
How many pieces of 0.40 meteres can be cut from a rod 47.5 meteres long Choose the correct choice from the following choices
A) 100
B) 118
C) 120
D) 125
E) 70

Solution: Explanation:   We need so simple divide 47.5/0.40,   =(4750/40) = 118   Option 118
Answer: B
The average age of a class of 20 students is 18 years. The average increased by 2 when the teacher's age also included. What is the age of the teacher?  Choose the correct choice from the following options
A) 40 years
B) 41 years
C) 42 years
D) 43 years
E) 44 years

Solution: If age of the teacher was 18, average would not have changed.   Since average increased by 2,   40 yearsge of the teacher=18+22×1=40   40 yearsNSWER:40 years
Answer: A
If 3x=9y=z, what is x+y, in terms of z?  Choose the correct choice from the following choices.
A) z/2 B) 2z C) z/3 D) 3z/5 E) 4z/9

Solution: 3x=9y=z   x = z/3   and y = z/9   x+y = z/3 + z/9 = 4z/9   Answer is 4z/9
Answer: E
Machine A and machine B are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 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?  Choices: A) 6 B) 6.6 C) 60 D) 100 E) 110

Solution: B takes x hours   6 takes x + 10 hours   rate of 6 = 660/x+10   rate of B = 660/x   thus, 660/x = (660/x+10)*1.10   x = 100   so B = 100   6 = 110 sprockets per hour    660/110= 
 660/110 = 6
6   6NSWER:6
Answer: A
If a book is sold at 8% profit instead of 8% loss, it would have brought Rs 12 more. Find out the cost price of the book Select the correct option:
A) Rs 75
B) Rs 72
C) Rs 60
D) Rs 70
E) Rs 80

Solution: Let C.P. of the book be Rs. ’X’   Given, 1.08 X - 0.92X = 12   => 0.16 X = 12 = 12/0.16= 
12/0.16 = 75
Rs 75   Rs 75NSWER:Rs 75
Answer: A
Two trains 140 m and 170 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?	Choose the correct choice from the following answers
A) 11.16 sec  B) 11.8 sec  C) 27.7 sec  D) 10.8 sec  E) 17.8 sec

Solution: Relative speed = 60 + 40= 
60 + 40 = 100
100 km/hr.= 100 * 5/18 = 250/9 m/sec.   Distance covered in crossing each other = 140 + 170= 
140 + 170 = 310
310 m.   Required time= 310 * 9/250= 
310 * 9/250 = 279/25 = around 11.16
11.16 sec.   11.16 secnswer: 11.16 sec
Answer: A
A and B together can do a work In 2 days. A alone can do it in 12 days. What time B will take to do the work alone?  Select.
A) 2.4 days B) 8 days C) 1.2 days D) 1.0 days E) 5 days

Solution: Explanation:   2.4 days and B 1day's work = 1/2   2.4 days alone can do 1day's work = 1/12   what time B will take to do the work alone?   B = (2.4 days+B) - 2.4 days = (1/2) - (1/12) = 2.4 Days   2.4 daysnswer: Option 2.4 days
Answer: A
In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers preceding it. What is x-y?	Choose the correct choice from the following:
A) 6 B) 3 C) 4 D) 5 E) 7

Solution: lets start from z, as per the question stem   z + 5 + 7 = 16   -->> z= 4   similarly, y + 4 + 5 = 7   --> y = -2   similarly,, x + -2 + 4 = 5   --> x = 3   hence , x-y = 3+2= 
3+2 = 5
5   ANSWER:5
Answer: D
A computer store offers employees a 15% discount off the retail price. If the store purchased a computer from the manufacturer for $500 dollars and marked up the price 15% to the final retail price, how much would an employee save if he purchased the computer at the employee discount (15% off retail price) as opposed to the final retail price.	Choose the correct choice:	A) 52.5	B) 54.5	C) 55.5	D) 57.5	E) 59.5

Solution: Cost price=500   Profit=15% =15% of 500=75   selling price=CP+ Profit   SP=575   a 57.5iscount of 10% to employees means 10% off on 575   so 10% of 575= 57.5   Ans 57.5
Answer: D
A shop owner sells 40mtr of cloth and gains SP of 10 mtrs. Find the gain %?
Pick:
A) 33.33%  B) 40%  C) 50%  D) 66.67%  E) 70%

Solution: Here, selling price of 10 m cloth is obtained as profit.   Profit of 10 m cloth = (S.P. of 40 m cloth) – (C.P. of 40 m cloth)   Selling price of 30 m cloth = Selling Price of 40 m of cloth   Let cost of each metre be Rs. 100.   Therefore, cost price of 30 m cloth = Rs. 3000 and S.P. of 30 m cloth = Rs. Rs. 4000   Profit% = 10/30 × 100 = 33.33%   Profit of 33.33% was made by the merchant.   33.33%
Answer: A
A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Select the correct option:
A) 77
B) 66
C) 20
D) 21
E) 24

Solution: M = 15   S = 5   DS = 15 + 5= 
15 + 5 = 20
20   Answer: 20
Answer: C
Solve the given two equations and find the inequality of X and Y. (a) X^2- 365 = 364 and (b) y- (324) ^(1/2) = (81)^(1/2) Choose the correct choice.
A) If x>y B) If x>=y C) If x<y D) If x<=y E) x=y or relationship cannot be established

Solution: Solution:-   X=4,-5   Y= -4,6   x=y or relationship cannot be established
Answer: E
In a group of 28 junior high school students, 5 take French, 10 take Spanish, and 4 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?	Choose the correct choice.
A) 7  B) 13  C) 9  D) 12  E) 10

Solution: B   13   Add 1 + 10 + 4 to get 15.   Then subtract 21 from the total students ⇒ 28 – 15 = 13.   Answer is 13
Answer: B
A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 15 days before the project is completed, in how many days total will the project be completed? Choose the correct choice from the following choices.
A) 18	B) 21	C) 24	D) 27	E) 30

Solution: A's rate is 1/20 of the project per day.   B's rate is 1/30 of the project per day.   The combined rate is 1/12 of the project per day.   In the last 15 days, B can do 1/2 of the project.   Thus A and B must complete 1/2 of the project, which takes 6 days.   The total number of days is  6 + 15= 
 6 + 15 = 21
21.   The answer is 21.
Answer: B
If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 171 games will be played during the tournament. What is the number of participants?
Select the correct option
A) 15	B) 16	C) 17	D) 18	E) 19

Solution: Let n be the number of participants.   The number of games is nC2 = n*(n-1) / 2 = 171   n*(n-1) = 342 = 19*18 (trial and error)   The answer is 19.
Answer: E
Henry gives a certain amount to his friend at 12% p.a. simple interest. If he wants to get thrice the amount given how many years does it take? Select the correct option:	A) 16 years 8 months	B) 12 years	C) 10 years 7 months 4 days	D) 15 years	E) 20 years

Solution: Solution: simple interest question   B=A[1+ (tr/100)]; where A is principal amount, B final amount, t time in years and r interest rate   after putting the values 12   3= [1+(12t/100)]   t= 50/3 which is (48+2)/3= 16 + 2/3 means 16 years and   (12*2)/3= 
  (12*2)/3 = 8
8 months.   16 years 8 monthsnswer is 16 years 8 months
Answer: A
A good train and a passenger train are running on parallel tracks in the same direction. The driver of the goods train observes that the passenger train coming from behind overtakes and crosses his train completely in 60 sec. Whereas a passenger on the passenger train marks that he crosses the goods train in 40 sec. If the speeds of the trains be in the ratio 1:2. Find the ratio of their lengths.	Choose the correct choice from the following answers.
A) 2:1 B) 3:1 C) 5:2 D) 1:1 E) None of these

Solution: Explanation :   Let, the speeds of the two trains be s and 2s m/s respectively.   Also, suppose that the lengths of the two trains are P and Q metres respectively.   Then,   =>(P+Q)/(2s−s)=60. --------------(1)   And,   =>P/(2s−s)=40. --------------(2)   On dividing (1) by (2), we get :-   =>(P+Q)/P=60/40.   The required ratio is P:Q = 2 : 1.   2:1nswer : 2:1
Answer: A
Tim came second in Math. When his mother asked him how much he had scored, he answered that he got the sum of the first 5 even numbers. His mother immediately worked out the answer. How much had he scored in Math?
Pick:
A) 80 B) 30 C) 40 D) 70 E) 60

Solution: 30   30   Sum = (n x n) + n   Hence, 5 x 5 = 25 + 5= 
25 + 5 = 30
30
Answer: B
In what ratio must water be mixed with milk to gain 16(2/3)% on selling the mixture at cost price?  Choose the correct choice from the following answers:
A) 1 : 6 B) 6 : 1 C) 2 : 3 D) 4 : 3 E) 3 : 2

Solution: Explanation:   Let C.P. of 1 litre milk be Re. 1.   S.P. of 1 litre of mixture = Re.1, Gain =	50/3 %   C.P. of 1 litre of mixture =(100 x	3/350 x 1)=6/7   By the rule of alligation, we have:   Ratio of water and milk =	1/7:6/7=1:6.   1 : 6NSWER IS 1 : 6
Answer: A
What will be the difference between simple interest and compound interest @ 10% per annum on a sum of Rs. 1000 after 3 years?
Choose the most appropriate option:  A) 22  B) 77  C) 26  D) 19  E) 31

Solution: Explanation:   S.I. = Rs. [(1000 x 10 x 3) / 100] = Rs. 300   C.I. = Rs. [1000 x (1 + (10/100))3 - 1000] = Rs. 331   Difference = Rs. (331 - 300) = Rs. 31   ANSW31R:31
Answer: E