MU-NLPC/Calc-aqua_rat huggingface dataset:
P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left? Choose the correct choice from the following answers:	A) 8/15	B) 7/15	C) 6/15	D) 5/15	E) 4/15

Solution: 8/15mount of work P can do in 1 day = 1/15   8/15mount of work Q can do in 1 day = 1/20   8/15mount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60   8/15mount of work P and Q can together do in 4 days = 4 × (7/60) = 7/15   Fraction of work left = 1 – 7/15= 8/15   8/15nswer is 8/15.
Answer: A
Given that x = 2^b – (8^32 + 16^5), which of the following values for b yields the lowest value for |x|?	Choose the correct choice from the following answers
A) 94	B) 95	C) 96	D) 97	E) 116

Solution: 8^32 + 16^5 = 2^96 + 2^20   Compared to 2^96, the value of 2^20 is negligible.   2^96 - (2^96 +2^20) will minimize the value of |x|.   The answer is 96.
Answer: C
In how many ways can the letters of the word "COMPUTER" be arranged?  Choose the correct choice from the following answers: A) 36480 B) 40320 C) 44290 D) 48360 E) 52810

Solution: The total ways of arranging the letters = 8! = 40320   The answer is 40320.
Answer: B
Alex deposited x dollars into a new account that earned 4 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?  Choose the correct choice:
A) w/(1+1.08)
B) w/(1.08+1.16)
C) w/(1.16+1.24)
D) w/(1.04+1.04^2)
E) w/(1.08^2+1.08^2)

Solution: Account at the end of the first year would be 1.04x dollars. At this time x dollars was deposited, hence the account at the beginning of the second year would be (1.04x+x) dollars. Account at the end of the second year would be (1.04x+x)*1.04=w --> x(1.04^2+1.04)=w --> x=w/(1.04+1.04^2).   Answer: w/(1.04+1.04^2).
Answer: D
Two-fifth of one-third of three-seventh of a number is 15. What is 40% of that number?  Choose the correct choice from the following answers.
A) 72 B) 84 C) 136 D) 140 E) None of these

Solution: Explanation:   Let the number be x. Then,   2/5 of 1/3 of 3/7 of   x = 15 => x = (15 * 5/3 * 3 * 5/2) = 525/2   40% of 525/2 = (40/100 * 525/2)= 
(40/100 * 525/2) = 105
105   Answer IS None of these
Answer: E
A certain bacteria colony doubles in size every day for 22 days, a which point it reaches the limit of its habitat and can no longer grow. If two bacteria colonies start growing simultaneously, how many days will it take them to reach the habitat’s limit?  Pick one
A) 6.33
B) 7.5
C) 21
D) 15
E) 19

Solution: Case 1: Consider the bacteria num to be B. As it doubles every day, number of bacteria at the end of each day would be   Day 1 – B   Day 2 – 2B   Day 3 – 4B   Day 4 – 8B   .   .   .   Day 22 – 2^19 B   It can be implied that the capacity of the habitat is 2^19 B.   Case 2: There are 2 bacteria which keep doubling every day. So, the count would be   Day 1 – 2B   Day 2 – 4B   Day 3 – 8B   .   .   .   Day 18 – 2^18 B   Day 19 – 2^19 B --> this is the point where the habitat is filled to its capacity.   Hence, 21 is the answer   21
Answer: C
A toy store sells small, medium, and large toy trucks in each of the colors red, green, and yellow. The store has an equal number of trucks of each possible color-size combination. If Paul wants a medium, red truck and his mother will randomly select one the trucks in the store, what is the probability that the truck she selects will have at least one of the two features Paul wants?
Pick one
A) 1/4  B) 1/3  C) 5/9  D) 7/12  E) 2/3

Solution: Probability of NOT selecting medium out of 3 sizes = 2/3   Probability of NOT selecting red out of 3 colours = 2/3   Total probability of NOT selecting red and medium = (2/3)*(2/3) = 4/9   Required probability = 1 - 4/9 (this will select at least one of red and medium)   = 5/9   The answer is 5/9.
Answer: C
A sales representative receives a salary of $100 per week and earns a commission of 20% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $600?	Choose the correct choice from the following options:
A) $3,000 B) $3,150 C) $4,000 D) $2,500 E) $5,000

Solution: We're told that a sales representative receives a salary of $100 per week and earns a commission of 20% on all sales she makes. We're asked how many dollars’ worth of sales will bring her total weekly income to $600.   Since the salesperson receives a $100 salary, the remaining $500 has to be accounted for by the 20% commission. Since those numbers are rather specific, we're likely dealing with a 'round number' for total sales.   Let's TEST Answer C: $4,000   Since 20% of $1,000 = $200   20% of $4,000 = 4($200) = $800   This is TOO HIGH (it's supposed to be $500), so we need a LOWER total sales figure.   Let's TEST Answer D: $2,500   Since 20% of $1,000 = $200   20% of $2,500 = 2.5($200) = $500   This is an exact MATCH for what we were told, so this MUST be the answer.   Final Answer:   $2,500
Answer: D
Mahesh marks an article 15% above the cost price of Rs. 540. What must be his discount percentage if he sells it at Rs. 496.80? Choose the correct answer
A) 22
B) 27
C) 20
D) 21
E) 12

Solution: CP = Rs. 540, MP = 540 + 15% of 540 = Rs. 621   SP = Rs. 496.80, Discount = 621 - 496.80= 
621 - 496.80 = 124.2
124.20   Discount %= 124.2/621 * 100= 
124.2/621 * 100 = 20
20%.Answer: 20
Answer: C
The perimeter of one face of a cube is 48 cm. Its volume will be: Choose the most appropriate option:
A) 125cm3 B) 400cm3 C) 250cm3 D) 625cm3 E) None of these

Solution: None of thesexplanation:   None of thesedge of cude = 48/4= 
48/4 = 12
12 cm   Volume= a*a*a = 12*12*12= 
12*12*12 = 1_728
1728 cm cube   Option None of these
Answer: E
A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?	Choose the most appropriate option:
A) 17 sec B) 14 sec C) 48 sec D) 87 sec E) 25 sec

Solution: D = 540 + 180= 
540 + 180 = 720
720   S= 54 * 5/18= 
54 * 5/18 = 15
15 mps   T= 720/15= 
720/15 = 48
48 sec   Answer:48 sec
Answer: C
30% of a number is more than 60% of 50 by 30. Find the number?	Choose the correct choice:  A) 120  B) 200  C) 180  D) 300  E) 140

Solution: (30/100) * X –   (60/100) * 50= 
  (60/100) * 50 = 30
30   2/7 X= 60   X = 200   Answer:200
Answer: B
N and B are integers. The expression (N+1)(B+1) is even. What can be said about N and B?
Choose the correct choice
A) They are both even numbers. B) At least one of them is even. C) At least one of them is odd. D) They are both odd. E) Nothing can be said surly on N and B

Solution: Odd x Odd = Odd   Odd x Even = Even   Even x Even = Even   To fulfill condition Either (N+1) or (B+1) needs to be Even   So either N or B needs to be odd   Or At least one of them is odd.   At least one of them is odd=At least one of them is odd.
Answer: C
15 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men? Choose the most appropriate option.
A) 32 B) 87 C) 30 D) 99 E) 77

Solution: 3W = 2M   15M ------ 21 * 8 hours   21 W ------ x * 6 hours   14 M ------ x * 6   15 * 21 * 8 = 14 * x * 6   x = 30   Answer: 30
Answer: C
If log4X + log4(1/6) = 1/2 then the value of X is?  Select the correct option
A) 18
B) 24
C) 16
D) 12
E) 10

Solution: log4X +log4(1/6) = 1/2   => log4[X x 1/6] = 1/2   =>log4 [X/6] = 1/2   => 41/2 = X/6   => 2 = X/6   Therefore, X = 12   ANSWER:12
Answer: D
Sum of the squares of 3 no.'s is 138 and the sum of their products taken two at a time is 131. Find the sum?	Choose the most appropriate option.
A) 20 B) 24 C) 26 D) 28 E) 30

Solution: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131   a + b + c = √400 = 20   20
Answer: A
A certain manufacturer of cake, muffin, and bread mixes has 120 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix? Pick
A) a. 1/10
B) b. 3/10
C) c. 1/4
D) d. 7/10
E) e. 9/10

Solution: C+M+B-CM-MB-CB-2CMB = 120   C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.   the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.   50 + 40 + B-CB-MB-20-2CMB = 120   B-CB-MB-2CMB = 30   hence the probability = 30/120 = 1/4.   c. 1/4
Answer: C
Jason's team scored 60 points in a game basketball and he accounted for 60 percent of their points. How much did he score?  Choose the most appropriate option
A) 42	B) 38	C) 36	D) 44	E) 40

Solution: 600/10 x (6/10) = 3600/100 or 36   Answer is 36
Answer: C
It is well known that a triangle’s area is √(p(p-a)(p-b)(p-c)),
when p=(a+b+c)/2, such that a, b, c are the lengths of sides of the triangle. If the triangle has 360, 300, and 360 as the side’s lengths, what is the triangle’s area?  Answers.
A) 34,200  B) 36,200  C) 38,200  D) 49,089  E) 43,200

Solution: It is well known that a triangle’s area is √(p(p-a)(p-b)(p-c)),   when p=(a+b+c)/2,   -> P=(360+300+360)/2= 
(360+300+360)/2 = 510
510, area=√(510(510-360)(510-300)(510-360))=49,089. Therefore, the answer is 49,089.
Answer: D
If E and F are non-zero integers, and E/F > 1, then which of the following must be true?  Choose the correct answer.
A) E > F	B) EF>F	C) E^2< F^2	D) 2E< F	E) E^3 < F^3

Solution: EF>F
Answer: B
A rectangular field is to be fenced on three sides leaving a side of 10 feet uncovered.If the area of the field is 600 sq.ft, how many feet of fencing will be required ?
Select
A) 130feet
B) 22feet
C) 20feet
D) 15feet
E) 10feet

Solution: Explanation:   We are given with length and area, so we can find the breadth.   as Length * Breadth = 130feetrea   => 10 * Breadth = 600   => Breadth = 60 feet   130feetrea to be fenced = 2B + L = 2*60 + 10= 
2*60 + 10 = 130
130 feet   130feetnswer: Option 130feet
Answer: A
4 dice are thrown simultaneously on the board. Find the probability show the same face.	Choose the correct choice from the following answers:
A) 1/213
B) 1/215
C) 1/216
D) 2/113
E) 3/114

Solution: The total number of elementary events associated to the random experiments of throwing four dice simultaneously is:   =6×6×6×6=64=6×6×6×6=64   n(S)=64n(S)=64   Let XX be the event that all dice show the same face.   X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}   n(X)=6n(X)=6   Hence required probability,   =n(X)n(S)=664=n(X)n(S)=664   =1/216   1/216
Answer: C
In measuring the sides of a rectangle, one side is taken 5% in excess, and the other 4% in deficit. Find the error percent in the area calculated from these measurements.  Choose the correct choice from the following answers:
A) 0.2%
B) 0.4%
C) 0.6%
D) 0.8%
E) 1%

Solution: Let x and y be the sides of the rectangle. Then, Correct area = xy.   Calculated area = (105/100)*x * (96/100)*y = (504/500 )(xy)   Error In measurement = (504/500)xy- xy= (4/500)xy   Error % = [(4/500)xy*(1/xy) *100] % = (4/5)= 
(4/5) = 4/5 = around 0.8
0.8%.   ANSWER 0.8% 0.8%
Answer: D
x is the 9 digit largest number(digits are 1 to 9 with out repeat) which is divisible by 11 and y second largest number which also divisible by 11 then difference between x and y is?  Choose the correct choice from the following: A) 160 B) 170 C) 188 D) 198 E) 208

Solution: "sum of digit at even place and sum of digit at odd places must be adjusted such that their difference is 0 or divisible by 11.   we have 9 digit without repetition,   so sum of digit from 1 to 9 =45   Let sum of digit at odd place will be 'w' and sum of even place will be 'Z'.   W + Z= 45   W - Z = 11   2W = 56   So W = 28 and Z = 17   now the digits at odd place are 2, 4, 6, 7, 9   sum of digit at odd place is   2+4+6+7+9= 
  2+4+6+7+9 = 28
28   the digits at even place are 1,3,5,8   sum of digits at even place is  1+3+5+8= 
 1+3+5+8 = 17
17   so the largest no will be find by put no. of odd and even places in increasing order accordingly   1st lasrgest no is 987563412   and 2nd largest no is 987563214   diference between them   X-Y=198   ANSWER:198
Answer: D
A and B together can do a piece of work in 4 days. If A alone can do the same work in 20 days, then B alone can do the same work in?
Pick one:
A) 0.35 days  B) 0.45 days  C) 0.55 days  D) 0.25 days  E) 0.2 days

Solution: B = 1/4 – 1/20 =0.2 days   ANSW0.2 daysR:0.2 days
Answer: E
If K is the sum of reciprocals of the consecutive integers from 13 to 18, inclusive, then K is closest in value to which of the following?
Choose the correct answer:
A) 1/12
B) 1/3
C) 1/7
D) 1/6
E) 1/4

Solution: 1/13 , 1/14 , 1/15 , 1/16 , 1/17 , 1/18   Hypothetically , assume all 6 Numbers to be 1/13   Hence sum of it would result in = 6/13 ( almost equals 1/2 , or slightly less than 1/2 - )   If all 6 nos were to be 1/8 ... Sum of which would result in 6/18 = 1/3 .   Hence answer should lie between 1/2 and 1/3   ------------ 1/2 ------------1/3 .   The only option that satisfies this criteria is option 1/3 i.e 1/3
Answer: B
A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train?  Choices:
A) 287
B) 23
C) 72
D) 27
E) 26

Solution: Length = Speed * time   Speed = L/T   S = 400/20= 
400/20 = 20
20 M/Sec   Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)   Speed = 72 Kmph   Answer:72
Answer: C
Pradeep has to obtain 35% of the total marks to pass. He got 185 marks and failed by 25 marks. The maximum marks are
Pick:
A) 300 B) 600 C) 800 D) 1000 E) 900

Solution: Explanation :   Let their maximum marks be x.   Then, 35% of x = 185 + 25   =>35/100x= 210   x = (210100/35)   x= 600.   Answer : 600
Answer: B
20 women can do a work in 9 days. After they have worked for 6 days. 6 more men join them. How many days will they take to complete the remaining work?
Select:  A) 4:3  B) 4:8  C) 4:5  D) 4:1  E) 4:4

Solution: (20 * 16) women can complete the work in 1 day.   1 woman's 1 day work = 1/320   (16 * 15) men can complete the work in 1 day   1 man's 1 day work = 1/240   So, required ratio = 1/240 : 1/320 = 4:3.   4:3nswer: 4:3
Answer: A
The average weight of a class is x pounds. When a new student weighing 70 pounds joins the class, the average decreases by 1 pound. In a few months the student’s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds. None of the other students’ weights changed. What is the value of x?  Choose the correct choice from the following options:
A) 26 B) 86 C) 88 D) 90 E) 92

Solution: When the student weighs 80 pounds the average weight is x - 1 pounds;   When the student weighs 110 pounds the average weight is x + 4 pounds.   So, the increase in total weight of 110 - 70= 
110 - 70 = 40
40 pounds corresponds to the increase in average weight of (x + 4) - (x - 1) =5 pounds, which means that there are 40/5 (  + 4) - (  - 1)= 
(  + 4) - (  - 1) = 5
5 pounds, which means that there are  40/5= 
 40/5 = 8
8 students (including the new one). So, initially there were 5 student.   Total weight= 5x + 70 = 8(x-1) --> x = 26 pounds.   26nswer: 26.
Answer: A
Buses A and B start from a common bus stop X. Bus A begins to travel in a straight line away from bus B at a constant rate of 20 miles per hour. One hour later, bus B begins to travel in a straight line in the exact opposite direction at a constant rate of 80 miles per hour. If both buses travel indefinitely, what is the positive difference, in minutes, between the amount of time it takes bus B to cover the exact distance that bus A has covered and the amount of time it takes bus B to cover twice the distance that bus A has covered?
Choose the correct choice from the following answers:
A) 36
B) 72
C) 132
D) 144
E) 180

Solution: 1st part: - In 1hr, Bus A covers 30 miles.   Relative speed of bus ABus B is   (80-30)= 
  (80-30) = 50
50mph.   So time required for Bus B to cover the exact distance as A is   50*t= 30   t=3/5 = 36min   2nd part   80*t=2d - B has to cover twice the distance   30*(t+1) = d - A traveled 1hr more and has to travel only only d   so   d/30 - 2d/80 = 1   D=120   T= 3hrs = 180 min   Question asks for +ve difference between part 1 and part 2 in minutes   = 180-36 = 132min   132
Answer: C
John can complete a given task in 18 days. Jane will take only 12 days to complete the same task. John and Jane set out to complete the task by beginning to work together. However, Jane was indisposed 6 days before the work got over. In how many days did the work get over from the time John and Jane started to work on it together?
Choose one
A) 11 B) 34/5 C) 44/5 D) 54/5 E) 12

Solution: In such questions, you need to start from the end. Last 4 days John works alone and completes 6 * (1/18) = 1/3 of the work.   So 2/3 of the work should have been completed by the two of them together before Jane left.   Their combined rate of work is 1/18 + 1/12 = 5/36   Time taken to complete 2/3 of the work = (2/3)/(5/36) = 24/5 days.   So total number of days taken to complete the work =24/5 + 6 = 54/5 days.   54/5
Answer: D
A rower can row upstream at 15 kph and downstream at 30 kph. What is the speed of the rower in still water?	Choose the correct choice from the following answers
A) 20.9 B) 21.3 C) 21.7 D) 22.1 E) 22.5

Solution: Let V be the rower's speed in still water.   Let S be the speed of the current in the stream   V-S = 15   V+S = 30   When we add the two equations, we get: 2V = 45   Then V = 22.5 kph.   The answer is 22.5.
Answer: E
A man counted his animals, 80 heads and 230 legs (ducks and goats). how many goats are there?  Answers:
A) 30
B) 40
C) 50
D) 60
E) 70

Solution: let no of ducks=d and no of goat=g   d+g=80(heads)----------> eq 1   each duck has 2 legs and goat has 4 legs   2d+4g=230 and divide 2d+4g=230 by 2 we get d+2g=115 -----------> eq2   subtract eq1 from eq2   we get no of goats=30   30NSWER:30
Answer: A
In how many ways, a committee of 5 members can be selected from 5 men and 5 ladies, consisting of 3 men and 2 ladies?	Choose the correct option.
A) 75 B) 152 C) 100 D) 200 E) 212

Solution: (3 men out 5) and (2 ladies out of 5) are to be chosen   Required number of ways = (51003 * 51002) = 100   Answer is 100
Answer: C
if a no. is divided by 342 then remainder is 47.then if that no. is divided by 18 then what will be the remainder?  Choose the correct choice from the following choices.
A) 11 B) 12 C) 13 D) 14 E) 15

Solution: let quotient be k if that no. is divided by 342 and remainder 47.   that no.= 342k+47 = (18*19k)+(18*2)+11   =18*(19k+2)+11   so remainder when divided by 18=11   answer 11
Answer: A
P is three times as fast as Q and working together, they can complete a work in 19 days. In how many days can Q alone complete the work?	Select the correct option.
A) 16 1/4 days B) 27 1/4 days C) 25 1/4 days D) 14 days E) 10 days

Solution: P = 3Q   P + Q = 3Q + Q = 4Q   These 4Q people can do the work in 19 days, which means Q can do the work in 76 days.   Hence, P can do the work in 25 1/4 days.   Answer:25 1/4 days
Answer: C
Pipe A can fill a tank in 5 hours. Due to a leak at the bottom, it takes 10 hours for the pipe A to fill the tank. In what time can the leak alone empty the full tank?  Choose the correct choice
A) 67 B) 10 C) 18 D) 26 E) 12

Solution: Let the leak can empty the full tank in x hours 1/5 - 1/x = 1/10   => 1/x = 1/5 - 1/10 = 1/10   => x = 10. Answer:10
Answer: B
A and B walk around a circular track. A and B walk at a speed of 4 rounds per hour and 4 rounds per hour respectively. If they start at 6 a.m. from the same point in opposite directions, how many times shall they cross each other before 7.00 a.m.?
Choose one.
A) 6  B) 5  C) 4  D) 8  E) 10

Solution: Relative speed = Speed of A + Speed of B (âˆ´ they walk in opposite directions)   = 4 + 4= 
4 + 4 = 8
8 rounds per hour=> They cross each other 8 times in 1 hour.   Time duration from 6.00 am to 7.00 am = 1 HOUR   Hence they cross each other 8 times before 7.00 am   Answer : 8
Answer: D
James is stacking piles of bricks. He has 2 in the first row and then one more in each row after that. If there are 20 rows all together, how many bricks are in the pile?  Select the correct option
A) 22 B) 243 C) 255 D) 242 E) 2200

Solution: =2 + 3 + 4 + ... + 22   =1 + 2 +... + 22 - 1   =(22)(23)/2 - 1   =(11)(23)-1   =243 - 1= 
243 - 1 = 242
242   Option 242
Answer: D
A multiple choice test consists of 4 questions, and each question has 5 answer choices. In how many W ways can the test be completed if every question is unanswered?	Choose the correct option.
A) 24
B) 120
C) 625
D) 720
E) 1024

Solution: 5 choices for each of the 4 questions, thus total W of 5*5*5*5 = 5^4 = 625 ways to answer all of them.   Answer: 625.
Answer: C
The average age of a husband and a wife is 23 years when they were married FOUR years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?	Choose the most appropriate option.
A) 7 years	B) 9 years	C) 6 years	D) 4 years	E) 5 years

Solution: 27 * 2= 
27 * 2 = 54
54   20 * 3= 
20 * 3 = 60
60   -----------   6 years   Answer: 6 years
Answer: C
Amy's sells kale at x dollar per pound for the first 25 pounds and .8x for every subsequent pound. Lucia's price is x per pound for the first 14 pounds and .9x for subsequent pounds. What is the minimum number of pounds over 15 for which Amy's becomes an equal or better deal?
Choose the correct choice from the following answers:
A) 24
B) 25
C) 36
D) 27
E) 28

Solution: For Amy's deal to be better, the cost has to be less or equal to Lucia's   Assuming 'n' is the number of pounds of kale, the equation is   25x + (n-25) (0.8x) <= 14x + (n-14)(0.9x)   Resolve it:   ==> 25x + 0.8nx - 20x <= 14x + 0.9nx - 12.6x   ==> 3.6x <=0.1nx   ==> 36x < =nx   ==> x (n-36) > = 0   as x cannot be 0,   ==> n - 36 >=0   ==> n > = 36   so the minimum value is 36   '36' would be the correct answer
Answer: C
4 brothers and 3 sisters is to be arranged in a row for a photograph. In how many ways can they be seated if all the sisters sit together?
Pick
A) 520 ways
B) 820 ways
C) 620 ways
D) 720 ways
E) 420 ways

Solution: Since all the sister sit together we can consider them as a single unit. this together and 4 brothers can be arranged in 5x4x3x2x1 ways. The three sisters themselves can be arranged in 3x2x1 ways. The total number arrangements required = 5x4x3x2x3x2 ways =720 Answer : 720 ways
Answer: D
The ratio of present ages of X and Y is 4:5. Which of the following cant be the ratio of ages of X and Y, 20 years ago? Choices: A) 2:4 B) 9:10 C) 2:3 D) 3:5 E) 3:6

Solution: 9:10   as ratio of X:Y can not be more than 4:5 earlier.   ANSWER:9:10
Answer: B
What is the greatest integer m for which the number 50!/14^m is an integer?  Choose the correct option:
A) 11  B) 10  C) 9  D) 8  E) 7

Solution: 14^m = 2^m*7^m.   Let's figure out how many 7's are in the prime factorization of 50!   The multiples of 7 are: 7, 14, 21, 28, 35, 42, 7*7.   Thus 7^8 will divide 50! but 7^9 will not.   Clearly 2^8 will divide 50!   So m=8 is the largest possible integer.   The answer is 8.
Answer: D
How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?  Choose the correct choice from the following answers
A) 22  B) 30  C) 88  D) 29  E) 26

Solution: Speed of train relative to man = 63 - 3= 
63 - 3 = 60
60 km/hr.= 60 * 5/18 = 50/3 m/sec.   Time taken to pass the man = 500 * 3/50= 
500 * 3/50 = 30
30 sec.   Answer: 30
Answer: B
The expression (11.98 x 11.98 + 11.98 x x + 0.02 x 0.02) will be a perfect square for x equal to:	Pick
A) 0.04  B) 0.004  C) 0.4  D) 0.0004  E) None of them

Solution: Given expression = (11.98)(power 2) + (0.02)(power 2) + 11.98 x x.   For the given expression to be a perfect square, we must have   11.98 x (x) = 2 x 11.98 x 0.02 or   x = 0.04   0.04nswer is 0.04
Answer: A