MU-NLPC/Calc-aqua_rat huggingface dataset:
How many different arrangements of A, B, C, D, and E are possible where A is adjacent to neither B nor D? Choose the correct choice.
A) 96	B) 60	C) 48	D) 36	E) 17

Solution: Total # of permutation of 5 distinct letters will be 5!=120;   Glue A and B together, consider it to be one unit: {AB}{C}{D}{E} --> # of permutation of these 4 units will be 4!=24, A and B within its unit also can be arranged in 2 ways : {AB} or {BA}, so total # of ways to arrange A, B, C, D, and E so that A and B to be together will be 4!*2=48;   The same for A and D: total # of ways to arrange A, B, C, D, and E so that A and D to be together will be 4!*2=48;   Now, the above   48+48= 
  48+48 = 96
96 cases will contain the arrangements when A is adjacent to both B and D, so we should subtract this cases to get rid of the double counting. The # of case when A is adjacent to both B and D will be: consider {BAD} {C}{E} --> # of permutation of these 3 units will be 3!, {BAD} also can be arranged in 2 ways: {BAD} or {DAB}, so total # of ways to arrange A, B, C, D, and E so that A is adjacent to both B and D will be 3!*2=12;   The # of arrangements when A is adjacent to neither B nor D will be total-(48+48-12)=120-84= 
120-84 = 36
36.   Answer: 36.
Answer: D
A boy asked a girl her name she replied your name is behind your scooty Behind the scooty is written 7.3 3.3 9.3 2.3 What is her name	Select the correct option:
A) RIAE B) RIAF C) RIAG D) RIBF E) SIAF

Solution: 7.3=21=r   3.3 =9=i   9.3=27%26=1=a   2.3=6=f   ANSWER=RIAF   ANSWER:RIAF
Answer: B
A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?	Select:	A) 79.7	B) 79.9	C) 79.5	D) 79.2	E) 79.1

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 8 => x = 8y   (x + 264)/20 = y   y = 22   Speed = 22 m/sec = 22 * 18/5= 
22 * 18/5 = 396/5 = around 79.2
79.2 km/hr.   Answer: 79.2
Answer: D
A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the direction opposite to that in which the train is going ?
Choose the correct choice from the following:
A) 3.6sec
B) 18sec
C) 36sec
D) 72sec
E) None

Solution: Solution   Speed of train relative to jogger =(45-9)km/hr =36km/hr   (36*5/18)m/sec = 10 m/sec   Distance to be covered = (240 +120)= 
(240 +120) = 360
360m   ∴ Time taken=(360/10)= 
(360/10) = 36
36 sec   Answer 36sec
Answer: C
In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed? Choose the correct choice from the following choices:
A) 83.33%	B) 83.93%	C) 83.73%	D) 83.23%	E) 83.33%

Solution: Percentage of milk in the mixture formed = [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100% = 5/6 * 100% = 83.33%.Answer83.33%
Answer: E
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 24 hrs and a machine of type S does the same job in 12 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
Choose the correct choice from the following.
A) 3 B) 4 C) 6 D) 8 E) 12

Solution: Type R completes 1/24 of the job each hour.   Type S completes 1/12 of the job each hour.   Together R and S complete 1/24 +1/12 = 1/8 of the job each hour.   Let n be the number of each type of machine.   2*n*(1/8) = 1 job completed   n = 4   The answer is 4.
Answer: B
How many ways are there to split a group of 10 students into two groups of 5 students each? (The order of the groups does not matter)  Choices.
A) 104  B) 126  C) 148  D) 172  E) 216

Solution: 10C5 = 252   If we consider these groups, each group will be counted twice.   The number of ways to choose 2 groups of 5 is  252/2= 
 252/2 = 126
126   The answer is 126.
Answer: B
In how many different number of ways 5 boys and 2 girls can sit on a shopa which can accommodate 5 persons?
Options.
A) 1802  B) 2500  C) 2000  D) 2100  E) None

Solution: Option 'None'   7p5 = 7 × 6 × 5 x 4 x 3= 2520
Answer: E
In a graduating class, 40 percent of the students are male. In this class, 40 percent of the male students and 30 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?  Choose the correct answer
A) 0.66  B) 0.72  C) 0.78  D) 0.84  E) 0.9

Solution: Let x be the total number of students.   The number students who are younger than 25 is 0.6*0.4x+0.7*0.6x = 0.66x   The answer is 0.66. 0.6*0.4 +0.7*0.6= 
 0.6*0.4 +0.7*0.6 = 0.66
0.66x   The answer is 0.66.
Answer: A
The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?  Options.
A) 5M  B) 4M  C) 9M  D) 2M  E) 6M

Solution: Explanation:   Let the sides of the rectangle be l and b respectively.   From the given data,   (√l2 + b2) = (1 + 108 1/3 %)lb   => l2 + b2 = (1 + 325/3 * 1/100)lb   = (1 + 13/12)lb   = 25/12 lb   => (l2 + b2)/lb = 25/12   12(l2 + b2) = 25lb   Adding 24lb on both sides   12l2 + 12b2 + 24lb = 49lb   12(l2 + b2 + 2lb) = 49lb   but 2(l + b) = 28 => l + b = 14   12(l + b)2 = 49lb   => 12(14)2 = 49lb   => lb = 48   Since l + b = 14, l = 8 and b = 6   l - b = 8 - 6= 
8 - 6 = 2
2m.   Answer: Option 2M
Answer: D
How many seconds will a 400 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? Select
A) 26 sec B) 30 sec C) 24 sec D) 19 sec E) 11 sec

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 = 400 * 3/50= 
400 * 3/50 = 24
24 sec.   Answer:24 sec
Answer: C
In 2008, the profits of Company N were 8 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
Choose the correct choice from the following choices
A) 150% B) 105% C) 120% D) 124.2% E) 138%

Solution: the profit 0f 2009 interms of 2008 = 0.8*15/8*100= 
0.8*15/8*100 = 150
150%   150%
Answer: A
A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
Pick: A) 298 m B) 178 m C) 197 m D) 150 m E) 167 m

Solution: Speed = 60 * 5/18 = 50/3 m/sec   Length of the train = speed * time   = 50/3 * 9= 
50/3 * 9 = 150
150 m   Answer:150 m
Answer: D
How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?  Choose the correct choice from the following answers:
A) 254
B) 100
C) 132
D) 503
E) 50

Solution: 1 million distinct 3 digit initials are needed.   Let the number of required alphabets in the language be ‘n’.   Therefore, using ‘n’ alphabets we can form n * n * n = n^3 distinct 3 digit initials.   Note distinct initials is different from initials where the digits are different.   For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.   This n^3 different initials = 1 million   i.e. n^3 = 106 (1 million = 106)   => n^3 = (102)^3 => n = 102 = 100   Hence, the language needs to have a minimum of 100 alphabets to achieve the objective.   Ans:100
Answer: B
The sum of the present age of Henry and Jill is 43. What is their present ages if 5 years ago Henry was twice the age of Jill? Choose the correct choice from the following answers.
A) and 27	B) and 24	C) and 22	D) and 29	E) of these

Solution: Let the age of Jill 5 years ago be x, age of Henry be 2x   x+5 + 2x+5 = 43   x = 11   Present ages will be 16 and 27   and 27nswer : and 27
Answer: A
Diana can buy watches at a price of M dollars per watch, which she marks up by a certain percentage before selling. If she makes a total profit of T by selling N watches, then in terms of M and T and N, what is the percent of the markup from her buy price to her sell price?
Choose the correct option.
A) 100-N/T	B) NMT/100	C) N-M/100T	D) 100T/(NM)	E) NM/100T

Solution: Algebraic Solution:If she makes a total profit of T for N watches, then that must be a profit of T/N for each watch. That must be the markup above cost on each watch, the amount of the increase. Well, percent increase = (amount of increase)/(starting amount) x 100% = (T/N)/M *100 = 100T/(NM)   Answer : 100T/(NM)
Answer: D
The ratio of the arithmetic mean of two numbers to one of the numbers is 4:6. What is the ratio of the smaller number to the larger number?
Select:  A) 1:5  B) 1:4  C) 1:3  D) 1:2  E) 2:3

Solution: For two numbers, the arithmetic mean is the middle of the two numbers.   The ratio of the mean to the larger number is 4:6, thus the smaller number must have a ratio of 2.   The ratio of the smaller number to the larger number is 2:6 = 1:3.   The answer is 1:3.
Answer: C
If a student loses 5 kilograms, he will weigh twice as much as his sister. Together they now weigh 110 kilograms. What is the student's present weight in kilograms? Choose the correct choice from the following options:
A) 71
B) 72
C) 73
D) 74
E) 75

Solution: Let x be the weight of the sister.   Then the student's weight is 2x+5.   x + (2x+5) = 110   3x = 105   x = 35 kg   Then the student's weight is 75 kg.   The answer is 75.
Answer: E
The Simple Interest on Rs. 7300 from 11 May, 1987 to 10 September 1987 ( Both day Include ) at 5% per annum is :
Pick
A) 120	B) 123	C) 125	D) 128	E) 130

Solution: Time from 11 May to 10 September, 1987   =21+30+31+31+10= 
21+30+31+31+10 = 123
123 days   Time : 123 days= 123/365 year   S.I =(7300x123x5)/(365x100)=Rs.123   answer :123
Answer: B
The average age of an adult class is 40years. 10new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was theoriginal strength of class? Choose the correct choice from the following choices:
A) 10	B) 12	C) 15	D) 17	E) 18

Solution: Let original strength = y   Then , 40y + 10 x 32 = ( y + 10) x 36   â‡’ 40y + 320 = 36y + 360   â‡’ 4y = 40   âˆ´ y = 10   10
Answer: A
The length of minute hand of a clock is 5.2 cm. What is the area covered by this in 10 minutes  Options.
A) 15.27  B) 14.15  C) 17.27  D) 18.27  E) 19.27

Solution: area of circle is pi*r^2   but in 10 minutes area covered is  (10/60)*360= 
 (10/60)*360 = 60
60 degree   so formula is pi*r^2*(angle/360)=3.14*(5.2^2)*(60/360)=14.15 cm^2   ANSWER:14.15
Answer: B
A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?	Choose the most appropriate option:	A) 22	B) 37	C) 30	D) 27	E) 18

Solution: US = 25   DS = 35   M = (35 + 25)/2= 
(35 + 25)/2 = 30
30   Answer:30
Answer: C
Excluding stoppages,the speed of the bus is 54kmph and
including stoppages,it is 45kmph.for how many min does the bus
stop per hr	Pick
A) 12 min
B) 11 min
C) 13 min
D) 19 min
E) 17 min

Solution: Due to stoppages,it covers 9km less.   time taken to cover 9 km is [  9/54 *60= 
  9/54 *60 = 10
10min   Answer is 17 min.
Answer: E
if a@b = a * b^(1/3) then 2@8 = ?
self made Choose one
A) 2	B) 6	C) 3	D) 8	E) 4

Solution: a@b = a * b^(1/3)   2@9 = 2*8^(1/3) = 2*2= 
2*2 = 4
4   Correct Option: 4
Answer: E
Sundar and Raju together can do a piece of work in 8 days. If Sundar alone can do the same work in 12 days, then Raju alone can do the same work in? Answers.
A) 20 days B) 22 days C) 24 days D) 26 days E) 28 days

Solution: Raju work = 1/8 - 1/2 = 1/24 => 24 days   ANSWER 24 days
Answer: C
Jamal had a bag of marbles. He had 12 yellow, 10 blue, 5 green and 1 black marbles. He decided to randomly select a ball from the bag. What is the proabilitly that he will draw a black marble?
Choose the correct choice.
A) 10/28	B) 1/28	C) 12/28	D) 28/1	E) 582/695

Solution: 1/28
Answer: B
Jake can dig a well in 16 days. Paul can dig the same well in 24 days. Jake, Paul and Hari together dig the well in 8 days. Hari alone can dig the well in	Choose the correct choice from the following options.
A) 96 days
B) 48 days
C) 32 days
D) 24 days
E) 28 days

Solution: jake 1 day work=1/16   paul 1 day work=1/24   j+p+h 1 ady work=1/8   1/16+1/24+1/x + +  1= 
 + +  1 = 1
1/8   1/16+1/24+1/x=1/8   1/x=1/48   x=48   so,Hari alone can dig the well in 48 days   ANSWER:48 days
Answer: B
What is the 32nd word of "WAITING" in a dictionary?
Choose the correct choice:
A) AIWTNG	B) AGNTWI	C) AIGNWT	D) AGNTIWI	E) None of these

Solution: Explanation :   Arranging the words of waiting in Alphabetical Order : A,G,I,I,N,T,W Start with A_ _ _ _ _ _ This can be arranged in 6!/2! ways=720/2= 
720/2 = 360
360 ways so can't be arranged starting with A alone as it is asking for 32nd word so it is out of range AG_ _ _ _ _then the remaining letters can be arranged in 5!/2! ways so,120/2=60 ways. Out of range as it has to be within 32 words. AGI_ _ _ _ Now the remaining letters can be arranged in 4! ways =24 AGN _ _ _ _ can be arranged in 4!/2! ways or 12 ways so,24+12 =36th word so out of range. So we should not consider all the words start with AGN now AGNI_ _ _can be arranged in 3! ways =6 ways so 24+6= 
24+6 = 30
30 within range Now only two word left so, arrange in alphabetical order. AGNTIIW - 31st word AGNTIWI - 32nd word   Answer : AGNTIWI
Answer: D
A tradesman by means of his false balance defrauds to the extent of 32%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?  Choose the correct answer
A) 74.5%	B) 74.24%	C) 84.6%	D) 24.89%	E) 45%

Solution: g% = 32 + 32 + (32*32)/100= 
32 + 32 + (32*32)/100 = 1_856/25 = around 74.24
74.24%   Answer: 74.24%
Answer: B
Four of the following five parts numbered (a), (b), (c), (d) and (e) in the following equation are exactly equal. Which of the parts is not equal to the other four? The number of that part is the answer.
Choose one.
A) xy2 – x2y + 2x2y2 B) xy2(1 – 2x) + x2y(2y – 1) C) xy2(1 + x) – x2y(1 – y) D) xy[y(1 + x) – x(1 – y)] E) xy(y – x + 2xy)

Solution: The other parts are equal to xy2 – x2y + 2x2y2.   Answer xy2(1 – 2x) + x2y(2y – 1)
Answer: B
The area of square ABCD above is 24. The shaded region is the intersection of the square and a circular region centered at C. What is the area of the shaded region?  Choose the correct choice from the following answers
A) 18−9/4∗π B) 24−9/2∗π C) 19+9/4∗π D) 24−6∗π E) 9/2−9/4∗π

Solution: =Square - Quarter circle   =24- pi*24/4   =24- pi*6   ANSWER:24−6∗π
Answer: D
If an integer n is to be chosen at random from the integers 1 to 92, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?  Choose the correct choice from the following answers.
A) 1/4 B) 3/8 C) 1/2 D) 29/46 E) 3/4

Solution: n(n+1)(n+2) will be divisible by 8 when n is a multiple of 2 or when (n+1) is a multiple of 8.   Thus when n is even, this whole expression will be divisible by 8.   from 1 to 96, there are 46 even integers.   Now when (n+1) is multiple by 8, we have 12 such values for (n+1)   probability that n(n+1)(n+2) will be divisible by 8   = (46 + 12)/92   = 58/96   = 29/46   Ans is 29/46
Answer: D
Donovan and Michael are racing around a circular 400-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 36 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time?
Pick one:	A) 8	B) 7	C) 6	D) 5	E) 9

Solution: One way of approaching this question is by Relative speed method   1. Speed/ Rate of Donovan = Distance/ time => 400/45 =>80/9   2. Speed/ Rate of Michael = Distance/ time => 400/36 => 100/9   Relative Speed between them = 100/9 - 80/9 => 20/9 (We subtract the Rates if moving in the same direction and add the rates if moving in the opposite direction)   In order to pass Donovan-   Distance to be covered = 400, Relative Rate = 20/9   Total Time taken by Micheal to surpass Donovan = Distance / rate => 400*9/20 => 3600/10 => 180   No. of laps taken by Michael = Total time / Michael's rate => 180/36= 
180/36 = 5
> 5   Hence correct answer is 5 Laps.   5
Answer: D
If x/(9p) is an even prime number, where x is a positive integer and p is a prime number, what is the least value of x?  Choose the correct answer
A) 22  B) 33  C) 44  D) 66  E) 99

Solution: x/(11p) = even prime number   x = even prime number * 11p   Least value of x = Lowest even prime number * 11 * Lowest value of p   = 2 * 11* 2= 
2 * 11* 2 = 44
44   Answer 44
Answer: C
If a number between 0 and 1/2 is selected at random, which of the following will the number most likely be between Answers
A) 0 and 3/20  B) 3/20 and 1/5  C) 1/5 and 1/4  D) 1/4 and 3/10  E) 3/13 and 1/2

Solution: E. 3/13 and 1/2   Definitely not. I am always happy to explain a given question or issue if I can. However, I sometime donot put my explanation if I am answering first because I want to put others first for their explanation.   Now you have excellent explanantion byscthakur. In fact the question is asking the likelyness of or high chances/probability of having a given number. Hope you already got it.3/13 and 1/2
Answer: E
A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.	Choose the correct choice from the following options.
A) 4
B) 5
C) 6
D) 7
E) 8

Solution: Speed downstream = (13 + 4) km/hr = 17 km/hr.   Time taken to travel 68 km downstream =	68/17= 
68/17 = 4
4 hrs.   4nswer: Option 4
Answer: A
Find the sum of prime numbers lying between 58 and 74? Choose the correct choice from the following.
A) 198
B) 201
C) 252
D) 331
E) None

Solution: Solution   Required sum	= 59 + 61 + 67 + 71 + 73)   = 331.   Answer 331
Answer: D
45 liters of mixture is created by mixing Liquid A and Liquid B in the ratio 3:2. How much more Liquid B must be added to make the ratio 9:11?
Choose the correct choice:	A) 9 Litres	B) 10 Litres	C) 12 Litres	D) 15 Lt	E) 16 Litres

Solution: In current ratio A = (3/5) * 45= 
(3/5) * 45 = 27
27   B is 18   Suppose "b" amount of b is added   new ratio= 27/(b+18) = 9/11   => b+18 = 33   => b = 15   So, answer will be 15 Lt
Answer: D
During a recent track meet, Peter ran x meters of the 100 meter dash in 7 seconds; running at the same rate, how many seconds will it take Peter to run z meters of the 200 meter dash?	Choose the correct choice from the following answers.
A) 7x/z B) 7zx C) 7z/x D) 7/xz E) xz/7

Solution: Speed of Peter = x/7 meters per second   Time needed to run z meters = DISTAN7z/xE/SPEED = z / (x/7) =7z/x   Option 7z/x   The values 100m and 200m have no role to play here and are just given to confuse you.
Answer: C
How many seconds will a train 250 meters long take to cross a platform 200 meters long if the speed of the train is 90 kmph? Choose the correct choice from the following choices.
A) 18 sec	B) 15 sec	C) 21 sec	D) 16 sec	E) 20 sec

Solution: D = 250+200= 
250+200 = 450
450   S= 90* 5/18= 
90* 5/18 = 25
25 mps   T= 450/25= 
450/25 = 18
18 sec   18 sec) 18 sec
Answer: A
If n=10^100and n^n=10k what is the value of k?  Select the correct option:
A) 200
B) 10^100
C) 10^102
D) 100^100
E) 1000^10

Solution: There is a simple logic to this question.   (a^m)^n = a^mn   So, (10^100)^(10^100) = 10^(100*(10^100))   = 10^((10^2)*(10^100))   = 10^(10^102)   and this equals 10^k   So, k = 10^102   ANSWER:10^102
Answer: C
In a class of 140 students, 60% of them passed. By what percent is the number of students who passed more than the number of failed students?  Choose the most appropriate option
A) 80%	B) 20%	C) 40%	D) 50%	E) None of these

Solution: Number of students passed = 60% of 140 = 60/100 * 140= 
60/100 * 140 = 84
84   Number of students failed= 140 - 84= 
140 - 84 = 56
56.   Required percentage= 28/56 * 100= 
28/56 * 100 = 50
50%.   ANSWER:50%
Answer: D
A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. How far is the place? Pick:
A) 2.29
B) 2.88
C) 2.2
D) 2.12
E) 2.14

Solution: M = 6   S = 1.2   DS = 6 + 1.2= 
6 + 1.2 = 7.2
7.2   US= 6 - 1.2= 
6 - 1.2 = 4.8
4.8   x/7.2 + x/4.8= 1   x = 2.88   Answer: 2.88
Answer: B
Approximately how many revolutions will be made by a car tire with a 15-inch diameter if the car travels 1⁄2 mile? Select
A) 669	B) 660	C) 360	D) 720	E) 1,440

Solution: Diameter of car tire = 15 inches   Radius of car tire = 7.5 inches = 7.5*2.54= 
7.5*2.54 = 19.05
19.05 cm   Circumference of the car tire= 2*pi * 19.05 = 2 *3.14 *19.05= 119.63 cm   Distance traveled by car = .5 mile = .5 *1.6= 
.5 *1.6 = 0.8
.8 km= 800 m = 8 * 10^4 cm   Number of revolutions =Distance traveled / Circumference of tire = 8 * 10^4 / 119.63 = 668.73   Since the answer choices are far apart we should use estimation in this question .   Ideally ,in the GMAT the conversion between units would be provided .   669nswer 669
Answer: A
How many words with or without meaning, can be formed by using all the letters of the word, 'DELHI' using each letter exactly once?
Choose the most appropriate option
A) 720	B) 24	C) None of these	D) 120	E) 247

Solution: Explanation :   The word 'DELHI' has 5 letters and all these letters are different.   Total words (with or without meaning) formed by using all these   5 letters using each letter exactly once   = Number of arrangements of 5 letters taken all at a time   = 5P5 = 5! = 5 x 4 x 3 x 2 x 1 = 120. Answer : Option 120
Answer: D
If X,Y is 26%,30% smaller than Z then how much percentage is Y greater than X?	Answers.
A) 5 15/37 % B) 13% C) 13 1/2% D) 14% E) 15%

Solution: X = 74 %   Y = 70 %   Z = 100 %   X-Y/X × 100 = 4/76 × 100 = 5 15/37% greater than X   5 15/37 %)
Answer: A
A can do 50% more work as B can do in the same time. B alone can do a piece of work in 20 hours. A, with help of B, can finish the same work in how many hours ? Choose the correct choice from the following: A) 12 B) 8 C) 13 1⁄3 D) 51⁄2 E) None of these

Solution: B alone can do a work in 20 hours.   ∴ A alone can do 3⁄2 of the work in 20 hours.   i.e., A alone can do the same work in 40⁄3 hours   ∴ (A + B)’s one hour’s work = 3⁄40 + 1⁄20 = 5⁄40 = 1⁄8   ⇒ A and B together can finish the whole work in 8 hours.   Answer 8
Answer: B
When a number is divided by 31, the remainder is 29. When the same number is divided by 16, what will be the remainder?	Pick:
A) 11	B) 13	C) 15	D) Data inadequate	E) none of these

Solution: Number= (31 * Q)+ 29.   Given data is inadequate.   ANSWER:Data inadequate
Answer: D
Speed of a boat in standing water is 8 kmph and the speed of the stream is 6 kmph. A man rows to place at a distance of 210 km and comes back to the starting point. The total time taken by him is:  Choose the correct choice from the following:
A) 120 hours	B) 240 hours	C) 160 hours	D) 480 hours	E) None

Solution: Sol.   Speed upstream = 2 kmph; Speed downstream = 14 kmph.   ∴ total time taken = [210/2 + 210/2] hours = 120 hours.   120 hoursnswer 120 hours
Answer: A
SCORE INTERVAL----------------NUMBER OF SCORES
50-59-------------------------- 2
60-69--------------------------10
70-79--------------------------16
80-89--------------------------10
90-99--------------------------18
The table above shows the distribution of test scores for a group of management trainees. Which score interval contains the median of the 28 scores?	Choose the correct choice from the following answers:	A) 39	B) 28th(50-79)	C) 32	D) 34	E) 36

Solution: Total scores= 2+10+16+10+18= 
2+10+16+10+18 = 56
56, which is odd, therefore the median is the Floor (56/2)= 
 (56/2) = 28
28th score. And the 37th score is in the 80-89 range, because 50-79 only reference 28 scores.   28th(50-79)
Answer: B
Light glows for every 18 seconds . How many times did it between 1:57:58 and 3:20:47 am
Choices:
A) 281 B) 277 C) 283 D) 384 E) 385

Solution: the diff in sec between 1:57:58 and 3:20:47 is 4969 sec, 4969/18 = 276.   so total 277 times light ll glow   ANSWER:277
Answer: B