MU-NLPC/Calc-aqua_rat huggingface dataset:
Liam is pulled over for speeding just as he is arriving at work.He explains to the police officer that he could not afford to be late today, and has arrived at work only four minutes before he is to start. The officer explains that if Liam had driven 5mph slower for his whole commute, he would have arrived at work exactly on time. If Liam's commute is 20 miles long,how fast was he actually driving?(Assume that Liam drove at a constant speed for the duration of his commute.)	Select.
A) 50 mph  B) 45 mph  C) 48 mph  D) 52 mph  E) 40 mph

Solution: Let t be the number of hours he would need to reach office on time.   when he is driving with over speed, he reached office 4 min earlier! so the equation for this is s(t - 4/60) = 20   where s is the speed and 20 is the distance.   if he decreases his speed by 5mph then he would have reached his office on time: (s-5)t = 20   if you solve above equations, you will arrive at t = 2/3 hr and s = 40mph   therefore answer is 40 mph
Answer: E
The cost of registration at a professional association meeting was $50 per person; a lunch for registrants only was available for an additional $22 per person. If the number of registrants who paid for lunch was 40 more than the number who did not, and if receipts for registration and lunch totaled $39,480, how many people paid just for registration at the meeting?  Choose the correct choice from the following
A) 700 B) 800 C) 300 D) 1,500 E) 1,800

Solution: Hope this might be useful to you.   Let the number of people who have opted only to register = x   Now since the registration cost is 50$ per person, the total amount sums to = 50x $   As per the information given in the question, the number of registrants who paid for lunch was 40 more than the number who did not. That means, total number of people who registered and paid for lunch = 40 + x.   For the people who registered for lunch the cost is 50 $ (for the event registration) + 22 $ (for lunch) = 72 $.   Total amount in this case sums to = 72(40 + x) = 2880 + 72x   Now, total amount received was 39480   Thus, from the above data,   50x + 2880 + 72x = 39480   122x = 39480 - 2880   122x = 36600   x = 300.   Hence the correct Ans is 300
Answer: C
A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?	Select:
A) 240 m  B) 200 m  C) 500 m  D) 360 m  E) 489 m

Solution: Explanation:   Speed = 54 * 5/18= 
54 * 5/18 = 15
15 m/sec.   Length of the train= 15 * 20= 
15 * 20 = 300
300 m.   Let the length of the platform be x m . Then,   (x + 300)/36= 15 => x = 240 m.   240 mnswer:240 m
Answer: A
If the area of a circle is 64pi square feet, find its circumference.  Choose the correct choice from the following:
A) 16 pi feet  B) 28 pi feet  C) 38 pi feet  D) 48 pi feet  E) 58 pi feet

Solution: The area is given by pi *r* r. Hence   pi * r *r = 64 pi   r * r = 64; hence r = 64 feet   The circumference is given by   2 * pi * r = 2 * pi * 8 = 16 pi feet   correct answer 16 pi feet
Answer: A
George baked a total of 75 pizzas for 7 straight days, beginning on Saturday. He baked 3/5 of the pizzas the first day, and 3/5 of the remaining pizzas the second day. If each successive day he baked fewer pizzas than the previous day, what is the maximum number of pizzas he could have baked on Wednesday?
Options:
A) 5
B) 4
C) 2
D) 6
E) 7

Solution: 3/5 of the 75 pizzas cooked on Saturday = 45 pizzas   3/5 of the remaining pizzas on Sunday = 18 pizzas   We're left with   (75-45-18)= 
  (75-45-18) = 12
12 pizzas for the remaining 5 days. The prompt tells us that each day has FEWER pizzas than the day before it, so we can't have duplicate numbers.   M T W TH F   5 4 2 1 0=12   W=2   2
Answer: C
A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The second wheel covers a distance of d feet in 400 revolutions. How many revolutions does the first wheel make in covering d feet?	Choose the correct choice from the following answers
A) 400xy  B) 400y - x  C) 400x - y  D) 400y/x  E) 400x/y

Solution: second Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)   first Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)   Revolutions = distance/circumference   So, from equation (1)   400 = d/(x*pi)   d = 400 * x * pi ---------- (3)   From equation (2)   Revolutions = d/(y*pi) = (400 * x * pi) / (y*pi) = 400x/y   Answer (400x/y)
Answer: E
One half of the people at the game wore the team colors. Two thirds of those people wore team
hats as well. One fourth of those with team colors and team hats had banners to wave.
Twenty five people had team colors and banners, but no hats. One hundred people had only
banners. If there were 1824 people at the game, how many had banners?  Choose one:
A) 177
B) 277
C) 377
D) 477
E) 577

Solution: 1/2 x 1824 = 912 with team colors   2/3 x 912 = 608 with hats and colors   1/4 x 608 = 152 with hats, colors, and banners   152 + 100 + 25= 
152 + 100 + 25 = 277
277 with banners   correct answer 277
Answer: B
Dany bought a total of 20 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?  Choose the most appropriate option:
A) 4	B) 10	C) 7	D) 8	E) 12

Solution: Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 20. Hence   X + Y = 20   If X is the number of cards at $0.25, then the X cards cost   0.25 X   If Y is the number of cards at $0.15, then the Y cards cost   0.15 Y   The total cost of the X cards and the the Y cards is known to be $4.2 and also given by   0.25 X + 0.15 Y = 4.2   We now need to solve the system of equations   X + Y = 20   0.25 X + 0.15 Y = 4.2   The first equation gives Y = 20 - X. Substitute y by 20 - x in the second equation and solve   0.25 X + 0.15 (20 - X) = 4.2   X(0.25 - 0.15) + 3 = 4.2   0.1 X = 1.2   X = 12 and Y = 20 - 12= 
20 - 12 = 8
8   correct answer 8
Answer: D
36 men can complete a piece of work in 18 days.In how days will 27 men can complete the work?
Choose the correct choice from the following answers.
A) 18
B) 20
C) 17
D) 24
E) 21

Solution: Let the required number of days be x   Less men,more days(indirect proportion)   27:36::18:x   27x=36*18   x=(36*18)/27= 
(36*18)/27 = 24
24 days   option is 24
Answer: D
Kunal electronic services assemble computers. Over a period of time the engineers made the following observation regarding the two vital components - the USB port and CD drive. The probability that USB port is defective is 0.1, that both the USB port and CD drive are defective is 0.02, while the probability that only the CD drive is defective is 0.03 . The probability that the USB port is defective when the CD drive has been found to be defective is?
Choose one:
A) 0.2 B) 0.3 C) 0.25 D) 0.4 E) 0.6

Solution: Explanation :   USB Defective	USB OK	Total   CD Defective	0.02	0.03	(0.05)   CD OK	(0.08)	(0.87)   (0.95)   Total	0.1	(0.9)   The figures enclosed in brackets follow as conclusions. The probability that USB part is defective, when the C0.4 drive is found to be defective is 0.02/0.02+0.03 = 2/5= 
2/5 = 2/5 = around 0.4
0.40   Answer : 0.4
Answer: D
In a simultaneous throw of a pair of dice, find the probability of getting a total more than 4  Choose the correct choice from the following
A) 1/2	B) 7/12	C) 5/13	D) 5/12	E) 1/3

Solution: Total number of cases = 3*3= 
3*3 = 9
9   Favourable cases= [(2,3),(3,2),(3,3)] = 3   So Probability = 3/9 = 1/3   Answer is 1/3
Answer: E
At an elementary school, 70% of the faculty members are women and 60% of the faculty members are married. If 2⁄3 of the men are single, what fraction of the men are married?
Choose one
A) 5⁄7	B) 7⁄10	C) 1⁄3	D) 7⁄30	E) 5⁄70

Solution: --------------------M------W--------Total   Marrried----------10-----50---------60   Not married-----20-----20---------40   Total-------------30-----70--------100   need married man/total man, so 10/30=1/3   1⁄3
Answer: C
Find out the wrong number in the series.
6, 12, 48, 94, 384, 768, 3072
Select the correct option:	A) 768	B) 384	C) 94	D) 488	E) 12

Solution: Each even term of the series is obtained by multiplying the previous term by 2.   2nd term = (1st term) x 2 = 6 x 2 = 12   4th term = (3rd term) x 2 = 48 x 2 = 96.   6th term = (5th term) x 2 = 384 x 2 =768.   4th term should be 96 instead of 94.   ANSWER:94
Answer: C
A team bought a total of 472 balls. If each player on the team bought at least 19 balls, then what is the greatest possible number of players on the team?
Choose the correct choice from the following answers:
A) 21 B) 22 C) 23 D) 24 E) 25

Solution: 472/19=24 plus remainder.   The answer is 24.
Answer: D
What percent of 12.4 kg is 20 gms ? Choose the most appropriate option.
A) 25 B) 16 C) 18 D) 19 E) 17

Solution: Explanation:   Required percentage = (20/12400 * 100)% = 4/25= 
4/25 = 4/25 = around 0.16
0.16%   Answer: 16) .16%
Answer: B
A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained? Pick
A) 10 B) 100 C) 1000 D) 10000 E) None of these

Solution: Along one edge, the number of small cubes that can be cut   = 100/10= 
100/10 = 10
10   Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut= 10 * 10 * 10= 
10 * 10 * 10 = 1_000
1000   ANSWER:1000
Answer: C
Of the following, which is greater than Â½ ?
Indicate ALL such fractions. Answers.
A) 4/0  B) 4/7  C) 4/2  D) 4/1  E) 4/8

Solution: Explanation:   One way to deal with fractions is to convert them all to decimals.   In this case all you would need to do is to see which is greater than 0.5.   Otherwise to see which is greater than Â½, double the numerator and see if the result is greater than the denominator. In B doubling the numerator gives us 8, which is bigger than 7.   Answer: 4/7
Answer: B
Find the simple interest on Rs.350 for 10 months at 5 paisa per month? Choose the correct option:
A) 277	B) 175	C) 288	D) 266	E) 121

Solution: I = (350*10*5)/100= 
(350*10*5)/100 = 175
175   Answer: 175
Answer: B
The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?	Choose the most appropriate option:  A) 76  B) 86  C) 56  D) 45  E) 17

Solution: Let the four integers be A, B, C and D where A > B > C > D.   (A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)   A = 93, D = 39 and B - C = 28   (1) => B + C = 276 - (A + D) = 276 - 132= 
276 - 132 = 144
144.   86 + 86 -28= 
86 + 86 -28 = 144
144   86= (144 + 28)/2= 
(144 + 28)/2 = 86
86   Answer: 86
Answer: B
A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 620 m?
Choose the correct answer.
A) 120 sec	B) 99 sec	C) 89 sec	D) 86 sec	E) 85 sec

Solution: Explanation:   v = 240/24 (where v is the speed of the train) = 10 m/s   t = (240+620)/10= 
(240+620)/10 = 86
86 seconds   Answer: Option 86 sec
Answer: D
How many integers between 1 and 1,400 are divisible by 25, and 35?  Choose the correct choice from the following.
A) 4	B) 5	C) 6	D) 7	E) 8

Solution: LCM of the given numbers   =175   Therefore , number of integers = 1400/175= 
1400/175 = 8
8   Answer is Option 8
Answer: E
A cistern 8 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm. What is the total area of the wet surface?
Choose the correct choice from the following answers:
A) 40 B) 48 C) 54 D) 62 E) 76

Solution: Area of the wet surface = [2(lb + bh + lh) - lb]   = 2(bh + lh) + lb   = [2 (4 x 1.25 + 8 x 1.25) + 8 x 4]   = 62   The answer is 62.
Answer: D
Anand and Deepak started a business investing Rs. 21,000 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is? Answers.
A) 2777	B) 2888	C) 8625	D) 2885	E) 2781

Solution: Ratio of their shares = 21000 : 35000 = 3:5   Deepak's share = 13800 * 5/8 = Rs. 8625.   Answer: 8625
Answer: C
A coin is tossed six times. What is the probability that there is at the least one tail?	Choose the correct choice from the following answers
A) 63/64
B) 31/64
C) 31/67
D) 31/64
E) 63/31

Solution: Let P(T) be the probability of getting least one tail when the coin is tossed six times.   = There is not even a single tail.   i.e. all the outcomes are heads.   = 1/64 ; P(T) = 1 - 1/64   = 63/64   63/64nswer: 63/64
Answer: A
Camel and carriage for Rs. 5000. He SP the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the CP of the camel?
Select.
A) Rs.2166.67
B) Rs.2187.67
C) Rs.2188
D) Rs.2200
E) Rs.2234.7

Solution: Now, in this numerical, there is no common loss and gain %.   Hence, solve it making equations.   Let cost price of camel be x.   As cost of camel and carriage = Rs 5000   Cost of carriage = Rs. (5000 – x)   After selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%.   Therefore,   20% of x – 10 % of (5000 – x) = 3 % of 5000   20 × x – 10 × (5000 – x) = 3 × 5000   100 100 100   x – (5000 – x) = 150   5 10   10x – (5000 – x) × 10 = 150 × 10   5 10   2x-5000+x=1500   3x=1500+5000   x=2166.67   The cost of camel = Rs.2166.67   Option (Rs.2166.67) is the correct answer
Answer: A
A 60 kg metal bar made of alloy of tin and silver lost 6 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar?
Select the correct option:
A) 1/4
B) 2/5
C) 1/2
D) 3/5
E) 2/3

Solution: you can simply use this formula to avoid confusion:   w1/w2 = (A2 - Aavg)/(Avg - A1)   Here is how you will find the values of A1 an A2.   We have an overall loss (average loss). The average loss is 6 kg when 60 kg alloy is immersed.   This is a loss of (6/60)*100= 
(6/60)*100 = 10
10%.   This is Aavg   The loss of tin is 1.375 kg for every 10 kg.   This means it loses   (1.375/10)*100= 
  (1.375/10)*100 = 13.75
13.75% of its weight in water.   This is A1.   The loss of silver is .375 kg for every 5 kg.   This means it loses   (.375/5)* 100= 
  (.375/5)* 100 = 7.5
7.5% of its weight in water.   This is A2.   Weight of Tin/Weight of Silver= (Silver's loss - Avg loss)/(Avg loss - Tin's loss)   X/Y = (7.5 - 10)/(10 - 13.75) = 2/3   2/3
Answer: E
A contractor undertakes to built a walls in 50 days. He employs 50 peoples for the same. However after 25 days he finds that only 40% of the work is complete. How many more man need to be employed to complete the work in time? Choose the correct answer:
A) 25  B) 30  C) 35  D) 20  E) None of these

Solution: 50 men complete 0.4 work in 25 days.   25pplying the work rule, m1 × d1 × w2 = m2 × d2 × w1   we have,   50 × 25 × 0.6 = m2 × 25 × 0.4   or m2 = 50×25×0.6/25×0.4 = 75 men   25nswer25
Answer: A
In how many ways can a committee of 4 people comprising at least 3 boys be formed using a group of 5 boys and 6 girls?  Choices:  A) 67  B) 64  C) 65  D) 66  E) None of these

Solution: There are 2 options: the selected groups have no girls or one girls.   -First case: 1 girl + 3 boys: 6651 * 5653 = 6*10= 
6*10 = 60
60   -Second case: 4 boys: 5654= 5   So there are  60 + 5= 
 60 + 5 = 65
65   ANS:65
Answer: C
Avinash is twice as fast as Bharat, and Bharat is one-third as fast as Chandra. If together they can complete a piece of work in 30 days, in how many days can Avinash, Bharat and Chandra do the work respectively? Answers.
A) 90,180,60
B) 90,180,68
C) 90,180,62
D) 90,180,69
E) 90,180,61

Solution: Let Chandra do the work in 2x days.   Bharat can do it in 6x days and Avinash can do it in 3x days.   1/(2x) + 1/(6x) + 1/(3x) = 1/30 1/(2 ) + 1/(6 ) + 1/(3 )= 
1/(2 ) + 1/(6 ) + 1/(3 ) = 1
1/30=> (3 + 1 +2)/6= 
(3 + 1 +2)/6 = 1
1/30=> x = 30   So, the time taken to complete the work by Avinash, Bharat, Chandra is 90, 180, 60 days respectively.   90,180,60nswer:a
Answer: A
If the wheel is 14 cm then the number of revolutions to cover a distance of 968 cm is?	Pick
A) A)15
B) B)10
C) C)14
D) D)12
E) E)11

Solution: 2 * 22/7 * 14 * x = 968 => x = 11   ANSW11R:11
Answer: E
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?
Choose one
A) 87  B) 56  C) 20  D) 67  E) 97

Solution: M = 15   S = 5   DS = 15 + 5= 
15 + 5 = 20
20   Answer: 20
Answer: C
Find the average of first 35 natural numbers? Choose the most appropriate option.
A) 21
B) 22
C) 23
D) 18
E) 25

Solution: Sum of first 100 natural numbers = 35*36/2= 
35*36/2 = 630
630Required average= 630/35= 
630/35 = 18
18Answer is 18
Answer: D
The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:  Choose the correct choice:
A) 17 kg	B) 20 kg	C) 26 kg	D) 31 kg	E) None

Solution: EXPLANATION   Let A, B, C represent their respective weights. Then, we have:   A + B + C = (45 x 3) = 135 …. (i)   A + B = (40 x 2) = 80 …. (ii)   B + C = (43 x 2) = 86 ….(iii)   Adding (ii) and (iii), we get: A + 2B + C = 166 …. (iv)   Subtracting (i) from (iv), we get : B = 31.   B’s weight = 31 kg.   Answer 31 kg
Answer: D
a student got 70% in one subject,80% in other.to get overall 75% how much he should get in third subject.  Select the correct option: A) 65% B) 75% C) 85% D) 95% E) 88%

Solution: Already average of two subjects is (70+80)/2= 
(70+80)/2 = 75
75%   To maintain the percentage at 75%, he shouls get 75% marks in third subject   ANSWER:75%
Answer: B
A list of measurements in increasing order is 4, 5, 6, 8, 15 and x. If the median of these measurements is 2/3 times their arithmetic mean, what is the value of x? Answers.
A) 20  B) 22  C) 25  D) 28  E) 30

Solution: The median is (6+8)/2= 
(6+8)/2 = 7
7   The mean is (4+5+6+8+15+x)/6= (38+x)/6   (38+x) /6 * 2/3 = 7   x = 63-38= 
63-38 = 25
25   The answer is 25.
Answer: C
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 answer: A) 25 B) 30 C) 40 D) 45 E) 50

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 probability of two events A and B are0.25 and 0.40 respectively. The probability that both A and B occur is 0.15. The probability that neither A nor B occur is _________	Pick:
A) 0.45	B) 0.4	C) 0.5	D) 0.05	E) 0.6

Solution: we are apply that formula..............   P(AorB)=P(A)+P(B)-P(A AND B)   =.25+.40-.15= 
.25+.40-.15 = 0.5
.50   but the probability of neither A nor B=1-.50= 
1-.50 = 0.5
0.50   ANSWER:0.5
Answer: C
For any integer n greater than 1, #n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers Q are there between #6 +2 and #6 +6 , inclusive?	Choose the correct choice from the following answers:
A) None
B) One
C) Two
D) Three
E) Four

Solution: None is the answer. A.   Because for every k 6! + k :: k, because 6! :: k, since k is between 2 and 6.None
Answer: A
On selling 11 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:	Choose the correct option:
A) s. 45
B) s. 50
C) s. 55
D) s. 60
E) s. 120

Solution: (C.P. of 11 balls) - (S.P. of 11 balls) = (C.P. of 5 balls)   C.P. of 6 balls = S.P. of 11 balls = Rs.720.   C.P. of 1 ball = Rs.720/6	= Rs. 120.   Answer: Option s. 120
Answer: E
A bucket full of nuts was discovered by the crow living in the basement. The crow eats a fifth of the total number of nuts in 6 hours. How many hours in total will it take the crow to finish a quarter of the nuts?
Choose the correct choice from the following options.
A) 6.5
B) 7.0
C) 7.5
D) 8.0
E) 8.5

Solution: In one hour, the crow eats 1/30 of the nuts.   (1/4) / (1/30)= 
(1/4) / (1/30) = 15/2 = around 7.5
7.5 hours   The answer is 7.5.
Answer: C
What is the probability T of randomly selecting an arrangement of the letters of the wordMEDITERRANEANin which the first letter is E and the last letter is R? Choose the most appropriate option:
A) 1/13  B) 1/20  C) 1/26  D) 1/50  E) 1/100

Solution: Why do you calculate the total combinations and everything, it is much easier to calculate as follows:   3/13 * 1 * 1 * 1 * 1 ..... * 2/12 = 6/156 = 1/26   This is because 3/13 = Probability that first letter will be E and 2/12 = probability that thefirstletter will be R. Between everything else cuts down to 1*1*1... e.g. probability T of the second letter is 11/11= 
11/11 = 1
1, > we do not care what's in between.1/26
Answer: C
A, B and C jointly thought of engaging themselves in a business venture. It was agreed that A would invest Rs. 6500 for 6 months, B, Rs. 8400 for 5 months and C, Rs. 10,000 for 3 months. A wants to be the working member for which, he was to receive 5% of the profits. The profit earned was Rs. 7400. What is the share of B in the profit. Pick one:
A) 2670
B) 2560
C) 2440
D) 2550
E) 2660

Solution: A is a working member and for that, he receives 5% of the profit   = 5% of 7400 =(5×7400)/100=370   Remaining amount =7400−370=7030   Ratio of their investments   =6500×6:8400×5:10000×3=65×6:84×5:100×3=13×6:84:20×3=13×2:28:20=13:14:10   Share of B in the profit   =7030×14/37=190×14=2660   Answer is 2660.
Answer: E
The sides of right triangle ABC are such that the length of side AC is 1.25 times the length of side AB, which itself is 4 units more than the length of side BC. If side AC = 20 units, what is the area of the triangle?  Options
A) 144 B) 69 C) 120 D) 160 E) 96

Solution: AC=1.25xAB, 20=1.25xAB, AB=16 units   AB=4+BC, BC=AB-4, BC=16-4= 
16-4 = 12
12 units   Area= (AB*BC)/2 = 96   96 is the correct option.
Answer: E
Two brothers took the GMAT exam, the higher score is X and the lower one is Y. If the difference between the two scores is 1/3, what is the value of X/Y ?
Choose the correct choice from the following answers:
A) 3.	B) 2.	C) 1/2.	D) 4	E) There isn't enough data to answer the question.

Solution: Answer is 4 : 4   X - Y = (X + Y)/2   Solving for X/Y = 4
Answer: D
There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.	Choose the correct choice from the following answers:
A) 87∏ cm  B) 56∏ cm  C) 12∏ cm  D) 16∏ cm  E) 75∏ cm

Solution: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.   a2 = 784 = (4)(196) = (22).(142)   a = (2)(14) = 28   a = 2l, l = a/2 = 14   l = (7/3)s   Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm.   Answer:12∏ cm
Answer: C
There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 60% play football, how many play both?  Choices.
A) 210  B) 150  C) 200  D) 180  E) 160

Solution: n(210) = 75*600/100= 
75*600/100 = 450
450   n(B)= 60*600/100= 
60*600/100 = 360
360   n(210UB)= 600   n(210nB) = 450+360-600= 
450+360-600 = 210
210   210nswer is 210
Answer: A
The average age of a husband, wife and their child 4 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is?
Choose the correct choice from the following answers.
A) 2.12 years	B) 4.4 years	C) 16.63 years	D) 15 years	E) 14.25 years

Solution: Sum of the present ages of husband, wife and child   = (23 * 2 + 5 * 2) = 57 years.   Required average   = 57/4= 
57/4 = 57/4 = around 14.25
14.25 years.   Answer:14.25 years
Answer: E
How many odd integers from 1 to 50 (both inclusive) have odd number of factors? Pick one
A) 13	B) 4	C) 5	D) 6	E) 7

Solution: Integers having odd number of factors will be perfect squares. Odd numbers will have odd perfect squares. Thus, the possible values for the perfect squares are :   1,9,25,49 and the corresponding integers are 1,3,5,7 (more than 3). Thus 4 is the correct answer .
Answer: B