MU-NLPC/Calc-aqua_rat huggingface dataset:
A farm has chickens, cows and sheep. There are 10 times the number of chickens and cows than sheep. If there are more cows than chickens or sheep, and together, cows and chickens have a total of 100 feet and heads, how many sheep live at the farm? Select the correct option:
A) 5	B) 8	C) 2	D) 14	E) 17

Solution: Chicken - ch   Cows - C   Sheep -S   ch+C=10S   C> ch and c>s   Each cow has 4 legs and 1 head   Each chicken has 2 legs and 1 head   So 5c+3ch=100 (sum of legs and head)   There are 2 possible solutions to this equation   c=11 and ch=9 or   c=14 and ch=10   Since from first equation where ch+c=10s   The sum of ch and c should be divisbile by 10. 24 is not so the only possible solution is c=11 and ch=9. So s=2   Answer : 2
Answer: C
The average age of 40 passengers in a ferry is 35. What is the average age of the new group formed when combining the passengers with the 5 crew members of ferry whose average age is 25?  Choose the correct choice from the following answers:
A) 36.45	B) 38.89	C) 39.67	D) 40.12	E) 41.88

Solution: Sum of ages of passengers= 40x35= 1400   Sum of ages of crew= 25x5= 125   Sum of ages of new group formed= 1525   Average=1525/45=38.89   Answer: 38.89
Answer: B
A certain animal in the zoo has consumed 39 pounds of food in six days. If it continues to eat at the same rate, in how many more days will its total consumption be 117 pounds?	Choose the correct choice from the following answers:	A) 8	B) 7	C) 12	D) 9	E) none of the above

Solution: Ans is 12:   39 pounds --> 6 days   117 pounds --> x days   x = 117*6/39= 
117*6/39 = 18
18   the animal has already consumed food in 6 days so the the number of days   for it's total consumption be 117 pounds is   18-6= 
  18-6 = 12
12
Answer: C
Tane and Thomas are among the 8 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 8 people if at least one of either Tane or Thomas is to be selected?  Choose the correct choice from the following answers:
A) 28 B) 46 C) 55 D) 63 E) 70

Solution: Ans:55   Solution:   T+T+6 = total 8 ,   we need to select at least one of the T and T or both= total 4 out of 8 - 4 out of 6   8554 - 6554   =55
Answer: C
The average temperature for Monday, Tuesday and Wednsday is 36.3 degrees C. The average temperature for Tuesday, Wednesday and Thursday is 36.7 degrees C. if Monday’s temperature recorded as 39 degrees c, find the Thursday’s temperature ? Choose the correct choice from the following options:
A) 60.2 degrees C B) 50.2 degrees C C) 40.2 degrees C D) 70.2 degrees C E) None of these

Solution: Explanation:   MOn + Tue + wed Temperature = 3X36.3 = 108.9   Tue + wed Temperature = 108.9 – 39 = 69.9   Tue + wed + Thu temperature = 3X36.7 = 110.1   So, Thursday’s temperature = 110.1 – 69.9 = 40.2 degrees 40.2 degrees C   Answer: 40.2 degrees C
Answer: C
Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:
Choose the correct answer.
A) broke even, B) lost 4 cents C) gained 4 cents D) lost 10 cents E) gained 10 cents

Solution: Solution:   20 % profit on $ 1.20   = $ 20/100 × 1.20   = $ 0.20 × 1.20   = $ 0.24   Similarly, 20 % loss on $ 1.20   = $ 20/100 × 1.20   = $ 0.20 × 1.20   = $ 0.24   Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.   Since both profit and loss amount is same so, it’s broke even.   broke even,nswer: broke even,
Answer: A
Find the average of first 50 natural numbers.
Answers
A) 20.5  B) 18  C) 25.5  D) 19  E) 17

Solution: Exp. Sum of first n natural numbers = n( n+1)/2   So, sum of first 50 natural numbers = 50*51/2= 
50*51/2 = 1_275
1275   Required average=1275/50= 
1275/50 = 51/2 = around 25.5
25.5   Answer:25.5
Answer: C
At what time between 3 o'clock and 4 o'clock, both the needles of a clock will coincide each other?
Choose one:
A) 16 2/11 minutes past 3 B) 16 4/11 minutes past 3 C) 16 7/11 minutes past 3 D) 16 8/11 minutes past 3 E) 16 4/11 minutes past 3

Solution: Here H = 3. Hands will be together at   =60H/11 minutes past 3   =60Ã—3/11 minutes past 3   =180/11 minutes past 3   =16 4/11 minutes past 3   Answer: 16 4/11 minutes past 3
Answer: E
When f is divided by 5, the remainder is 3. When y is divided by 5, the remainder is 4. What is the remainder when f + y is divided by 5?
Pick:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: In my view the answer should be 2   f/5 has Remainder=3 -> f = 5 x Q + 3   Y/5 has a Remainder=4 -> Y = 5 x Q + 3   2ombining both   ((5 x Q1 + 3) + (5 x Q2 + 3))/5 =   5(Q1+Q2)/5 + 7/5 =   Q1+Q2 + 7/5   7/5 = 1+ 2/5 => Remainder 2   Answer 2
Answer: C
A reduction of 50% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?  Pick one:
A) 2.75
B) 8.75
C) 7.75
D) 3.75
E) 1.75

Solution: Explanation:   40*(50/100)= 
40*(50/100) = 20
20 --- 64   ? --- 12=> Rs.3.75   Answer: 3.75
Answer: D
In his pocket, a boy has 5 red marbles, 6 blue marbles, and 7 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?	Select.
A) 11 B) 12 C) 13 D) 14 E) 15

Solution: The worst case scenario would be that he has taken 6 blue and 7 green, a total of 13 marbles, and still doesn't have 3 distinct colors. But the next draw, marble number 14, will surely be red as only the red marbles are left in his pocket.   The answer is 14.
Answer: D
Two hundred multiples of seven are chosen at random, and 200 multiples of eight are chosen at random. Approximately what percentage of the 400 selected numbers are odd? Select the correct option:
A) 20%	B) 25%	C) 40%	D) 50%	E) 80%

Solution: About half the multiples of seven will be odd while all the multiples of eight are even.   The percentage of odd numbers is about (1/2)(200) / 400 = 25%   The answer is 25%.
Answer: B
Two pipes A and B can separately fill a tank in 12 and 15 minutes respectively. A third pipe C can drain off 56 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?
Choose one.
A) 549
B) 540
C) 542
D) 672
E) 279

Solution: 1/12 + 1/15 - 1/x = 1/15   x = 12   12 * 56= 
12 * 56 = 672
672   Answer: 672
Answer: D
How many times does the minute hand and the second hand make a straight line?
Answers.
A) 21	B) 2823	C) 2822	D) 2832	E) 2833

Solution: D   2832   make a straight line 59 x 2 times = 118 times.   24 hours in a day, so in a day minutes and second hand make a straight line   24 x 118 times = 2832 times.
Answer: D
Dacid obtained 96, 95, 82, 97 and 95 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks? Pick one.
A) 79  B) 93  C) 88  D) 88  E) 75

Solution: Average = (96+ 95+ 82+ 97+95)/5   = 465/5= 
465/5 = 93
93.   Answer:93
Answer: B
There are 8 red, 7 blue and 6 green balls, 1 ball is picked up randomly thenwhat is the probability that neither blue nor green?  Choose the correct choice from the following.
A) 2/31
B) 3/41
C) 4/45
D) 4/57
E) 8/21

Solution: Total number of balls = (8 + 7 + 6)= 
(8 + 7 + 6) = 21
21   Let E= event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.   Therefore, n(E) = 8.   P(8/21) = 8/21.
Answer: E
What is the sum W of all 3 digit numbers that leave a remainder of '2' when divided by 3?  Choose the correct choice:	A) 897	B) 164,850	C) 164,749	D) 149,700	E) 156,720

Solution: The series is => 101+...998   Number of terms => 300   sum => 300/2 * [101+998]   hence sum W=> 164850 i.e. option 164,850
Answer: B
Company T produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company T last month, 2/3 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?	Choose the correct choice from the following:	A) 8/22	B) 4/22	C) 6/22	D) 7/22	E) 5/22

Solution: # of basic stereos was 3/4 of total and # of deluxe stereos was 1/4 of total, let's assume total=16, then Basic=12 and Deluxe=4.   Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be  12*1= 
 12*1 = 12
12 and total time for 7/22eluxe would be 4*7/5=28/5 --> total time for both of them would be 12+28/5=88/5 --> deluxe/total=28/5 / 88/5= 28/88 =7/22   7/22
Answer: D
Steve traveled the first 2 hours of his journey at 40 mph and the last 4 hours of his journey at 80 mph. What is his average speed of travel for the entire journey? Choose the correct choice from the following choices
A) 53.33 mph
B) 56.67 mph
C) 60 mph
D) 64 mph
E) 66.67 mph

Solution: Average Speed = Total distance/ Total time = (40 * 2 + 80 * 4)/(2 + 4) = 400/6 = 66.6   Answer: 66.67 mph
Answer: E
A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 29 m * 2 m * 0.75 m? Options.
A) 29000  B) 27908  C) 78902  D) 25000  E) 27991

Solution: 29 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x   29 = 1/100 * x => x   = 29000   29000nswer: 29000
Answer: A
34.99 + 240.016 + 23.98 = ? Answers:  A) 298.986  B) 298.694  C) 289.496  D) 289.469  E) 298.964

Solution: 34.99   240.016   + 23.98   --------   298.986   298.986nswer is 298.986.
Answer: A
An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between the highest and the lowest incentive received by the 5 salesmen in the month?  Answers:
A) $4000  B) $13,000  C) $9000  D) $5000  E) $11,000

Solution: The arithmetic mean of the incentives is $7000.   The median of the incentives is also $7000.   There is only one mode and the mode is $12,000.   Let their incentives be a, b, c, d, and e such that a ≤ b ≤ c ≤ d ≤ e   Therefore, the median of these values is 'c'.   So, c = $7000.   The sum of their incentives a + b + c + d + e = 5 * 7000 = $35,000   There is only one mode amongst these 5 observations.   The mode is that value that appears with the maximum frequency.   Hence, $12,000 is the incentive received by the most number of salesmen.   The incentive that c has got is $7000   So, the incentive received by d and e has to be greater than or equal to $7000   But the mode is $12,000   So, d and e should have got $12,000 each.   Therefore, c + d + e = 7000 + 12,000 + 12,000 = $31,000   Hence, a + b = 35,000 - 31,000 = $4000   As there is only one mode, the incentives received by a and b have to be different   So, a received $1000 and b received $3000.   Maximum incentive : $12,000   Minimum incentive : $1000   Difference between maximum and minimum incentive : $11,000   Answer $11,000
Answer: E
In how many of ways can 5 balls be placed in 5 tins if any number of balls can be placed in any tin?
Choose the correct answer:
A) 5C4
B) 5P4
C) 54
D) 4^5
E) 5^5

Solution: Now, each of the 5 different balls has 5 choices (5 tins to go to), so total # of distribution is 5*5*5*5*5=5^5.   Answer: 5^5.
Answer: E
A baker charges Q dollars for a birthday cake. Next week, she intends to earn 320 dollars selling cakes. If she were to reduce the price of the cake by 20 percent, she would have to sell two more cakes to earn the same amount of revenue. How many cakes does she intend to sell next week?  Choose the correct choice from the following answers:
A) 2
B) 4
C) 6
D) 8
E) 10

Solution: We're told that by selling cakes at Q dollars/cake, a baker will make $320.   Reducing the price by 20% and selling 2 MORE cakes will also make her $320.   We're asked for the original number of cakes that the baker intends to sell.   $320 is a rather interesting number. Based on the answer choices, we're almost certainly dealing with integer values for the number of cakes AND the price per cake. As such, 6 is probably NOT going to be part of the solution (either as 4 and 6 cakes or as 6 and 8 cakes). As such, we can avoid Answers B and C....   Let's TEST ANSWER D: 8 cakes   IF....   Original cakes = 8   8(Q) = $320, so Q = $40/cake   20% off = $8 off = 40-8= 
40-8 = 32
$32/cake   +2 more cakes= 8+2= 
8+2 = 10
10 cakes   10(32)= $320   This is an exact MATCH for what we were told, so this MUST be the answer.   Final Answer:   8
Answer: D
A man saves Rs 500 at the end of each year and lends the money at 5% compound interest. How
much will it become at the end of 3 years.
Choices
A) Rs 662
B) Rs 1665.01
C) Rs 1662.02
D) Rs 1655.06
E) None of these

Solution: Explanation:   =[500(21/20×21/20×21/20)+500(21/20×21/20)+500(21/20)]=1655.06   Answer: Rs 1655.06
Answer: D
Because he’s taxed by his home planet, Mork pays a tax rate of 30% on his income, while Mindy pays a rate of only 20% on hers. If Mindy earned 3 times as much as Mork did, what was their combined tax rate?	Choose the correct choice from the following choices
A) 32.5%  B) 34%  C) 35%  D) 36%  E) 22.5%

Solution: Say Morks income is - 100   So tax paid will be 30   Say Mindys income is 3*100= 
3*100 = 300
300   So tax paid is 20% * 300= 60   Total tax paid = 30+60= 
30+60 = 90
90.   Combined tax % will be 90/100+300= 22.5%
Answer: E
The probability that a number selected at random from the first 50 natural numbers is a composite number is?  Pick:	A) 11/15	B) 13/15	C) 17/25	D) 25/17	E) 11/25

Solution: Explanation:   The number of exhaustive events = ⁵⁰C₁ = 50.   We have 15 primes from 1 to 50.   Number of favorable cases are 34.   Required probability = 34/50 = 17/25   17/25
Answer: C
Walking with 4/5 of my usual speed, I arrive at the bus stop 9 minutes later than normal. How many minutes does it take to walk to the bus stop at my usual speed?
Choose the most appropriate option.
A) 24  B) 28  C) 32  D) 36  E) 40

Solution: Let t = usual time = distance / usual speed   t + 9 = distance / (4* usual speed/5) = (5 * distance) / (4 * usual speed) = 5t/4   t = 36   The answer is 36.
Answer: D
A fair sided die labeled 1 to 6 is tossed three times. What is the probability the sum of the 3 throws is 16?
Choose the correct choice from the following choices.
A) 1/6
B) 7/216
C) 1/36
D) 9/216
E) 11/216

Solution: the total number of possible outcomes is, of course, 6^3.   Fortunately, there are only two combinations of three dice throws that will give you a sum of 16:   5, 5, 6   4, 6, 6   (I have a hard time remembering a real GMAT question that would give you 12, as the number of potential combinations is indeed inordinately large and difficult to map out.)   However, our denominator counts out the number of throwing sequences (permutations) and not just combinations, so we will need to do the same. Effectively there are three throwing sequences for either combination:   6, 5, 5   5, 6, 5   5, 5, 6   4, 6, 6   6, 4, 6   6, 6, 4   So 6 throwing sequences we want divided by 6^3 throwing sequences we could get gives us 1/(6^2) or 1/36.   ANSWER:1/36
Answer: C
Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? Answers:	A) Rs.190	B) Rs.180	C) Rs.220	D) Rs.230	E) Rs.250

Solution: Let the amount paid to X per week = x   and the amount paid to Y per week = y   Then x + y = 550   But x = 120% of y = 120y/100 = 12y/10   ∴12y/10 + y = 550   ⇒ y[12/10 + 1] = 550   ⇒ 22y/10 = 550   ⇒ 22y = 5500   ⇒ y = 5500/22 = 500/2 = Rs.250   Rs.250)
Answer: E
Two trains start from A & B and travel towards each other at
speed of 60kmph and 70kmph resp. At the time of the meeting the
second train has traveled 200km more than the first.the distance
between them.  Choose the correct option:
A) 2200 km	B) 2400 km	C) 2600 km	D) 2800 km	E) 3000 km

Solution: Let the distance traveled by the first train be x km   then distance covered by the second train is x + 200km   x/60 = x+200 / 70   x= 1200   so the distance between A & B is x + x + 200 = 2600 km   Answer is 2600 km.
Answer: C
A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 6% of bananas were rotten. Find the percentage of fruits in good condition? Choices:
A) 92.5%
B) 88.6%
C) 85.2%
D) 96.8%
E) 78.9%

Solution: Total number of fruits shopkeeper bought = 600 + 400= 
600 + 400 = 1_000
1000   Number of rotten oranges= 15% of 600   = 15/100 × 600   = 9000/100= 
9000/100 = 90
90   Number of rotten bananas= 6% of 400   = 24   Therefore, total number of rotten fruits = 90 + 24= 
90 + 24 = 114
114   Therefore Number of fruits in good condition= 1000 - 114= 
1000 - 114 = 886
886   Therefore Percentage of fruits in good condition= (886/1000 × 100)%   = (88600/1000)= 
(88600/1000) = 443/5 = around 88.6
88.6%   Answer:88.6%
Answer: B
The average weight of 8 persons increases by 1.5 kg. If a person weighing 65 kg is replaced by a new person, what could be the weight of the new person?  Choose the correct choice from the following answers:
A) 76 kg
B) 77 kg
C) 76.5 kg
D) Data inadequate
E) None of these

Solution: total weight increases = 8 × 1.5 = 12 kg   so the weight of new person = 65 + 12= 
65 + 12 = 77
77 kg   Answer 77 kg
Answer: B
There are two numbers. If 10% of the first number is added to the second number, then the second number increases to its five-fourth. What is the ratio of the first number to the second number?
Pick one
A) 3 : 2	B) 2 : 7	C) 8 : 5	D) 5 : 2	E) 6 : 5

Solution: Let the two numbers be x and y.   (1/10) * x + y = (5/4) * y   (1/10) * x = (1/4) * y   x/y = 10/4 = 5/2   The answer is 5 : 2.
Answer: D
If two typists can type two pages in two minutes, how many typists will it take to type 72 pages in nine minutes? Choose one:
A) 3 B) 4 C) 6 D) 16 E) 36

Solution: In 2 minutes 2 typists type 2 pages which means that in 9 minutes they will type 9 pages but to type 72 pages (8 times) we need 8 times more typists i.e. 2 x 8 = 16 typists.   16
Answer: D
A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 9 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?	Choose the correct choice from the following choices:
A) 1:4 B) 1:5 C) 3:2 D) 1:2 E) 2:5

Solution: The cost price of a mango = 1/5 dollars.   The selling price of a mango from the first stack = 1/3 dollars --> the profit from one mango = 1/3 - 1/5 = 2/15 = 4/30 dollars.   The selling price of a mango from the second stack = 1/9 dollars --> the loss from one mango = 1/5 - 1/9 = 4/45 dollars.   The profit from one mango from the first stack is 4 times the loss from one mango from the second stack.   the ratio is 4/30*45/4 =3:2   3:2
Answer: C
Find the odd man out.
2, 5, 10, 17, 26, 37, 50, 64  Choices:
A) 33
B) 38
C) 27
D) 64
E) 20

Solution: Explanation:   (1*1)+1 , (2*2)+1 , (3*3)+1 , (4*4)+1 , (5*5)+1 , (6*6)+1 , (7*7)+1 , (8*8)+1   But, 64 is out of pattern.   Answer: 64) 64
Answer: D
(35423+7164+41720)-(317x89)=?
Pick one.
A) 28213 B) 84307 C) 50694 D) 54094 E) None of them

Solution: =(84307)-317x89   =84307-(317x(90-1))   =84307-(317x90-317)   =84307-28213   =54094   Answer is 54094
Answer: D
Jane and Ashley take 8 days and 40 days respectively to complete a project when they work on it alone. They thought if they worked on the project together, they would take fewer days to complete it. During the period that they were working together, Jane took an eight day leave from work. This led to Jane's working for four extra days on her own to complete the project. How long did it take to finish the project ? Choose the most appropriate option:
A) 14 Days	B) 15 Days	C) 16 Days	D) 18 Days	E) 20 Days

Solution: Let us assume that the work is laying 40 bricks.   Jane = 5 bricks per day   Ashley = 1 brick per day   Together = 6 bricks per day   Let's say first 8 days Ashley works alone,   No of bricks = 8   Last 4 days Jane works alone,   No. of bricks = 20   Remaining bricks = 40 - 28= 
40 - 28 = 12
12   So together, they would take   12/6= 
  12/6 = 2
2   Total no. of days= 8 + 4 + 2= 
8 + 4 + 2 = 14
14   14 Daysnswer is 14 Days
Answer: A
Today is Sunday. The day after 59 days will be Select the correct option: A) Monday B) Wednesday C) Saturday D) Sunday E) None of these

Solution: Explanation :   59 days = 8 weeks 3 days = 3 odd days   Hence if today is Sunday, After 59 days, it will be = (Sunday + 3 odd days)   = Wednesday. Answer : Option Wednesday
Answer: B
A can finish a piece of work in 4 days. B can do it in 14 days. They work together for two days and then A goes away. In how many days will B finish the work?	Options:	A) 4	B) 5	C) 6	D) 7	E) 8

Solution: 2/4 + (2 + x)/14 = 1 => x = 5 days   Answer: 5
Answer: B
In how many words can be formed by using all letters of the word BHOPAL	Pick one
A) 420  B) 520  C) 620  D) 720  E) None of these

Solution: Explanation:   Required number   =6!=6∗5∗4∗3∗2∗1=720   Option 720
Answer: D
A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.35000, find their shares?	Pick:	A) s.14000, Rs.15020	B) s.14000, Rs.15700	C) s.10000, Rs.21090	D) s.10000, Rs.21000	E) s.14000, Rs.21000

Solution: The ratio of their profits A:B   = 8:12 = 2:3   Share of A in the total profit   = 2/5 * 35000   = Rs.14000 Share of A in the total profit = 3/5 * 35000   = Rs.21000   Answer: s.14000, Rs.21000
Answer: E
What are the last two digits of (301*402*502*604*646*547*448*349)^2	Select the correct option.
A) 96
B) 76
C) 56
D) 36
E) 16

Solution: ((301*402*502*604*646)*(547*448*349))^2   If you observe above digits, last digit are: 1,2,2,4,6,7,8,9; 3&5 are missing; so I have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01,02,02,04,46 and final three as 47*48*49.   Solving for only last two digits and multiplying them we get:( (04*04*46)(56*49))^2 = (36*44)^2=84^2=56   Hence answer is 56
Answer: C
If x ≠ 0 and (y^2 − xy)/x=y-x, which of the following expressions is equal to its opposite? Choose the correct choice from the following answers.
A) x^2  B) x^2 – y^2  C) y^2  D) (y + x)^2  E) (x – y)^2

Solution: (y^2 − xy)/x=y-x   => y^2 − xy = xy -x^2   => x^2 - 2xy + y^2 = 0   => (x-y)^2 = 0   Answer (x – y)^2
Answer: E
If x and y are positive integers, and x^3*y^4 = 432, which of the following is the value of xy?	Choose the most appropriate option
A) 2	B) 4	C) 6	D) 8	E) 10

Solution: 432 = 2^4*3^3   xy = 2*3= 
2*3 = 6
6   The answer is 6.
Answer: C
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 10 years ago was 20 years. The present age of the husband is: Choose the correct choice from the following answers.
A) 20 years B) 34 years C) 60 years D) 30 years E) 35 years

Solution: D   30 years   Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.   Sum of the present ages of wife and child = (20 x 2 + 10 x 2) years = 60 years.   Husband's present age = (90 - 60)= 
(90 - 60) = 30
30 years.
Answer: D
James Horner is having two coins in his hand. Out of the two coins, one is a real coin and the second one is a faulty one with Tales on both sides. He blind folds himself choose a random coin and tosses it in the air. The coin falls down with Tale facing upwards.
What is the probability that this is the faulty coin?	Options:	A) 3/6	B) 2/3	C) 1/3	D) 3/5	E) 1/8

Solution: 2/3   2/3   While tossing the coins in this case only two cases are favorable:   1) A1 (H) A2 (H)   2) A2 (H) A1 (H)   3) 2/31 (H) 2/32 (T)   4) 2/32 (T) 2/31 (H)   Since the fourth case is not feasible, the probability is 2/3.
Answer: B
Find the compound interest on $30000 in 2years at 4% per annum, the interest being compounded half-yearly?  Pick:
A) $645.56
B) $824.32
C) $954.26
D) $2472.96
E) $1020.45

Solution: Principle = $10000   Rate = 2% half yearly = 4 half years   Amount = 30000*(1 + 2/100)^4 = 30000 * 51/50 * 51/50 * 51/50 * 51/50   = $32472.96   C.I. = 32472.96-10000 = $2472.96   Answer is $2472.96
Answer: D