MU-NLPC/Calc-aqua_rat huggingface dataset:
What is the smallest integer that is the sum of 2 distinct prime integers, each greater than 140?  Select the correct option:
A) 270  B) 372  C) 273  D) 199  E) 300

Solution: A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. Here are the first few prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, etc.   Immediate two prime numbers after 70 are - 71 and 73   Sum = 149 + 151= 
149 + 151 = 300
300   Answer - 300
Answer: E
In one hour,a boat goes 13 km along the stream and 9 km against the stream.The speed of the boat in still water (in km/hr) is : Choose the correct choice from the following answers:
A) 3
B) 5
C) 11
D) 9
E) 10

Solution: Solution   Speed in still water =1/2(13+9)kmph.= 11 kmph. Answer 11
Answer: C
A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 25% lemonade syrup? Choose the correct choice from the following
A) 1.5  B) 1.75  C) 2.14  D) 2.34  E) 2.64

Solution: Let the total solution is 150 L with 80 L water70 L syrup.   To make 25% syrup solution, the result solution must have 112.5 L syrup and 37.5 L syrup.   Therefore we are taking 32.5 L of syrup from initial solution and replacing with water.   using urinary method:   70 L syrup in 150 L solution   32.5 L syrup in 69.6 L solution   We started by multiplying 10   Now to get to the result we need to divide by 32.5 => amount of solution to be replaced with water = (69.6/32.5) = 2.14.   2.14orrect option : 2.14
Answer: C
A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?  Choose the correct choice from the following answers:
A) 31/145
B) 23/145
C) 36/145
D) 31/115
E) 41/215

Solution: The probability that first ball is white:   =12C130C1=12C130C1   =1230=1230   =25=25   Since, the ball is not replaced; hence the number of balls left in bag is 29.   Hence, the probability the second ball is black:   =18C129C1=18C129C1   =1829=1829   Required probability,   =(25)×(1829)=(25)×(1829)   =36/145   23/145
Answer: B
The number of people at Ovations Bar in the hour from 12 p.m. to 1 p.m. was 30% greater than the number of people there from 11 a.m. to 12 p.m. The number of the people at the bar from 11 a.m. to 12 p.m. was 20% less than the number there from 10 a.m. to 11 a.m. If 92 people were at the bar from 11 a.m. to 1 p.m., which of the following is the number of people in the bar from 10 a.m. to 11 a.m.?
Pick one
A) 10
B) 20
C) 30
D) 40
E) 50

Solution: No of people from 10 - 11 is x   No of people from 11 - 12 is 4x/5   No of people from 12 to 1 is (13/10)(4x/5)   Given that 4x/5 + (13/10)(4x/5) = 92x/50 = 92   Then x = 50   50
Answer: E
A number exceeds 20% of itself by 40. The number is ?	Pick.
A) 50 B) 60 C) 80 D) 320 E) None

Solution: Answer   ∵ A - 20% of A = 40   ⇒ A - A/5 = 40   ⇒ 4A/5 =40   ∴ A = (5 x 40)/4 = 50.   Correct Option: 50
Answer: A
Aish started a business investing Rs. 25,000 in 2010, In 2011, he invested an additional amount of Rs. 10,000 and Roshan joined him with an amount of Rs. 35,000. In 2012, Aish invested another additional amount of Rs. 10,000 and Atul joined them with an amount of Rs. 35,000. What will be Roshan’s share in the profit of Rs. 2,70,000 earned at the end of 3 years from the start of the business in 2010?
Options.
A) Rs.45000 B) Rs.50000 C) Rs.60000 D) Rs.90000 E) None of these

Solution: Explanation :   Aish : Roshan : Atul   = (25000 x 12 + 35000 x 12 + 45000 x 12) : (35000 x 24) : (35000 x 12)   = 1260000 : 840000 : 420000 = 3 : 2 : 1   Roshan's share = Rs. 270000 x 2/6   = Rs. 90000.   Answer : Rs.90000
Answer: D
If one-third of one-fourth of a number is 12, then three-tenth of that number is:
A. 35  Options:
A) 43.2
B) 87
C) 26
D) 54
E) 01

Solution: Explanation:   The number is 1/3 of 1/4 is =15 then 1/3 Ã— 1/4 = 12   Number is 144 then 144 Ã— 3/10 = 43.2   43.2nswer: 43.2
Answer: A
Three pipes A, B and C can fill a tank from empty to full in 20 minutes, 20 minutes and 30 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution P in the liquid in the tank after 3 minutes? Choose one.
A) 3/8	B) 2/8	C) 6/7	D) 3/5	E) 2/5

Solution: Part filled by (3/8 + B + C) in 3 minutes = 3(1/20 + 1/20 + 1/30) = 6/15   Part filled by 3/8 in 3 minutes = 3/20   Required ratio = 3/20 * 15/6 =3/8   3/8nswer:3/8
Answer: A
In a certain habitat, animals live in groups of two and groups of three. Each time a new animal
arrives at the habitat, it randomly chooses a group. If the chosen group has two animals in
it, the new animal joins the group forming a group of three animals. If the chosen group has
three animals in it, the new animal takes one of the animals away from the group of three and
forms a separate group of two animals.
If initially there are five animals in the habitat, and new animals arrive one at a time, what is
the probability that the fourth new animal joins a group of two animals?
Pick:
A) 1/3
B) 1/2
C) 5/9
D) 5/8
E) none of the previous choices

Solution: After the first new animal arrives there will be either three groups of 2 animals or two groups   of 3 animals. After the second new animal arrives, in both cases we will end up with two groups   of 2 animals and one group of 3 animals. The third new animal will either A: join a group of two   animals, or B: join a group of three animals. Event A happens with probability 2=3 and we end up   with one group of 2 animals and two groups of 3 animals; Event B happens with probability 1=3   and we end up with four groups of 2 animals. If event A happens, the fourth new animal joins a   group of 2 animals with probability 1=3. If event B happens, the fourth animal joins a group of 2   animals with probability 1. The probability of the fourth new animal joining a group of 2 animals   is (2=3)(1=3) + (1=3)(1) = 5=9.   correct answer 5/9
Answer: C
If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 1 year the amount to be paid is?  Select
A) 3377	B) 2688	C) 2688	D) 7800	E) 1268

Solution: A = 7500(26/25)^1 = 7800   Answer: 7800
Answer: D
A pair of toys was bought for $162 at a discount of 10%. What must be the marked price of each of the toy?  Choose the correct option: A) $300 B) $500 C) $90 D) $400 E) $600

Solution: S.P. of each of the article = 162/2= 
162/2 = 81
$81   Let M.P= $x   90% of x = 81   x = 81*100/90= 
81*100/90 = 90
$90   Answer is $90
Answer: C
33 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?  Select the correct option.
A) 22
B) 77
C) 36
D) 25
E) 13

Solution: Explanation:   Less Men, means more Days {Indirect Proportion}   Let the number of days be x   then,   27 : 33 :: 18 : x   [Please pay attention, we have written 27 : 33 rather than 33 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]   {\color{Blue} x=\frac{33\times 18}{27}}   x = 22   So 22 days will be required to get work done by 27 men.   22nswer: 22
Answer: A
Tom can hit a target 3 times in 6 shots, Karan can hit the target 2 times in 6 shots & Ashwini can hit 4 times in 4 shots. What is the probability that at least 2 shots hit the target ?	Select:  A) 1/2  B) 1/3  C) 2/3  D) 3/5  E) 3/7

Solution: Ashwini hits the target definitely, hence required probability that atleast 2 shots hit the target is given by   Karan hits tha target and Raja not hit the target.   or   Karan does not hit the target and Raja hits the target.   or.   Karan hits the target and Raja hits the target   = 2/6 x 3/6 + 4/6 x 3/6 + 2/6 x 3/6   = 24/36 = 2/3   2/3
Answer: C
A can do a piece of work in 3 days of 5 hours each and B alone can do it in 5 days of 3 hours each.how long will they take it to do working together
3/4 hours a day?  Select.
A) 6 days B) 5 days C) 10 days D) 9 days E) 8 days

Solution: A's work per hour=1/15   B's work per hour=1/15   A & B's work per hour together=(1/15)+(1/15)=2/15   so a & B together complete the work in 15/2 hours...   if they work 2 1/2=5/2 hours a day,   it will take  (15/2)/(3/4)= 
 (15/2)/(3/4) = 10
10 days...   ANSWER: 10 days
Answer: C
If (1/2)^18 (1/81)^k = 1/18^18, then k =  Answers.
A) 9
B) 12
C) 16
D) 24
E) 36

Solution: I'm going to focus on denominator only..   (2^18) . ((3^4)^k = 18^18   (2^18) . ((3^4k) = (2. 3^2)^18   (2^18) . ((3^4k) = (2^24) . (3^2)^18   hence   4k = 36   k = 9   answer 9   I hope it's quite clear
Answer: A
Will must choose a 3-character computer password, consisting of 1 letter from the alphabet and 2 distinct digits, in any order.From how many different passwords can Will choose? Choose the correct answer:	A) 390	B) 2,340	C) 4,680	D) 7,020	E) 14,040

Solution: Take the task of creating a password and break it into stages.   Stage 1: Select the one letter to be used in the code   There are 26 letters from which to choose, so we can complete this stage in 26 ways.   Stage 2: Select the two digits to be used in the code   Since the order in which we select the two digits does not matter, we can use combinations.   We can select 2 digits from 10 women in 10C2 ways (45 ways)   So, we can complete stage 2 in 45 ways   NOTE: We now have the 3 characters to be used in the code. At this point, we need to arrange those 3 characters.   Stage 3: Arrange the 3 selected characters.   RULE: We can arrange n unique objects in n! ways.   So, we can arrange the 3 characters in 3! ways (6 ways)   So we can complete stage 3 in 6 ways.   By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a password ) in (26)(45)(6) ways   (26)(45)(6) = 7020 ANS:7,020
Answer: D
A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is : Choose the most appropriate option:	A) 1/4	B) 1/10	C) 7/15	D) 8/15	E) 9/15

Solution: Explanation:   A's 1 day's work =	1/15   B's 1 day's work =	1/20   (A + B)'s 1 day's work =	(1/15 + 1/20)=7/60   (A + B)'s 4 day's work =7/60 X 4 = 7/15   Therefore, Remaining work =	1-7/15 =8/15   ANSWER IS 8/15
Answer: D
The difference of the squares of two consecutive even integers is divisible by which of the following integers ?  Select the correct option
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: Let the two consecutive even integers be 2n and (2n + 2). Then,   (2n + 2)2 = (2n + 2 + 2n)(2n + 2 - 2n)   = 2(4n + 2)   = 4(2n + 1), which is divisible by 4.   Answer: Option 4
Answer: B
A train 200 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: Choose the correct answer.
A) 45 km/hr
B) 50 km/hr
C) 77 km/hr
D) 55 km/hr
E) 56 km/hr

Solution: Speed of the train relative to man = (200/10) m/sec = 20 m/sec. [20 * (18/5)] km/hr = 72 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 72==> x = 77 km/hr.   ANSWER: 77 km/hr
Answer: C
In how many ways can 6 arts and 4 science students be arranged in a row so that the arts and the science students are placed alternately? Choices:  A) 12880  B) 11850  C) 13260  D) 15200  E) 17280

Solution: The six art students can be arranged in those 6 A-slots in 6! = 720 ways.   The four science students can be arranged in those 4 S-slots in 4! = 24 ways.   Total arrangements = 720*24= 
720*24 = 17_280
17280   Answer=(17280)
Answer: E
Nina has exactly enough money to purchase 6 widgets. If the cost of each widget were reduced by $1.5, then Nina would have exactly enough money to purchase 8 widgets. How much money does Nina have?	Choose the correct choice from the following options:
A) $22	B) $24	C) $30	D) $36	E) $40

Solution: D its is.   Let price = X   (x-1.5)8 = 6X   X= 6   hence total money = 6*6= 
6*6 = 36
36
Answer: D
1 blue dice and 2 red Dice are thrown....what is the probability that the no. appeared on blue dice is always greater than both the no. appeared on the 2 red dice..  Choose the correct choice from the following
A) 55/216
B) 56/216
C) 57/216
D) 54/216
E) 53/216

Solution: if the no. on blue dice is 2 then 2 red dice can take (1,1) value = 1^2   if the no. on blue dice is 3 then 2 red dice can take (1,1)(1,2)(2,1)(2,2) = 2^2   if the no. on blue dice is 4 then 2 red dice can take (1,1)(1,2)(2,1)(2,2)(1,3)(2,3)(3,2)(3,1)(3,3) = 3^2   Similarly, if the no. on blue dice is 5 then 2 red dice can take = 4^2   and if the no. on blue dice is 6 then 2 red dice can take = 5^2   therefor, probability = total no. of favourable outcome/total no. of possible outcome   = 1^2+2^2+3^2+4^2+5^2 / 216   = 55/216   55/216NSWER:55/216
Answer: A
The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?  Choose the correct choice.
A) 4 years
B) 8 years
C) 10 years
D) 15 years
E) None of these

Solution: Explanation:   Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years.   Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50   5x = 20 => x = 4.   Age of youngest child = x = 4 years.   4 yearsNSWER IS 4 years
Answer: A
A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?	Choose the correct answer
A) 80  B) 85  C) 90  D) 92  E) 98

Solution: Let number of notes of each denomination be x.   Then x + 5x + 10x = 480   16x = 480   x = 30.   Hence, total number of notes = 3x = 90.   90
Answer: C
It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 440 cubic metres in 5 minutes. The inner radius of the pipe should be :	Answers.
A) √2 m	B) 2 m	C) 1⁄2 m	D) 1⁄√2 m	E) None of these

Solution: Let inner radius of the pipe be r.   Then, 440 = 22⁄7 × r2 × 7 × 5   or r2=440/22×5=4   or r = √4 = 2 m   Answer 2 m
Answer: B
A and B together can complete a piece of work in 4 days.If A alone can complete the same work in 12 days, in how many days can B alone complete that work?	Choose the correct choice from the following options: A) 5 B) 7 C) 6 D) 4 E) 8

Solution: A and B's one day work=1/4   A's 1 day's work=1/12   B's 1 day's work=(1/4)-(1/12)=2/12=1/6   Hence B alone can complete the work in 6 days.   Answer is option 6
Answer: C
A metallic sheet is of rectangular shape with dimensions 48 m x 38 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:	Choose the correct choice from the following:
A) 4830 B) 5632 C) 6420 D) 7500 E) 8960

Solution: l = (48 - 16)= 
(48 - 16) = 32
32 m,   b= (38 -16)= 
(38 -16) = 22
22 m,   h= 8 m.   Volume of the box = (32 x 22 x 8) m3 = 5632 m3.   Answer: Option 5632
Answer: B
In a race of length X metres, Johnson beats Lewis by M metres and Greene by N metres, By how many metres does Lewis beat Greene in the same race ? (M<N)
Choose the most appropriate option:
A) X(X-N) / X-M
B) X(N-M) / X-M
C) X-N
D) M-N
E) M+N

Solution: As the time is constant, the ratio of distances will be the same as the ratio of speeds.   If Sj,Sl,Sg are the speeds of Johnson, Lewis, and Greene respectively, then   Sj/Sl = X/(X-M)   and Sj/Sg = X/(X-N)   => Sg/Sl = (X-N)/(X-M)   Therefore the speeds of Lewis and Greene are in the ratio (X-M)/(X-N)   When Lewis finishes the race, the time run by him and Greene are same   => The ratio of the speeds of Lewis and Greene will be the same as the ratio of distances run by them.   => Distance run by Greene when Lewis finishes the race = (X-N)/(X-M) * X   => Lewis beats Greene by X- X*(X-N)/(X-M) = X [ 1 - (X-N)/(X-M)] = X (N-M) / (X-M)   Option (X(N-M) / X-M) is therefore correct.
Answer: B
If the product of the integers a, b, c and d is 546 and if 1 < a < b < c < d, what is the value of b+c?
Pick
A) 273 B) 185 C) 21 D) 10 E) 4

Solution: Make prime factorization of 546: 546=2*3*7*13.   Now, since given that 1 < a < b < c < d, then a=2, b=3, c=7 and d=13 --> b+c=3+7= 
3+7 = 10
10.   Answer: 10.
Answer: D
What is the least value of x, so that 23x57 is divisible by 3 Pick one
A) 2 B) 0 C) 1 D) 3 E) 4

Solution: Explanation:   23257 is not divisible by 3   23057 is not divisible by 3   23157 is divisible by 3   23357 is not divisible by 3   2+3+1+5+7= 
2+3+1+5+7 = 18
18   18/3= 
18/3 = 6
6.   x= 1   Answer: Option 1
Answer: C
The average of seven numbers is 18. The average of first three numbers is 16 and the average of last three numbers is 20. What is the middle number? Choose one.
A) 20
B) 22
C) 25
D) 18
E) 24

Solution: The total of seven numbers = 7X18 = 126   The total of first 3 and last 3 numbers is = 3 X 16+3 X 20 = 108   So, the middle number is  (126 - 108 )= 
 (126 - 108 ) = 18
18   18
Answer: D
I chose a number and divide it by 4. Then I subtracted 18 from the result and got 7. What was the number I chose?  Select the correct option
A) 600
B) 100
C) 800
D) 900
E) None

Solution: Solution:   Let x be the number I chose, then   x/4âˆ’18=7   x/4=25   x=100   Answer 100
Answer: B
What are the total number of divisors of 600(including 1 and 600)? Select the correct option:  A) 4  B) 24  C) 40  D) 16  E) 20

Solution: Write the prime factorization.   600 = (2^3)(3^1)(5^2)   The number of divisors (including 1 and the number itself) is the product of one plus the exponents.   (3+1)(1+1)(2+1) = 24   ANSWER:24
Answer: B
f n = 3^3 - 2^3, which of the following is NOT a factor of n?  Pick one
A) 18
B) 19
C) 38
D) 57
E) 76

Solution: 27-8= 
27-8 = 19
19 . nineteen is prime umber and factor. any number not a multiplication of 19 is not a factor.   18
Answer: A
A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 20% while buying and by 10% while selling. What is his percentage profit? Choose the correct choice from the following choices:
A) 10.22%
B) 20.22%
C) 21.22%
D) 20%
E) Can't be calculated

Solution: The owner buys 100kg but actually gets 120kg;   The owner sells 100kg but actually gives 90kg;   Profit: (120-90)/90*100=20%   Answer: 20%.
Answer: D
If the average marks of three batches of 60, 60 and 45 students respectively is 50, 55 and 60, then the average marks of all the students is Answers:	A) 53.33	B) 54.54	C) 55	D) 57	E) None

Solution: Sol.   Required average = [60x50 + 60x55 + 45x60 / 60 + 60 + 45]   = [3000 + 3300 + 2700 / 165]   = 9000 / 165 = 54.54.   Answer 54.54
Answer: B
How many 3-digit numerals begin with a digit that represents a prime number?  Choose one
A) 16	B) 80	C) 400	D) 180	E) 240

Solution: prime digits 2,3,5 and 7.   three digit numbers _ _ _   1st place can be filled in 4 ways   2nd place can be filled in 10 ways   3rd place can be filled in 10 ways   Total=4*10*10= 
4*10*10 = 400
400   Ans : 400
Answer: C
A man sells two articles for Rs.3600 each and he gains 30% on the first and loses 30% on the next. Find his total gain or loss? Choose the correct choice from the following.
A) 9% B) 8% C) 2% D) 5% E) 3%

Solution: (30*30)/100= 
(30*30)/100 = 9
9%loss   9%nswer: 9%
Answer: A
If 133,414 cans of paint need to be placed on crates and each crate can contain at most 9 cans of paint. How many cans of paint will be on the last unfilled crate?	Select
A) 1 bottle B) 3 bottles C) 5 bottles D) 7 bottles E) 9 bottles

Solution: The number of cans of paint that can be placed on crates of 9 cans is the first number that is divisible by 9 that occurs before 133,414.   In order to divide the sum in 9 parts, the amount must be divisible by 9   Divisibility rule of 9: The sum of the digits must be divisible by 9   Sum of digits of 133,414 = 16 and 9 is divisible by 9.   Hence, we need to remove 7 to this number for it to be divisible by 9   Correct Option: 7 bottles
Answer: D
A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:
Select
A) 100 m  B) 125 m  C) 130 m  D) 150 m  E) 160 m

Solution: Explanation:   Let the length of the train be x meters and its speed be y m/sec.   They, x / y = 15 => y = x/15   x + 100 / 25 = x / 15   x = 150 m.   ANSWER IS 150 m
Answer: D
A train with 120 wagons crosses John who is going in the same direction, in 36 seconds. It travels for half an hour from the time it starts ove(who is also riding on his horse) coming from the opposite direction in 24 seconds. In how much time after the train has crossed the Mike do the John meets to Mike?rtaking the John (he is riding on the horse) before it starts overtaking the Mike Options
A) 2534
B) 3545
C) 3521
D) 4564
E) 3576

Solution: Let the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S respectively, then   ---------- (i)   and ---------(ii)   From eq.(i) and (ii)   3(R - A ) = 2 (R + K)   R = 3A + 2K   In 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers 1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the train has just crossed Sriram   = 1800 ( R - A) - 24 ( A + K)   Time required =   = (3600 - 24)= 
(3600 - 24) = 3_576
3576 s   3576
Answer: E
In a college, the ratio of the number of boys to girls is 8 : 5. If there are 225 girls, the total number of
students in the college is	Choose the correct option:
A) 420
B) 520
C) 585
D) 620
E) None of these

Solution: Explanation:   Let the boy are 8x and Girls are 5x   => 5x = 225   => x = 45   Total students = 8x+5x = 13x 8 +5= 
8 +5 = 13
13x= 13(45) = 585   Answer: 585
Answer: C
The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 9 percent, what was the annual interest rate last year?	Select the correct option:  A) 1%  B) 1.1%  C) 8.18%  D) 10%  E) 10.8%

Solution: 9=1.1*x   X=8.18%   Answer 8.18%)
Answer: C
The perimeter of a semi circle is 216 cm then the radius is? Choose the correct choice.
A) 26	B) 48	C) 98	D) 37	E) 42

Solution: 36/7 r = 216   => r   = 42   Answer: 42
Answer: E
The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?
Options
A) 290
B) 240
C) 2870
D) 289
E) 292

Solution: 4a = 68 => a = 17   172 – 82 = 152   1/2 * 16 * 30= 
1/2 * 16 * 30 = 240
240   Answer: 240
Answer: B
In a single throw with two dice, find the probability that their sum is a multiple either of 3 or 4.
Pick one.
A) 22	B) 29	C) 28	D) 10	E) 11

Solution: Answer:29
Answer: B
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?
Choices:
A) 90,180,66	B) 90,180,67	C) 90,180,61	D) 90,180,62	E) 90,180,60

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.Answer: 90,180,60
Answer: E
A sum at simple interests at 13 ½ % per year amounts to Rs.2502.50 after 4 years find the sum. Options
A) 1265
B) 1256
C) 1562
D) 1526
E) 1625

Solution: Let sum be Rs. x then , S.I.=Rs.(x*(27/2) *4*(1/100) ) = Rs.27x/50   therefore, amount = (Rs. x+(27x/50)) = Rs.77x/50   therefore, 77x/50 = 2502.50   = x = 2502.50 * 50/77= 
2502.50 * 50/77 = 1_625
1625   Hence , sum= Rs.1625.   Answer is 1625.
Answer: E
A and B walk around a circular track. They start at 9 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 11.30 a.m.? Pick.
A) 8	B) 17	C) 16	D) 15	E) 3

Solution: Sol.   Relative speed = (2 + 3)= 
(2 + 3) = 5
5 rounds per hour.   So, they cross each other 5 times in an hour and 2 times in half an hour.   Hence, they cross each other 17 times before 11.30 a.m.   Answer 17
Answer: B