MU-NLPC/Calc-aqua_rat huggingface dataset:
A magician has five animals in his magic hat: 3 doves and 2 rabbits. If he pulls two animals out of the hat at random, what is the chance W that he will have a matched pair?  Choose the correct choice: A) W=2/5 B) W=3/5 C) W=1/5 D) 1/2 E) 7/5

Solution: P(both doves) + P(both rabbits) = p(matched pair)   (3/5)*(2/4) + (2/5)*(1/4) = 2/5   Hi How did you get the probability 2/4 and 1/4???   You have 3 doves and 2 rabbits i.e. a total of 5 animals.   The probability that you pick a dove on your first pick is 3/5 (since there are 3 doves)   The probability that you pick a dove on your second pick too is 2/4 (because now only 2 doves are left after we picked a dove in the first pick. ALso only 4 animals are left to choose from)   Similarly,   The probability that you pick a rabbit on your first pick is 2/5 (since there are 2 rabbits)   The probability that you pick a rabbit on your second pick too is 1/4 (because now only 1 rabbit is left after we picked a rabbit in the first pick. W=2/5lso only 4 animals are left to choose from)   Probability of picking a matched pair = 3/5 * 2/4 + 2/5 * 1/4 = 2/5
Answer: A
A trader bought a car at 20% discount on its original price. He sold it at a 40% increase on the price he bought it. What percent of profit did he make on the original price? Choose the correct choice from the following options.
A) 18%
B) 22%
C) 12%
D) 92%
E) 14%

Solution: Original price = 100   12%P = 80   S = 80*(140/100)= 
80*(140/100) = 112
112   100 - 112= 12%   Answer: 12%
Answer: C
M is the sum of the reciprocals of the consecutive integers from 601 to 700, inclusive. Which of the following is true? Answers.
A) 1/7 < M < 1/6
B) 1/5 < M < 1/3
C) 1/7 < M < 1/5
D) 1/9 < M < 1/7
E) 1/12 < M < 1/9

Solution: M = 1/601 + 1/602 + 1/603 + ...... + 1/700   If we replace the first 99 terms by 1/700, then we get a sum = 100/700 = 1/7. Since the actual terms are larger than 1/700, the sum is larger than 1/7.   If we replace the all the 100 terms by 1/600, we get a sum = 100/600 = 1/6. Since the actual terms are smaller than 1/600, the sum is less than 1/6.   Therefore 1/7 < M < 1/6   Choice 1/7 < M < 1/6
Answer: A
Donovan and Michael are racing around a circular 300-meter track. If Donovan runs each lap in 45 seconds and Michael runs each lap in 40 seconds, how many laps will Michael have to complete in order to pass Donovan, assuming they start at the same time? Pick:
A) 6 B) 9 C) 8 D) 7 E) 10

Solution: One way of approaching this question is by Relative speed method   1. Speed/ Rate of Donovan = Distance/ time => 300/45 =>60/9   2. Speed/ Rate of Michael = Distance/ time => 300/40 => 30/4   Relative Speed between them =30/4 - 60/9 => 270 -240/36 = 30/36 =5/6 (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 = 300, Relative Rate = 5/6   Total Time taken by Micheal to surpass Donovan = Distance / rate => 300*6/5 => 1800/5= 
1800/5 = 360
> 360   No. of laps taken by Michael= Total time / Michael's rate => 360/40= 
360/40 = 9
> 9   Hence correct answer is 9 Laps.   9
Answer: B
A wheel rotates 10 times every minute and moves 40 cm during each rotation. How many metres does
the wheel move in one hour?
Select the correct option
A) 123 metre
B) 240 metre
C) 120 metre
D) 1200 metre
E) 2200 metre

Solution: Expl : Number of times wheel moves in 1 hour = 10 * 60= 
10 * 60 = 600
600   :. Distance moves= (600 *40)= 
(600 *40) = 24_000
24000 cm   In metres= 240 metre   Answer: 240 metre
Answer: B
The speed of a boat in still water is 50kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?  Pick one.
A) 70,30 kmph B) 80,40 kmph C) 10,40 kmph D) 80,80 kmph E) 84,40 kmph

Solution: Speed downstream = 50 + 20= 
50 + 20 = 70
70 kmph   Speed upstream= 50 - 20= 
50 - 20 = 30
30 kmph   70,30 kmphnswer: 70,30 kmph
Answer: A
A certain violet paint contains 30 percent blue pigment and 70 percent red pigment by weight. A certain green paint contains 50 percent blue pigment and 50 percent yellow pigment. When these paints are mixed to produce a brown paint, the brown paint contains 40 percent blue pigment. If the brown paint weighs 10 grams, then the red pigment contributes how many grams of that weight?  Choose the most appropriate option.
A) 2.8 B) 3.5 C) 4.2 D) 5 E) 7

Solution: 10 Grams of combined mixture and 40% blue pigment means that the mixtures were mixed 50% each.   Thus 5 grams a piece. Out of the 5 grams of the violet paint, 70% is red.   Therefore, 5*.7 = 3.5 Grams of red pigment   ANSWER:3.5
Answer: B
Arun and Amit started walking from two different points 'A' and 'B' respectively.Arun walks 2 kms North and turns to the East and walks 3 kms and again turns to North walks 4 kms and finally turns to East and Walks 5kms to reach point 'C'. Similarly, Amit walks 2 kms North and turns to west and walks 3 kms and finally turns to North, walks 4 kms and meets Arun at point 'C'. What is the distance between Arun and Amit's starting points?	Answers
A) 5 km B) 8 km C) 11 km D) 13 km E) 15 km

Solution: Explanation:   Where A= Arun's starting point; B = Amit's starting point; C = The point where Arun and Amit meet   PQ + RC + ST = 3 + 5 + 3= 
3 + 5 + 3 = 11
11 kms.   ANSWER IS 11 km
Answer: C
Find the missing number in the given sequence : 1,2,3,5,?,13,21,?
Select the correct option:
A) 8 & 34
B) 7 & 34
C) 9 & 34
D) 7 & 35
E) 7 & 36

Solution: 1+2= 
1+2 = 3
3   2+3= 
2+3 = 5
5   3+5= 
3+5 = 8
8   5+8= 
5+8 = 13
13   8+13= 
8+13 = 21
21   13+21= 
13+21 = 34
34   8 & 34NSWER:8 & 34
Answer: A
The average of 11 numbers is 9.6. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?	Choose the correct answer:
A) 9.5 B) 10 C) 10.5 D) 11.5 E) 25.8

Solution: 25.8xplanation:   1 to 11 = 11 * 9.6= 
11 * 9.6 = 105.6
105.6   1 to 6= 6 * 10.5= 
6 * 10.5 = 63
63   6 to 11= 6 * 11.4= 
6 * 11.4 = 68.4
68.4   63 + 68.4= 
63 + 68.4 = 131.4
131.4 – 105.6= 25.8   6th number = 25.8   Option 25.8
Answer: E
Set C consists of 19 elements. The average of set C is L. If a new element is added to the set and the average grows by K, what is the value of the new element?	Choose the correct choice
A) a) L(1 + K / 5)
B) b) L * (K/100) - 20L
C) c) 20L(1+K/100)
D) d) 20(1+K/100)-19L
E) e) L*(K/5)-19

Solution: Let's assume the value of new element to bea. So converting the word problem into equation,   (19*L + a) / (19 + 1) = L + k ==> after solving the equation we will get a (value of newly added element) = L + 20K   But according to the answer options, problem writer wanted to conveyk% percent rise in average value.   If we consider this case than resulting equation will be,   (19*L + a) / ( 19+1 ) = L + (K/100)*L ==> 19L + a = 20 [ L + KL/100]   ==> a= 20L + KL/5 -19L   ==> a= L + KL/5 , which is equivalent to option [a) L(1 + K / 5)]
Answer: A
Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/6, 1/2 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?
Choose the correct choice from the following.
A) 1/32	B) 7/8	C) 9/64	D) 5/64	E) 3/64

Solution: P(Xavier will solve)=1/6   P(Yvonne will solve)=1/2   P(Zelda will NOT solve) = 1- 5/8 = 3/8.   Now, we need to multiply all this Ps to find an answer:   p= (1/6)*(1/2)*(3/8) = 1/32.   Ans. 1/32.
Answer: A
The bankers discount and the true discount of a sum at 15% per annum simple interest for the same time are Rs.120 and Rs.60 respectively. What is the sum and the time? Choices
A) Sum = Rs.160 and Time = 6.6 years
B) Sum = Rs.120 and Time = 6.6 years
C) Sum = Rs.140 and Time = 6.6 years
D) Sum = Rs.200 and Time = 6 years
E) None of these

Solution: Explanation :   BD = Rs.120   TD = Rs.60   R = 15%   F = BD ×TD/(BD – TD)=120×60/(120–60)=120×60/60=Rs. 120   Sum = Rs.120 and Time = 6.6 yearsD = Simple Interest on the face value of the bill for unexpired time =FTR/100   ⇒120 = (120×T×15)/100   ⇒1200 = 12 × T × 15 ⇒100 = 15 × T   ⇒ T = 100/15 = 6.6 years Answer : Option Sum = Rs.120 and Time = 6.6 years
Answer: B
Anil can do a work in 15 days while Sunil can do it in 25 days. How long will they take if both work together? Choose the correct option:	A) 9 3/6	B) 9 3/4	C) 9 3/8	D) 5 3/2	E) 9 3/2

Solution: 1/15 + 1/25 = 8/75   75/8 = 9 3/8 days   Answer:9 3/8
Answer: C
There are 18 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station? Pick one
A) 987
B) 177
C) 357
D) 267
E) 380

Solution: The total number of stations = 20   From 20 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in ²⁰P₂ ways.   ²⁰P₂ = 20 * 19= 
20 * 19 = 380
380.   Answer:380
Answer: E
A sells a bicycle to B and makes a profit of 25%. B sells the same bicycle to C at a profit of 25%. If the final S.P. of the bicycle was Rs. 225, find out the cost price of the bicycle for A. Choose the most appropriate option.
A) 237	B) 126	C) 971	D) 611	E) 144

Solution: 144xplanation:   Let CP be 100   A sells at 25% profit so SP=125   B sells at 25% profit = 125 x (1+25/100) = 156.25   CP SP   100--- 156.25   x --- 225   CP = 225 x 100/156.25 = 144   ANSW144R: 144
Answer: E
Average of first five multiples of 4 is Choose the correct choice from the following choices.
A) 12 B) 11 C) 13 D) 15 E) 16

Solution: Explanation:   12verage=4(1+2+3+4+5)/5=12   12nswer: Option 12
Answer: A
A card shop contains 5 birthday cards, 4 holiday cards, and 3 graduation cards. If three cards are purchased at random from the shop, what is the probability that the three cards will be graduation cards? Pick:  A) 1/33  B) 6/264  C) 1/44  D) 1/264  E) 1/1320

Solution: It doesn't matter which type of card you choose, so:   Probability of choosing 1st card: 3/12   Probability of choosing 2nd card of the same type: 2/11   Probability of choosing 3rd card of the same type: 1/10   Multiply and you get 1/264   Answer 1/264.
Answer: D
A train crosses a platform of 180 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
Select the correct option
A) 30 B) 887 C) 167 D) 197 E) 161

Solution: Length of the train be ‘X’   X + 180/15 = X + 250/20   20X + 3600 = 15X + 3750   5x=150   X = 30m   30nswer: 30
Answer: A
Each night before he goes to bed, Jordan likes to pick out an outfit to wear the next day. He has 12 different shirts, 10 different pairs of jeans, and 5 pairs of sneakers. If an outfit consists of 1 shirt, 1 pair of jeans, and 1 pair of sneakers, how many different outfits does Jordan have? Choose the most appropriate option:
A) 30
B) 90
C) 600
D) 480
E) 960

Solution: Total # of outfits = 12 * 10 *5= 
12 * 10 *5 = 600
600   Answer - 600
Answer: C
A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
Choices
A) 2/28  B) 2/27  C) 2/21  D) 2/89  E) 2/11

Solution: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³2/21₂/¹⁵2/21₂ = (3 * 2)/(15 * 14) = 1/35   Probability that both are yellow = ²2/21₂/¹⁵2/21₂ = (2 * 1)/(15 * 14) = 1/105   Probability that one blue and other is yellow = (³2/21₁ * ²2/21₁)/¹⁵2/21₂ = (2 * 3 * 2)/(15 * 14) = 2/35   Required probability = 1/35 + 1/105 + 2/35   = 3/35 + 1/105 = 1/35(3 + 1/3)   = 10/(3 * 35)   = 2/21   Answer: 2/21
Answer: C
A bag contains 10 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is  Answers.
A) 8/15
B) 21/44
C) 3/5
D) 11/15
E) 7/15

Solution: Drawing two balls of same color from ten green balls can be done in 10C₂ ways.   Similarly from eight white balls two can be drawn in ⁸C₂ ways.   P = 10C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂ = 21/44   ANSWER:21/44
Answer: B
Each of three charities in Novel Grove Estates has 8 persons serving on its board of directors. If exactly 4 persons serve on 3 boards each and each pair of charities has 5 persons in common on their boards of directors, then how many distinct persons serve on one or more boards of directors?
A.
B.
C.
D.
E. Choose the correct choice from the following choices:
A) 8 B) 13 C) 16 D) 24 E) 27

Solution: Each group has 8 = 8+8+8= 
8+8+8 = 24
24 max   4 people are in 2 groups, subtract 4 people twice as they are counted twice   Each pair of groups has 5 in common, so in addition to the 4 people subtract 1 from each group   Ans: 8+8+8-(2(4)) - 3= 13   ANSWER:13
Answer: B
What approximate value should come in place of the question mark (?) in each of the following equations ?
27.874 x 15.01 3 = ?	Choose the correct choice from the following.
A) 135
B) 137
C) 139
D) 28
E) 27

Solution: Explanation :   27.9 x 15 3 = 27 - 9 x 5 = 139.5   Answer : Option 139
Answer: C
Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 8160, how much money did he borrow?  Pick one:	A) 8000	B) 2787	C) 27766	D) 9976	E) 21671

Solution: Let the sum be Rs. x. Then,   [(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 8160   18x + 45x + 39x = (8160 * 100)   102x = 816000 => x = 8000.   8000nswer: 8000
Answer: A
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was?
Choose the most appropriate option:	A) 9 years	B) 10 years	C) 11 years	D) 14 years	E) 16 years

Solution: Let the son's present age be x years. Then, (38 - x) = x   2x = 38.   x = 19.   Son's age 5 years back (19 - 5)= 
(19 - 5) = 14
14 years.   14 years)
Answer: D
If the sides of a triangle are 28 cm, 26 cm and 12 cm, what is its area?  Choose the correct answer
A) 120 cm2	B) 156 cm2	C) 178 cm2	D) 189 cm2	E) 176 cm2

Solution: The triangle with sides 28 cm, 26 cm and 12 cm is right angled, where the hypotenuse is 28 cm.   Area of the triangle   = 1/2 * 26 * 12= 
1/2 * 26 * 12 = 156
156 cm2   Answer: 156 cm2
Answer: B
A pipe can fill the tank in 5 hours. Due to leakage at the bottom it is filled in 6 hours. When the tank is full, in how much time will it be empties by the leak? Choose the correct choice from the following choices:
A) 30 hours	B) 28 hours	C) 27 hours	D) 25 hours	E) 24 hours

Solution: When there is no leakage, the pipe can fill the cistern in 5 hours.   Therefore, The pipe fills 1/5 th part of the tank in one hour.   When there is a leakage, the pipe can fill the cistern in 6 hours.   In case of leakage, the pipe fills 1/6 th part of the tank in one hour.   So, in 1 hour due to leakage (1/5 – 1/6) th   = (6 – 5)/30 th   = 1/30 th   The part of the tank is emptied.   So, the tank will be emptied by leakage in 30 hours.   answer :30 hours
Answer: A
There are 10 people and 7 chairs. In how many different ways people can occupy the chairs?	Choose the correct choice from the following options:  A) 800  B) 810  C) 820  D) 830  E) 840

Solution: number of ways = 10*9*8*7= 
10*9*8*7 = 5_040
5040   Answer is 820
Answer: C
A company decreased the price of its main product by 30%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product?
Pick:	A) 1.26	B) 2.54	C) 5.23	D) 4.23	E) 3.33

Solution: For the total revenue to remain the same when the price is 3/10, the number of products sold must 3/10 times. Therefore increase in the number of products sold is 100%   => The required ratio = 100%/30% = 3.33   Answer : 3.33
Answer: E
What is the greatest positive integer R such that 3^R is a factor of 9^10? Pick:
A) R=5 B) R=9 C) R=10 D) R=20 E) 30

Solution: What is the greatest positive integer R such that 3^R is a factor of 9^10?   9^10 = (3^2)^10 = 3^20   D. 20
Answer: D
there are digits from 1 to 6 .from that 5 digit no are to be formed such that they are divisible by 4. find no of possible combinations?  Answers
A) 1944 ways.  B) 1844 ways.  C) 1744 ways.  D) 1644 ways.  E) 1544 ways.

Solution: A) w/o repeatations.   possible last two digits= 12, 16, 24, 32, 36, 52, 56, 64   so total of 8 ways to fill last two digit.   remaining 3 digits can be filled by  (6-2)= 
 (6-2) = 4
4! ways=24 ways   so total no of ways=24*8= 
24*8 = 192
192 ways.   B)with repeataions   possible last two digits= 12, 16, 24, 32, 36,44, 52, 56, 64   so total of 9 ways to fill last two digit.   remaining 3 digits can be filled by  6*6*6= 
 6*6*6 = 216
216 ways   so total no of ways=216*9= 
216*9 = 1_944
1944 ways.   1944 ways.NSWER:1944 ways.
Answer: A
Students are partnered in the class and are given stickers for their behavior. Green stickers are for good behavior, yellow stickers are for okay behavior, and red stickers for for behavior requiring discipline. The students' desks are labeled A, B, C, and D. If A:B = green/yellow, B:C = yellow/red, C:D = red/student absent no sticker, and then D:A are partnered. What will D:A sticker color be if behavior does not change?  Choose the most appropriate option.
A) green only B) yellow only C) red only D) A & C E) none of the above

Solution: Solution   A : B = green : yellow, B : C = yellow : red, C : D = red : student absent no sticker   âˆ´Aâˆ¶Bâˆ¶Câˆ¶D= green : yellow : red : student absent no sticker.   Thus, green only : D = green : student absent no sticker Or D : green only = student absent no sticker: green   Correct Option green only
Answer: A
If p is an even integer and q is an odd integer, which of the following must be an even integer?
Choices
A) 2p-q B) 3p+2q-1 C) p+q D) 3p-q E) 3p-2q

Solution: p is even; for this assume p=2   q is odd; for this assume q = 1   (2*2)-1= 
(2*2)-1 = 3
3 Odd    (3*2)+(2*1)-1= 
 (3*2)+(2*1)-1 = 7
7 Odd    2+1= 
 2+1 = 3
3 Odd    (3*2)-1= 
 (3*2)-1 = 5
5 Odd    (3*2)-(2*1)= 
 (3*2)-(2*1) = 4
4 3p-2qven   Answer:3p-2q
Answer: E
Difference between the length &breadth of a rectangle is 5 m. If its perimeter is 45 m, then its area is??
Choose the correct choice from the following options.
A) 500 m^2	B) 2340 m^2	C) 2520 m^2	D) 2556 m^2	E) 2534 m^2

Solution: We have: (l - b) = 5 and 2(l + b) = 90 or (l + b) = 45   2l = 50 => l = 25 & b = 20   area = 25 * 20= 
25 * 20 = 500
500 m^2   500 m^2nswer : 500 m^2
Answer: A
Carl is facing very difficult financial times and can only pay the interest on a $20,000 loan he has taken. The bank charges him a quarterly compound rate of 5%. What is the approximate interest he pays annually?  Choose one.
A) $1200 B) $2000 C) $2150 D) $4000 E) $12000

Solution: Usually, you are given the annual rate of interest and it is mentioned that it is annual rate.   The bank charges him a quarterly compounded ANNUAL rate of 20%.   Here you find per quarter rate as  (20/4)= 
 (20/4) = 5
5%   I have actually never seen a question with quarter rate given but since this question did not mentionannual rate of interestand since the options did not make sense with 5% annual rate of interest, it is apparent that the intent was a 5% quarterly rate. So the bank charges 5% every quarter and compounds it in the next quarter. Had it been a simple quarterly rate, we would have just found 4 * 5% of 20,000= $4000 as our answer.   But since, the interest is compounded, it will be a bit more than $2000. Option ($4000) looks correct.
Answer: D
A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 280-mile journey? Assume that the train makes no intermediate stops.  Pick:
A) 8
B) 7
C) 9
D) 7.5
E) 6

Solution: A train travels at the rate of 10 miles/hr for the first hour of a trip, at 20 miles/hr for the second hour, at 30 miles/hr for the third hour and so on. How many hours will it take the train to complete a 280-mile journey? Assume that the train makes no intermediate stops.   I think the easiest way to solve this problem would be simply to count the number of miles it travels per hour (and in total)   Hour miles/hour Total miles   1 10 10   2 20 30   3 30 60   4 40 100   5 50 150   6 60 210   7 70 280   It takes a total of nine hours to cover the 280 mile distance.   ANSWER: 7
Answer: B
A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 5 rounds per hour and 5 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m. ?  Choose one:	A) A)5	B) B)6	C) C)8	D) D)15	E) E)9

Solution: Relative speed = 5 + 5= 
5 + 5 = 10
10 rounds per hour.   So, they cross each other 10 times in an hour and 5 times in half an hour.   Hence, they cross each other 15 times before 9.30 a.m.   ANSWER:15
Answer: D
Elena purchased Brand X pens for $4.00 apiece and brand Y for $2.20 apiece. If Elena purchased a total of 12 of these pens for $42.00, how many brand X pens did she purchase? Choose the correct choice from the following answers:
A) 4	B) 5	C) 6	D) 7	E) 8

Solution: 4x+2.8y=42 --> multiply by 2.5 (to get the integers) --> 10x+7y=105 --> only one positive integers solutions x=6 and y=5 (how to solve: 7y must have the last digit of 5 in order the last digit of the sum to be 5).   Answer: 6.
Answer: C
Fill in the sequence:
1 2 3 2 1 2 3 4 2 ?	Choose the correct option.
A) 5	B) 4	C) 3	D) 2	E) 1

Solution: 1   1   Number of characters used in writing the numbers in roman numerals
Answer: E
The ratio of the volumes of two cubes is 729 : 1000. What is the ratio of their total surface areas?  Choices:
A) 1:12
B) 81:13
C) 46:51
D) 86:16
E) 56:13

Solution: Ratio of the sides   = ³√729 : ³√1000 = 9 : 10   Ratio of surface areas   = 92 : 102 = 46:51   Answer:46:51
Answer: C
Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science? Choices
A) 18 B) 87 C) 57 D) 17 E) 16

Solution: S:E = 1:3   E:M = 3:5   ------------   S:E:M = 3:9:15   3/27 * 162= 
3/27 * 162 = 18
18   18nswer: 18
Answer: A
A half of Arunâ€™s marks in mathematics exceed a third of his marks in English by 50.If he got 250 marks in two subjects together how many marks did he got in English?  Select the correct option:
A) 120,60	B) 160,90	C) 180,90	D) 190,40	E) None of them

Solution: Let Arunâ€™s marks in mathematics and english be x and y   Then (1/2)x-(1/3)y=50   3x-2y=300â€¦â€¦>(1)   x+y=250â€¦â€¦.>(2)   solving (1) and (2)   x=160   and y=90   Answer is 160,90.
Answer: B
How many prime numbers between 1 and 100 are factors of 7,150?	Choose the correct choice from the following answers.
A) One  B) Two  C) Three  D) Four  E) Five

Solution: Make prime factorization of 7,150 --> 7,150=2*5^2*11*13. So 4 prime numbers between 1 and 100 (namely 2, 5, 11, and 13) are factors of 7,150 (you shouldn't count one prime factor twice).   Answer: Four.
Answer: D
In simple interest what sum amounts of Rs.1120/-in 4 years and Rs.1200/-in 5 years ?  Pick:
A) Rs. 500
B) Rs. 600
C) Rs. 800
D) Rs. 900
E) Rs. 700

Solution: For 1 year interest= 1200-1120= 
1200-1120 = 80
80   for 4 year 320   then sum= 1120-320= 
1120-320 = 800
800   ANSWER:Rs. 800
Answer: C
Which of the following describes all values of x for which 36-x^2 ≥ 0 ?  Choose the most appropriate option
A) x ≥ 1
B) x ≤ -1
C) 0 ≤ x ≤ 1
D) x ≤ -1 or x ≥ 1
E) -6 ≤ x ≤ 6

Solution: 36-x^2 >= 0 ---> x^2-36<=0   --> (x+6)(x-6)<=0   Above equation true for   i) x+6<=0 and x-6>=0 ---> x<= -6 and x>=6 ---> this is not possible ---Strike out this solution   ii) x+6>=0 and x-6<=0 ---> x>=-6 and x<=6 --> -6<=x<=6   Answer -6 ≤ x ≤ 6
Answer: E