MU-NLPC/Calc-aqua_rat huggingface dataset:
John takes 18 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?
Select:  A) 2 hours, 10 minutes  B) 2 hours, 30 minutes  C) 3 hours, 10 minutes  D) 3 hours, 45 minutes  E) 4 hours, 10 minutes

Solution: The rate of John plus Bill is 1/18 + 1/6 = 4/18 of the job completed per hour.   If Steve worked at the same rate as John, the rate would be 4/18 + 1/18 = 5/18   The slowest possible time would be 18/5 hours = 3 hours, 36 minutes.   If Steve worked at the same rate as Bill, the rate would be 4/18 + 1/6 = 7/18   The fastest possible time would be 18/7 hours = 2 hours + 4/7 hours.   The actual time is somewhere between these two extreme points.   The answer is 3 hours, 10 minutes.
Answer: C
If the speed of Y meters per minute is equivalent to the speed of X kilometers per hour, what is X in terms of Y? (1 kilometer=1000 meters)
Choose the correct choice from the following answers:
A) 15y/18	B) 6y/5	C) 18y/5	D) 6y/100	E) 3600000y

Solution: If the speed of Y meters per second is equivalent to the speed of X kilometers per hour, what is X in terms of Y? (1 kilometer=1000 meters)   We need to find an equation with y in the answer...   convert all measurements so they are alike (i.e. convert km to m, minutes to hours, etc)   Speed = y/t   y meters/second   (60) x meters/hour   Speed = x/t   x KM/hour   Speed = x(1000m)/hour   x(1000meters)/hour = (60) x meters/hour   x(1000)/1hour = y(60) / 1 hour   x(1000) = y(60)   x = 0.06y   Answer: D. 6y/100
Answer: D
An item is being sold for $10 each. However, if a customer will “buy at least 3” they have a promo discount of 17%. Also, if a customer will “buy at least 10” items they will deduct an additional 8% to their “buy at least 3” promo price. If Sam buys 10 pcs of that item how much should he pay?
Answers
A) $92.00	B) $88.00	C) $87.04	D) $80.96	E) $75.00

Solution: Without any discount Sam should pay 10*10= 
10*10 = 100
$100. Now, the overall discount would be slightly less than 27%, thus he must pay slightly more than $73. Only answer choice E fits.   Answer: $75.00
Answer: E
A string of 15 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T? Choose the correct choice
A) 1 - (0.94)^15  B) (0.06)^15  C) 1 - (0.06)^15  D) (0.94)^15  E) 0.06^150

Solution: The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.   The opposite event is when none of the 15 light bulbs fails, since the probability of each light bulb not to fail is 1-0.06= 
1-0.06 = 0.94
0.94 the probability that none of the 15 light bulbs fails is 0.94^15.   Hence, the probability that at least one light bulb fails is 1-0.94^15.   Answer: A.   Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 15, then according to your logic the probability that the string of light bulbs will fail would be 100*0.06= 
100*0.06 = 6
6, which is not possible since the probability of an event cannot be more than 1 (100%).
Answer: A
A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train? Choose the correct choice:	A) 28.9 km/hr	B) 89.9 km/hr	C) 28.9 km/hr	D) 79.2 km/hr	E) 19.9 km/hr

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 8 => x = 8y   (x + 264)/20 = y   y = 22   Speed = 22 m/sec = 22 * 18/5= 
22 * 18/5 = 396/5 = around 79.2
79.2 km/hr.   Answer:79.2 km/hr
Answer: D
Andrew purchased 7kg of grapes at the rate of 68 per kg and 9 kg of mangoes at the rate of 48 per kg. How much amount did he pay to the shopkeeper?	Choose the most appropriate option:
A) 1000  B) 908  C) 930  D) 1075  E) 1080

Solution: Cost of 7 kg grapes = 68 × 7 = 476.   Cost of 9 kg of mangoes = 48 × 9 = 432.   Total cost he has to pay = 476 + 432= 
476 + 432 = 908
908   908
Answer: B
If x and y are different integers and x^2 = xy, which of the following must be true ?
I. y = 0
II. x = 0
III. x = y	Choose the most appropriate option
A) I only  B) II only  C) III only  D) I and III only  E) II, and III

Solution: Answer choice A is correct.   The question gives you x^2=xy   you can simplify that as x^2-xy=0   x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.   Answer II, and III
Answer: E
If f(x) = -*5 (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?
Choose the correct option.
A) f(x)	B) -f(x)	C) 1/f(x)	D) 5f(x)	E) 2*f(x)

Solution: -5*f(1/x) =-5* ((1/x)^4 - 1) / ((1/x)^2)   = -5*((1/x^4) - 1) / (1/x^2)   = -5*((1-x^4)/(x^4)) / (1/x^2)   = -5* (1-x^4)/(x^2)   = -5* ( (x^4) -1) / (x^2)   = 5f(x)   Answer is 5f(x).
Answer: D
The cost of fencing a square field @ Rs. 20 per metre is Rs.10.080.How much will it cost to lay a three meter wide pavement along the fencing inside the field @ Rs. 50 per sq m	Choices
A) 73828  B) 73829  C) 73811  D) 73800  E) 73129

Solution: perimeter = total cost / cost per m = 10080 /20= 
10080 /20 = 504
504m   side of the square= 504/4= 
504/4 = 126
126m   breadth of the pavement= 3m   side of inner square = 126 - 6= 
126 - 6 = 120
120m   area of the pavement= (126 x126) - (120 x 120) = 246 x 6 sq m   cost of pavement = 246*6*50 = Rs. 73800   Answer: 73800
Answer: D
In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 50 questions and secures 130 marks, the no of questions he attempts correctly is :
Choose the correct option:
A) A)36
B) B)38
C) C)90
D) D)88
E) E)37

Solution: Let the number of correct answers be X.   Number of incorrect answers = (60 – X).   4x – (50 – x) = 130   => 5x = 180   => x = 36   36nswer:36
Answer: A
How many cones of radius 4 m, height 2 m can be formed from a cylinder of 12 m radius, 10 m height:	Select the correct option
A) 135  B) 125  C) 145  D) 115  E) 155

Solution: (Cylinder volume)/(Cone volume)   (πr(power2)h)/(1/3 πr(power2)h)   = (π × 12 × 12 × 10)/(1/3 π × 4 × 4 × 2) = 135   135nswer is 135.
Answer: A
A sum at simple interests at 13 ½ % per annum amounts to Rs.2502.50 after 4 years find the sum.
Select the correct option:
A) Rs.1645. B) Rs.1675. C) Rs.1625. D) Rs.1635. E) Rs.1655.

Solution: Let sum be Rs. x then , S.I.=Rs.(x*(27/2) *4*(1/100) ) = Rs.27x/50   amount = (Rs. x+(27x/50)) = Rs.77x/50   77x/50 = 2502.50  x = (2502.50 * 50)/77= 
(2502.50 * 50)/77 = 1_625
1625   Hence , sum= Rs.1625.   Answer is Rs.1625..
Answer: C
Frank is 14 years younger then John. In 5 years John will be twice as old as Frank. How old will Frank be in four years?  Pick one.
A) 8	B) 10	C) 13	D) 14	E) 16

Solution: Frank is 15 years younger then John --> F+14=J;   In 5 years John will be twice as old as Frank (in 5 year John will be J+5 years old and Frank will be F+5 years old) --> J+5=2*(F+5) --> (F+14)+5=2*(F+5) --> F=9;   In 4 years Frank will be 9+4= 
9+4 = 13
13 years old.   Answer: 13.
Answer: C
A room contains 160 people, 20 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
Answers.
A) 10
B) 20
C) 40
D) 60
E) 80

Solution: Say group of x people left the room.   # of women in the room was 0.2*160= 
0.2*160 = 32
32;   # of women in the group that left 0.3x;   # of women in the room after the group left it is 0.1(160-x);   So, 32-0.3x= 0.1(160-x) --> x=80.   Answer: 80.
Answer: E
A 250 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ? Choose the correct answer
A) 41.1 sec
B) 20.2 sec
C) 31.8 sec
D) 50.4 sec
E) none of the above

Solution: Speed = 55 Km/hr   (to convert km/hr in to M/s)   = 55 x 5/18 M/s   50.4 secistance = 250 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )   = 770 m   Time = 50.4 secistance / Speed   = 770 x 18 / (5 x 55)   = 50.4 sec   Ans is :50.4 sec
Answer: D
The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:  Choose the correct answer:
A) 5:2  B) 7:3  C) 9:2  D) 10:4  E) 13:4

Solution: Let the ages of father and son 10 years ago be 3x and x years respectively.   Then, (3x + 10) + 10 = 2[(x + 10) + 10]   3x + 20 = 2x + 40   x = 20.   Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3.   Answer: Option 7:3
Answer: B
In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?
Select.
A) 67 kg. B) 68 kg. C) 69 kg. D) Data inadequate E) None of these

Solution: EXPLANATION   Let Arun’s weight by X kg.   According to Arun, 65 < X < 72   According to Arun’s brother, 60 < X < 70.   According to Arun’s mother, X <= 68   The values satisfying all the above conditions are 66, 67 and 68.   Required 67 kg.verage =( 66 + 67 + 68 /3 )= (201/3)= 
(201/3) = 67
67 kg   67 kg.nswer 67 kg.
Answer: A
A crate of apples contains 1 bruised apple for every 30 apples in the crate. Two out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate?
Options:
A) 720	B) 360	C) 480	D) 600	E) 840

Solution: as given 2 out of every 4 bruised apple is not fit to sell   or, 50% of the bruised apples are not fit to sell.   as per the question 12 are not fit to sell   or,   0.0.5x=12   x=1200/50= 
1200/50 = 24
24   thus total number of bruised apples=24   total number of apples =30*24= 
30*24 = 720
720   720nswer:720
Answer: A
A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 5 days starting with sunday is	Answers
A) 1215
B) 1314
C) 2900
D) 1710
E) 2750

Solution: Explanation:   As the month begin with sunday, so there will be five sundays in the month. So result will be:   =(510×5+240×25/30)=(8550/5)= 
(8550/5) = 1_710
1710   Answer: Option 1710
Answer: D
If 2n+4 - 2n+2 = 3, then n is equal to :	Choose the correct option: A) 2 B) -2 C) 1 D) -1 E) None

Solution: Sol.   2n+4 - 2n+2 = 3 ⇔ 2n+2 (22 - 1) = 3 ⇔ 2n+2 = 1 = 20   ⇔ n+2 = 0 ⇔ n= -2.   Answer -2
Answer: B
Which of the following is true about 0<|x|-x/2<5?	Choose one.
A) -1<x<0	B) 0<x<1	C) 1<x<2	D) 2<x<3	E) 3<x<4

Solution: when can be |x|-4x be greater than 0..   NEVER when x is positive..   ONLY A is left..   you can also substitute any value within the given range to check for answer   Example - put x as -0.5 for A. -1<x<0..   so |x|-x/2 = |-0.5|- (-0.5)/2 = 0.75 and it satisfies 0<|x|-4x<5   -1<x<0
Answer: A
A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Choose the most appropriate option
A) 6 kmph  B) 5 kmph  C) 2 kmph  D) 8 kmph  E) 1 kmph

Solution: Speed downstream = d/t = 85/(2 1/2) = 34 kmph   Speed upstream = d/t = 45/(2 1/2) = 18 kmph   The speed of the stream = (34 - 18)/2= 
(34 - 18)/2 = 8
8 kmph   Answer:8 kmph
Answer: D
In a games hour 4 different types of players came to the ground? cricket 22, hokey 15, football 21, softball 19. How many players are present in the ground?  Choices.
A) 70
B) 52
C) 62
D) 77
E) 79

Solution: total number of players= 22+15+21+19= 
22+15+21+19 = 77
77   Answer is 77
Answer: D
A man buy a book in Rs50 & sale it Rs90. What is the rate of profit ???	Choose the correct choice from the following choices.
A) 10%
B) 80%
C) 30%
D) 25%
E) 28%

Solution: cp=50   sp=90   profit=90-50= 
90-50 = 40
40   %=40/50*100= 
40/50*100 = 80
80%   ANSWER:80%
Answer: B
A train can travel 50% faster than a car. Both start from point A at the same time and reach point B at 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is?	Choose the correct choice
A) 179 km/hr B) 197 km/hr C) 120 km/hr D) 109 km/hr E) 187 km/hr

Solution: Let speed of the car be x km/hr.   Then, speed of the train = 150/100 x = 3/2 x km/hr.   75/x - 75/(3/2 x) = 125/(10 * 60)   75/x - 50/x = 5/24 = 120 km/hr.   Answer: 120 km/hr
Answer: C
A car has been driven with an average speed of 30 kilometers per hour during the first 30 kilometers of a journey. Upon reaching the 30th kilometer, the car then travels at 45 kilometers per hour for the next 30 kilometers. Find out the average speed of the car if it has not been stopped at all during the journey. Options.
A) 35  B) 36  C) 37.5  D) 38  E) 40

Solution: Avg speed = Total distance/ total time taken   = 60 km/ 100 min   = .6 km/m   = .6 * 60= 
.6 * 60 = 36
36 km   ANSWER:36
Answer: B
If k > 0, x + k = y, and y + 5k = z, what is the ratio between z - x and y - x ?	Choose the correct answer:  A) 2 to 1  B) 3 to 1  C) 4 to 1  D) 5 to 1  E) 6 to 1

Solution: y-x = k   z-y = 5k   Let's add the two equations together:   z-x = 6k   The ratio of z-x to y-x is 6:1.   The answer is 6 to 1.
Answer: E
For how many integers n is 1^n+2 = (n+2)^1?
Choose the correct choice from the following answers.
A) 0	B) 1	C) 2	D) None of these	E) 3

Solution: If n=0   1^0+2 = (0+2)^1   1^2 = 1 ; 2^1 =2 not ok   If n=1   1^1+2 =1 ; (1+2)^1=3^1=3 not OK   So, Answer : None of these
Answer: D
How many different sevevn letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?	Choose the correct choice from the following answers
A) 65 B) 11!/(2!*2!*2!) C) 56 D) 23 E) 11!/(3!*2!*2!*2!)

Solution: E- -R   We are left with the following 11 letters: {M, D, I, T, R, EE, AA, NN} out of which 8 are distinct: {M, D, I, T, R, E, A, N}.   We should consider two cases:   1. If the two middle letters are the same, we'd have 3 words: EEER, EAAR and ENNR.   2. If the two middle letters are distinct, then we are basically choosing 2 letters out of 8 when the order of the selection matters, so it's 8P2 = 56.   Total = 56 + 3 = 65.   65nswer: 65.
Answer: A
The average age of A and B is 22 years. If C were to replace A, the average would be 44 and if C were to replace B, the average would be 33. What are the age of A, B and C?
Choose the correct choice from the following answers:  A) 11,33,55  B) 20, 20, 18  C) 22, 44, 33  D) 44, 88, 66  E) None of the above

Solution: Given 11,33,55 + B = 44â€¦(i)   C + B = 88 â€¦ (ii)   11,33,55 + C = 66â€¦(iii)   (i) + (ii) + (iii) â‡’ 11,33,55 + B + C =99 â€¦(iv)   from (i) and (iv), we get   C = 55 years   âˆ´ B = 33 years and 11,33,55 = 11years   11,33,55nswer 11,33,55
Answer: A
Of the 70 house in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool. How many houses in the development have neither a two-car garage nor an in-the-ground swimming pool?	Choices.
A) 10
B) 15
C) 20
D) 25
E) 30

Solution: Neither Car nor Garage   = Total - Garage - (Swim - Common)   = 70 - 50 - (40-35) = 70-55= 
70-55 = 15
15   Answer 15
Answer: B
In how many different ways can the letters of the word ‘SMART’ be arranged?	Choose the correct answer
A) 120 B) 354 C) 126 D) 214 E) 124

Solution: A   120   The word SMART has 5 distinct letters.   Number of arrangements = 5!   = 5 × 4 × 3 × 2 × 1 = 120
Answer: A
A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.14200 after a year? Pick:  A) 3630  B) 9232  C) 4260  D) 2387  E) 2813

Solution: 6300:4200:10500   3:2:5   3/10 * 14200= 
3/10 * 14200 = 4_260
4260   Answer: 4260
Answer: C
Donna, Chris, and Austin have a total of $93 in their wallets. Donna has $7 more than Chris. Austin has 3 times what Donna has. How much do they have in their wallets?	Answers:
A) Donna $10 -Chris $45 -Austin $90
B) Donna $20-Chris $13 -Austin $60
C) Donna $30 -Chris $34-Austin $70
D) Donna $40 -Chris $56 -Austin $100
E) Donna $50 -Chris $23 -Austin $80

Solution: Let the amount in Chris’s wallet be $x   Donna has $7 more than Chrish's wallet = $(x + 7)   Austin has 3 times than Donna's wallet = $3(x + 7)   According to the problem, Donna, chris, and Austin have a total of $93 in their wallets.   Therefore,   x + (x + 7) + 3(x + 7) = 93   x + x + 7 + 3x + 21 = 93   5x + 28 = 93   - 28 -28 (subtract 28 from both sides)   5x = 65   or, 5x/5 = 65/5 (Divide both sides by 5)   x = 13   Amount in Chris wallet = $x = $13   Amount in Donna's wallet = $(x + 7) = $(13 + 7)= 
(13 + 7) = 20
$20   Amount in Austin 's wallet= $3(x + 7) = $3(13 + 7) = $3(20) = $ 60   Answer: Amount in Chris’s wallet: $13   Amount in Donna's wallet: $20   Amount in Austin's wallet: $60   correct answer Donna $20-Chris $13 -Austin $60
Answer: B
if m is a positive integer greater than 8, which of the following must be divisible by 4?	Choose the correct choice from the following answers:  A) m(m-1)(m+2)(m+3)  B) m(m-1)(m+3)(m+4)  C) m(m-3)(m+2)(m+4)  D) m(m-3)(m+2)(m+3)  E) m(m+1)(m+3)(m+4)

Solution: D.   For any integer m, D is the only answer choice which will always be divisible by 4.   A product of 4 consecutive integers will always be divisible by 4. Since, none of the answer choices are a product of 4 consecutive integers, we have to ensure at least one of the integers is always a multiple of 4. The best way to do that is to ensure the answer choice ism* [(m-1)OR(m+3)] * [(m-2)OR(m+2)] * [(m-3)OR(m+1)]. (answer m(m-3)(m+2)(m+3))
Answer: D
An athlete runs 200 metres race in 24 seconds. What is his speed?  Choose the correct choice from the following answers
A) 20 km/hr  B) 30 km/hr  C) 25 km/hr  D) 35 km/hr  E) 40 km/hr

Solution: speed = dist/time = 200/24   200/24 * 18/5 = 40*3/4= 
40*3/4 = 30
30 km/hr   ANSWER 30 km/hr
Answer: B
A train running at the speed of 90 km/hr crosses a pole in 9 sec. What is the length of the train?  Choose the correct choice:  A) 288  B) 225  C) 277  D) 272  E) 150

Solution: Speed = 90 * 5/18= 
90 * 5/18 = 25
25 m/sec   Length of the train= speed * time = 25 * 9= 
25 * 9 = 225
225 m   Answer: 225
Answer: B
A bag contains 9 red and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?  Choose the correct choice from the following answers.
A) 4/7 B) 2/3 C) 5/8 D) 9/14 E) 5/7

Solution: Total number of balls = 9+5= 
9+5 = 14
14   number of white balls= 9   Probability = 9/14   Answer is 9/14
Answer: D
Find the cost of fencing around a circular field of diameter 36 m at the rate of Rs.3.50 a meter? Choose the correct choice from the following options.
A) 438  B) 395  C) 378  D) 279  E) 222

Solution: 2 * 22/7 * 18 = 113   113 * 3 1/2   = Rs.395   Answer: 395
Answer: B
A trader sells 45 meters of cloth for Rs. 4500 at the profit of Rs. 12 per metre of cloth. What is the cost price of one metre of cloth? Pick one
A) Rs. 80	B) Rs. 85	C) Rs. 88	D) Rs. 100	E) None of these

Solution: SP of 1m of cloth = 4500/45 = Rs. 100   CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth   = Rs. 100 - Rs. 12 = Rs. 88.   ANSWER:Rs. 88
Answer: C
If 4 women can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in?
Choose the correct choice from the following options:
A) 1/5 day B) 1 day C) 2 days D) 3 days E) 4 days

Solution: The length of cloth painted by one woman in one day = 48 / 4 × 2 = 6 m   No. of days required to paint 36 m cloth by 6 women = 36/ 6 × 6 = 1 day.   1 day)
Answer: B
If n is the product of three consecutive integers, and n is divisible by 3, which of the following is not necessarily a divisor of n ? Answers:
A) 18	B) 20	C) 24	D) 22	E) 26

Solution: IF ONE NO. IS 4 THEN OTHER CONSEQUTIVE NO. ARE   1*2*3= 
  1*2*3 = 6
6 , 2*3*4=24 , 3*4*5 =60   24 IS NOT A DIVISOR OF N   24
Answer: C
After Naomi received her order, she found that she could make a scarf from one skein of the yarn
that cost $5.99 a skein. After taking into account the discount, taxes, and shipping for the yarn, how
much would it cost to make five scarves?  Choose the correct choice from the following.
A) $40.45	B) $60.45	C) $10.45	D) $20.45	E) $30.45

Solution: $5.99 x 5 = $29.95   .10 x $29.95 = 2.995 rounds to $3.00   $29.95 - $3.00 = $26.95 discounted price   $26.95 x 1.13  29.95 -  3.00= 
 29.95 -  3.00 = 26.95
$26.95 discounted price   $26.95 x 1.13= $30.45 with tax and shipping   correct answer $30.45
Answer: E
In the above number, A and B represent the tens and units digits, respectively. If the above number is divisible by 25, what is the greatest possible value of B x A?	Choose the correct choice from the following:  A) 0  B) 15  C) 20  D) 25  E) 35

Solution: I also was confused when I was looking forabove number:D   As far as I understood, 25 is a factor of AB. In other words, the values of B (units digits can be 5 or 0. Better to have option for 5 in this case to havebigger result). Now let's try 25x1 (A=2, B=5 respectively we have =10). But we don't have this number in answer choices, move on. (avoid even multiples of 2,4,6,8 etc (we will have 0 in units thus making our result 0)   25x3 = 75 (A=7 B=5 respectively. Hey! that's 35. This is the greatest possible value of B x A   IMO 35.
Answer: E
The area of sector of a circle whose radius is 12 metro and whose angle at the center is 38° is?
Choose the correct choice from the following.
A) 30m2  B) 40m2  C) 47.7m2  D) 50m2  E) 55m2

Solution: 38/360 * 22/7 * 12 * 12   = 47.7 m2   Answer:47.7m2
Answer: C
A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?	Choose the correct choice from the following:
A) neither profit nor loss
B) 1%
C) 2%
D) 3%
E) 4%

Solution: Profit on first article = 20% of 1000 = 200.   This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.   neither profit nor lossNSWER:neither profit nor loss
Answer: A
How many numbers from 2 to 9 are exactly divisible by 2?  Choose the correct choice from the following options:
A) A)2
B) B)3
C) C)5
D) D)4
E) E)8

Solution: 2/2= 
2/2 = 1
1 and 9/2= 4   4 - 1= 
4 - 1 = 3
3   3 + 1= 
3 + 1 = 4
4 Numbers.   Answer : 4
Answer: D
18.05 Ã— 0.001 = ?  Choose the most appropriate option.
A) 0.1805 B) 0.01805 C) 1.805 D) 0.001805 E) None of these

Solution: 18.05 Ã— 0.001 = ?   or,? = 0.01805   Answer 0.01805
Answer: B
If the operation Ø is defined for all positive integers x and w by x Ø w = (2^x)/(2^w) then (4 Ø 2) Ø 2 = ?	Choose the correct choice from the following
A) 2 B) 4 C) 8 D) 16 E) 32

Solution: 4 Ø 2 = 2^4/2^2 = 4   4 Ø 2 = 2^4/2^2 = 4   The answer is 4.
Answer: B
The average of 10 numbers is calculated as 21. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
Select
A) A)16	B) B)18	C) C)19	D) D)22	E) E)24

Solution: Explanation:   10 * 21 + 36 – 26 = 220=>220/10= 
220/10 = 22
22   22)
Answer: D
Danny obtained 76, 65, 82, 67 and 75 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?  Choices
A) A)87  B) B)99  C) C)68  D) D)82  E) E)73

Solution: Average = (76 + 65 + 82 + 67 + 75)/5   = 365/5= 
365/5 = 73
73.   Answer:73
Answer: E