MU-NLPC/Calc-aqua_rat huggingface dataset:
It took Malcom 3.5 hours to drive from city A to city B. On his way back to city A, he increased his speed by 20 km per hour and it took him 3 hours.
Find the average speed for the whole journey. Options:	A) 134.9 km/hr	B) 129.2 km/hr	C) 119.6 km/hr	D) 140.5 km/hr	E) 155.3 km/hr

Solution: Let x and x + 20 be the speeds of the car from A to B and then from B to A. Hence the distance from A to B may expressed as 3.5 x and the distance from B to A as 3(x + 20)   The average speed = total distance / total time = (3.5 x + 3 (x + 20)) / (3.5 + 3)   The distance from A to B is equal to the distance from B to A, hence: 3.5 x = 3(x + 20). Solve for x to obtain x = 120 km/hr.   We now substitute x by 120 in the formula for the average speed to obtain.   average speed = 129.2 km/hr   correct answer 129.2 km/hr)129.2 km/hr
Answer: B
Three dice are thrown together, Find the probability of getting a total of atmost 5?	Choose the most appropriate option:  A) 2/35  B) 1/8  C) 3/31  D) 2/9  E) 5/108

Solution: Three different dice are thrown at the same time.   Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216.   Number of events of getting a total of atmost 5 = 10   i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1), (1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1) and (1, 2, 2).   Therefore, probability of getting a total of atmost 5   P(5/108) = Number of favorable outcomes/Total number of possible outcome   = 10/216   = 5/108
Answer: E
There is rain at a rate of 12 centimeters per hour all over New Jersey. Somewhere downtown in New Jersey a group of students are waiting for the rain to stop. If the rain filled a tank the with a base area of 250 square centimeters and a depth of 6 centimeters, how long did the students wait for the rain to stop?	Choose the correct choice from the following answers.
A) 8 hours	B) 4 hours 25 minutes	C) 3 hours 15 minutes	D) 6 hours	E) 2 hours

Solution: Answer is : E, 4 hours and 30 mins   The volume of the tank is irrelevant and only height matters since rain fell all over the city.   Thus, it takes only . 12 / 6 = 2 hours of rain to fill the tank.
Answer: E
Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 8 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?  Select:
A) 17:7	B) 18:8	C) 19:9	D) 19:5	E) 19:4

Solution: Quantity of alcohol in vessel P = 62.5/100 * 8= 
62.5/100 * 8 = 5
5 litres   Quantity of alcohol in vessel Q= 87.5/100 * 4 = 7/2 litres   Quantity of alcohol in the mixture formed = 5 + 7/2 = 17/2= 
17/2 = 17/2 = around 8.5
8.5 litres   As 12 litres of mixture is formed, ratio of alcohol and water in the mixture formed= 8.5 : 3.5 = 17 : 7.   17:7nswer:17:7
Answer: A
If sequence T is defined for all positive integers n such that t(n +1) = t(n) + n, and t 3 = 14, what is t 24?
Choose the correct choice from the following answers:
A) 101
B) 187
C) 191
D) 201
E) 287

Solution: here is my way of solving this :   tn +1 = tn + n,   t 3 = 14   so:   t 4 = t 3 + 3   t 5 = t 4 + 4, so we replace t 4 with the previous result : t 5 = (t 3 + 3 ) + 4   ....   so we get   t 24 = t 3 + 3 + 4 + 5 + 6....+ 23   the 3 + 4 + 5 + ... + 23 sequence is equal the sequence 1 + 2 + ... + 23, minus 1 + 2 at the beginning (so, minus 3)   and the 1 + 2 ... + 23 sequence is equal to n*(n+1)/2 with n being 23, so equal to  23 * 24 / 2= 
 23 * 24 / 2 = 276
276   so :   t 20= t 3 + 276 - 3   t 20 = 14 + 276 - 3 = 276 + 11= 
276 + 11 = 287
287, hence answer 287
Answer: E
The difference between simple and compound interest on Rs. 1300 for one year at 10% per annum reckoned half-yearly is?	Choose the most appropriate option:	A) 8.0	B) 3.25	C) 9.15	D) 3.13	E) 2.0

Solution: S.I. = (1300 * 10 * 1)/100 = Rs. 130   C.I. = [1300 * (1 + 5/100)2 - 1300]   = Rs. 133.25 Difference = (133.25 - 130)   = Rs.3.25   Answer:3.25
Answer: B
If the ratio of the roots of the equation x2+3px-6=0 is equal to that of the roots x2+6rx-12=0, then: Select the correct option:
A) 5r=3p  B) 2p=r  C) r=p  D) 2r=p  E) None

Solution: x2+3px-6=0 for this eqn... roots are R1=-3p R2=6   x2+6rx-12=0 for this eqn... roots are R3=-6r R4=12   As per Question, -3p/6=-6r/12   => r=p   ANSWER:r=p
Answer: C
A car averages 45 mph for the first 4 hours of a trip and averages 75 mph for each additional hour. The average speed for the entire trip was 65 mph. How many hours long is the trip?	Choose one
A) 12  B) 11  C) 10  D) 9  E) 8

Solution: Let the time for which car averages 75 mph = t   65*(t+4)= 45*4 + 75 t   =>10 t= 80   => t = 8   Total duration of the trip = 8+4= 
8+4 = 12
12   12nswer 12
Answer: A
39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?	Pick one.
A) 10  B) 16  C) 13  D) 18  E) 19

Solution: C   13   Let the required number of days be x.   Less persons, More days (Indirect Proportion)   More working hours per day, Less days (Indirect Proportion)   Persons 30 : 39 :: 12 : x   Working hours/day 6 : 5   30 x 6 x x = 39 x 5 x 12   x = (39 x 5 x 12)/(30 x 6)   x = 13
Answer: C
A reduction of 15% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg? Choose the correct choice from the following answers
A) 12  B) 16  C) 24  D) 28  E) 32

Solution: 800*(15/100)= 
800*(15/100) = 120
120 ---- 5   ? ---- 1=> Rs.24   Answer: 24
Answer: C
Pam and Stanley packed several boxes with reams of paper. While both packed, Pam packed 20% of the boxes. After Pam stopped, Stanley packed the same number of boxes that he had packed while working with Pam. What is the ratio of the number of boxes Pam packed to the number of boxes Stanley packed?	Choose one:  A) 1 to 4  B) 1 to 8  C) 3 to 5  D) 3 to 4  E) 3 to 2

Solution: Correct Answer: B   Solution: B. We know that when Pam and Stanley were both working, the ratio was 1 boxes by Pam to 4 boxes by Stanley. We also know that Stanley continued working after Pam stopped. He packed as many boxes alone as he had packed whlie working with Pam, effectively doubling his number of boxes. Thus, the ratio of Pam's boxes to Stanley's boxes is 1 to 8. Answer 1 to 8 is correct.
Answer: B
A clothing manufacturer has determined that she can sell 100 suits a week at a selling price of Rs. 200 each. For each rise of Rs. 4 in the selling price she will sell 2 less suits a week. If she sells the suits for Rs. x each, how many rupees a week will she receive from the sales of the suits?  Choose the correct choice from the following answers: A) x2/2 B) 200−x/2 C) 50x - (x^2)/4) D) 150x - (x^2)/4) E) 200x - (x^2)/2)

Solution: Explanatory Answer   Assume that she sells the suits at Rs.204; then she will sell two suits lesser or 98 suits.   Substitute x = 204 in each of the answer choices and check where the answer is 98.   For choice (2), the answer is 98 and this is the quickest way to find the answer.   Answer 200−x/2
Answer: B
Which of the following is equal to 1(1/6)%?  Choose the correct answer:  A) 0.012/100  B) 0.12/100  C) 1.1/100  D) 12/100  E) 12/10

Solution: This notation may be confusing for some, since it looks like we're multiplying 1 and 1/6   How about adding a space:Which of the following is equal to (1 1/6)%   (1 1/6)% = 1.1% = 1.1/100   Answer:   1.1/100
Answer: C
A rectangular window is twice as long as it is wide. If its perimeter is 18 feet, then what are its dimensions in feet?	Pick: A) 3/2 by 7/2 B) 5/3 by 10/3 C) 2 by 4 D) 3 by 6 E) 10/3 by 20/3

Solution: Let x be the width of the window. Then the length is 2x.   x+2x+x+2x = 18   6x = 18   x = 18/6= 
18/6 = 3
3   The width is 3 and the length is 6.   The answer is 3 by 6.
Answer: D
If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.36 then sum is
Choose the correct choice from the following options.
A) s.5000
B) s.5100
C) s.5800
D) s.6000
E) s.3600

Solution: p(r/100)^2=C.I-S.I   P(10/100)^2=36   3600   ANSWs.3600R:s.3600
Answer: E
If a train, travelling at a speed of 90 kmph, crosses a pole in 5 sec, then the length of train is?  Answers:  A) 338  B) 125  C) 726  D) 268  E) 171

Solution: D = 90 * 5/18 * 5= 
90 * 5/18 * 5 = 125
125 m   Answer:125
Answer: B
The salaries of A and B together amount to $500. A spends 90% of his salary and B, 80% of his. If now, their savings are the same, what is A's salary?
Choose the correct answer:  A) $50  B) $150  C) $69  D) $34  E) $52

Solution: Let A's salary is x   B's salary = 500-x   (100-90)% of x = (100-80)% of (500-x)   x = $34 (approximately)   Answer is $34
Answer: D
A gardener changed the size of his rectangle shaped garden by increasing it's length by 40% & decreasing is's width by 20%.Find area of new garden.
Choose the correct answer:
A) 1.04	B) 1.12	C) 1.24	D) 1.4	E) 1.5

Solution: A1= l*b   A2= (l*140/100)*(b*80/100)=1.12*lb   so, area of garden is by 1.12 times of old area.   ANSWER:1.12
Answer: B
d, q, and r are positive integers. If d, q, and r are assembled into the six-digit number dqrdqr, which one of the following must be a factor of dqrdqr?	Pick one
A) 23	B) 19	C) 17	D) 7	E) none of the above

Solution: One short way -   dqrdqr = 1000dqr + dqr = (1000+1)= 
(1000+1) = 1_001
1001dqr   Therefore any factor of 1001 is a factor of dqrdqr   7 is a factor of 1001   So 7
Answer: D
Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $288 per week. How much does she earn in dollars per hour?  Answers
A) 11
B) 10
C) 9
D) 8
E) 7

Solution: Let Sheila earn x dollars per hour   So, on Monday, Wednesday and Friday , she earns 8x each   And, on Tuesday and Thursday, she earns 6x each   In total , over the week she should earn, 3(8x) + 2(6x) = 36x   She earns $288 per week   36x =288   x =8   Correct Option : 8
Answer: D
A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 20 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours? Answers:
A) 18/79
B) 1/6
C) 1/25
D) 1/50
E) 1/100

Solution: So there are 900 cars that they have to search.. Each takes 20mins, total of 18000 mins.. Have to find in 180 mins.. Prob180/18000 = 1/100
Answer: E
♠n denotes the number obtained when n is rounded to the nearest tenth. For example ♠4.31 = 4.3
♠3.32 - ♠2.42 =	Choose the most appropriate option.
A) 1.05  B) 0.9  C) -1.05  D) -1.0  E) -0.1

Solution: ♠3.32 - ♠2.42 =   3.3 - 2.4= 
3.3 - 2.4 = 0.9
0.9   Answer : 0.9
Answer: B
In a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 35 and 200, then the least and greatest integer on the card would be	Choose the correct choice from the following answers.
A) 3 and 15  B) 3 and 20  C) 4 and 13  D) 4 and 14  E) 5 and 14

Solution: Given: 35<x(x+1)<200.   Now, it's better to test the answer choices here rather than to solve:   If x=5 then x(x+1)=30>35 --> so, the least value is 5. Test for the largest value: if x=14 then   x(x+1)=14*15= 
14*15 = 210
210>200   Answer: 5 and 14.
Answer: E
David received Rs.6000 as his share out of the total profit of Rs.9000 which he and Dave earned at the end of 1 years. If David invested Rs.120000 for 6 months, whereas Dave invested his amount for the whole yr, what was the amount invested by Dave?	Select.
A) 28000  B) 30000  C) 34000  D) 35000  E) 36000

Solution: Suppose Ramesh invested Rs. x. Then,   Manoj : Ramesh = 120000 * 6 : x *12.   720000/12x: 6000/3000   x = 30000   (30000)
Answer: B
I. a^2 - 9a + 20 = 0,
II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b?
Choices:	A) a < b	B) a ≤ b	C) the relationship between a and b cannot be established	D) a > b	E) a ≥ b

Solution: I. (a - 5)(a - 4) = 0   => a = 5, 4   II. (2b + 3)(b - 4) = 0   => b = 4, -3/2 => a ≥ b   Option a ≥ b
Answer: E
In a set of numbers from 100 to 1000 inclusive, how many integers are odd and do not contain the digit "5"?	Choose the correct choice from the following choices.
A) 180  B) 196  C) 286  D) 288  E) 324

Solution: let say number= XYZ   Z= units digit   Y= tenths digit   X= Hundredth's digit   For any 3 digit number to be odd, Unit digit must be odd   So Z can be filled with 1,3,7,9 (we are excluding digit 5) = 4 ways.   Y can be filled with 0,1,2,3,4,6,7,8,9 (we are excluding digit 5) = 9 ways   X can be filled with 1,2,3,4,6,7,8,9 (we are excluding digits 0 and 5..) = 8 ways   No of ways= 4*9*8= 
4*9*8 = 288
288   Answer : 288
Answer: D
A car gets 33 miles to the gallon. If it is modified to use a solar panel, it will use only 75 percent as much fuel as it does now. If the fuel tank holds 16 gallons, how many more miles will the car be able to travel, per full tank of fuel, after it has been modified?
Choose the correct choice from the following answers:  A) 168  B) 172  C) 176  D) 180  E) 184

Solution: Originally, the distance the car could go on a full tank was   16*33= 
  16*33 = 528
528 miles.   After it has been modified, the car can go  33/0.75= 
 33/0.75 = 44
44 miles per gallon.   On a full tank, the car can go  16*44= 
 16*44 = 704
704 miles, thus 176 miles more.   The answer is 176.
Answer: C
A train 275 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?  Select the correct option.
A) 15 B) 6 C) 7 D) 8 E) 9

Solution: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr   [66 * 5/18] m/sec = [55/3] m/sec.   Time taken to pass the man = [275 * 3/55= 
275 * 3/55 = 15
15 sec   15nswer: 15
Answer: A
In an arithmetic progression the difference between the any two consecutive terms is a constant. What is the arithmetic mean of all of the terms from the first to the 27th in an arithmetic progression if the sum of the 12th and 16th terms of the sequence is 98?
Select the correct option
A) 47 B) 49 C) 51 D) 53 E) 55

Solution: Let x be the difference between any two consecutive terms.   The mean of a sequence like this is the middle term, thus the 14th term in the sequence.   Then the mean of the 13th and 15th term is also equal to the overall mean, because the 13th term is (14th term - x) and the 15th term is (14th term + x).   Similarly the mean of the 12th and 16th term is also equal to the mean.   etc...   Thus the mean is   98/2= 
  98/2 = 49
49   The answer is 49.
Answer: B
In 120 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:  Pick.
A) 24 m B) 25 m C) 22.5 m D) 9 m E) 12 m

Solution: Distance covered by B in 9 sec. =	120/45 x 9	m = 24 m.   A beats B by 24 metres.   24 mnswer: Option 24 m
Answer: A
If A is the average (arithmetic mean) of 3 consecutive negative integers, which of the following must be true?
I. A is a negative integer.
II. A is a nonzero integer.
III. A is a multiple of 3.	Choose the most appropriate option
A) I only	B) II only	C) III Only	D) I and III only	E) I and II only

Solution: Consider any negative integer , a   we can form a series as a , a-1 , a-2   Arithmetic Mean = a+(a-1)+(a-2)/3 = a-1   So,   I) is always true, since 'a' is a negative integer   II) is always true, even if 0 is in the series. i.e. 0, -1, -2   III) not always true, a can be any integer as we considered, not necessarily multiple of 3   Ans - I and II only
Answer: E
The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 8 cm each. The radius of the sphere is  Select
A) 3 cm B) 4 cm C) 6 cm D) 8 cm E) None

Solution: Solution   4Î R2	= 2Î 4x8   â‡’ R2 = (4x8/2)   â‡’ 16   â‡’ R = 4 cm.   Answer 4 cm
Answer: B
There were P people in a room when a meeting started. Q people left the room during the first hour, while R people entered the room during the same time. What expression gives the number of people in the room after the first hour as a percentage of the number of people in the room who have been there since the meeting started?  Choices.
A) (P−Q)/(P−Q+R)
B) 100 x (P−Q+R)/(P−Q)
C) (P+R)/(P−Q)
D) 100 x (P−Q)/(P−Q+R)
E) 100 x (P+R)/(P−Q)

Solution: Explanatory Answers   The meeting started with P people. Q left the room during the first hour.   So, (P - Q) people have been in the room since the meeting started.   This expression is obviously the denominator of the expression.   To start with there were P people, Q of whom left the room and another R joined the group.   So, the number of people in the room after the first hour = P - Q + R.   This expression is the numerator of the expression.   Required expression = 100 x (P - Q + R)/(P - Q)   Answer 100 x (P−Q+R)/(P−Q)
Answer: B
A store owner decided to raise the price of a particular item by exactly 10%. Of the following which is NOT the new price?  Choose the correct option
A) $1.10 B) $8.80 C) $11.00 D) $57.30 E) $78.10

Solution: Let price be $ 10   The store owner decided to raise the price of a particular item by exactly 10%, so the new price must be   110 *10 /100= 
  110 *10 /100 = 11
>11   So, The new price must be a multiple of 11   From the given options check for all the multiples of 11   Test of divisibility of 11 is   if the difference of the sum of digits at odd places and the sum of its digits at even places, is either 0 or divisible by 11, then clearly the number is divisible by 11.   A. $1.10   B. $8.80   C. $11.00   By a quick glance even a 2nd grader can eliminate options A,B and C , because they are all divisible by 11 , let with only 2 options check for the divisibility rule for options D and E   D. $57.30   Sum of even digits is  5+3= 
 5+3 = 8
8   Sum of odd digits is 7 +0= 
7 +0 = 7
7   Difference of the even and odd digits is   8 - 7= 
  8 - 7 = 1
1 ; not divisible by 11   Hence this is our answer.   E. $78.10   Further inspection is not required since we have already found out the answer at ($57.30)
Answer: D
How many number of 3's would be used to type numbers from 1 to 700 Choose the correct answer
A) 230 B) 240 C) 250 D) 260 E) 270

Solution: 1-99--20 (3,13,23,30,31,32,33,34,35,36,37,38,39,43,53,63,73,83,93)   likewise   100-199--20   200-299--20   300-399--120 (300-399 there is extra 100 3's)   400--499--20   500--599--20   600-700--20   20+20+20+120+20+20+20= 
20+20+20+120+20+20+20 = 240
240   ANSWER:240
Answer: B
The average (arithmetic mean) of eight numbers is 49.1. If the sum of half of these numbers is 158.4, what is the average of the other half?  Choose the correct choice: A) 12.8 B) 24.2 C) 58.6 D) 72.1 E) 96.8

Solution: arithmetic mean = sum / total numbers   sum = 49.1 * 8= 
49.1 * 8 = 392.8
392.8   sum of half of these numbers is 158.4. So, 4 numbers sum is 158.4. Rest 4 numbers sum= 392.8-158.4= 
392.8-158.4 = 234.4
234.4   Arithmetic mean of the 4 nos= 234.4/4= 
234.4/4 = 58.6
58.6   Hence, 58.6 is the answer.
Answer: C
A number when divided by 6 leaves a remainder 3. When the square of the same number is divided by 6, the remainder is  Options:
A) 0
B) 1
C) 2
D) 3
E) 4

Solution: Sol.   Let x = 6q + 3.   Then x2 = (6q + 3)2   = 36q2 + 36q + 9 = 6(6q2 + 6q + 1) + 3.   So, when x2 is divided by 6, remainder = 3.   Answer 3
Answer: D
Find the odd man out
5,15,45,60,90,180 Options:
A) 60  B) 180  C) 90  D) 5  E) 15

Solution: 5*3= 
5*3 = 15
15   15*3= 
15*3 = 45
45   45*2= 
45*2 = 90
90   90*2= 
90*2 = 180
180   180*2= 
180*2 = 360
360   60NSWER:60
Answer: A
Sonika deposited Rs.7000 which amounted to Rs.9200 after 3 years at simple interest. Had the interest been 2% more. She would get how much?
Choose the correct choice from the following answers: A) 9680 B) 2277 C) 9620 D) 2774 E) 1212

Solution: (7000*3*2)/100= 
(7000*3*2)/100 = 420
420   9200   --------   9620   Answer:9620
Answer: C
An error 2%in excess is made while measuring the side of a square. What is the percentage of error in the calculated area of the square? Pick
A) 4.04 %	B) 2.02 %	C) 4 %	D) 2 %	E) 2.40 %

Solution: Explanation:   Error =2% while measuring the side of a square.   Let correct value of the side of the square =100   Then, measured value =100+2= 
100+2 = 102
102 (∵ 2 is 2%of 100)   Correct area of the square=100×100=10000   Calculated area of the square =102×102=10404   Error =10404−10000=404   Percentage error =error /actual value×100   =404/10000×100=4.04%   4.04 %nswer: Option 4.04 %
Answer: A
What will come in place of the x in the following Number series? 12, 38, 116, 350, 1052, x  Choose one
A) 4300 B) 4500 C) 4000 D) 4569 E) 3158

Solution: 12   12 × 3 + 2 = 38   38 × 3 + 2 = 116   116 × 3 + 2 = 350   350 × 3 + 2 = 1052   1052 × 3 + 2 = 3158   3158
Answer: E
2 men and 3 women are lined up in a row. What is the number of cases where they stand with each other in turn? (The number of cases in which men (or women) do not stand next to each other)  Pick one
A) 12 B) 15 C) 18 D) 21 E) 24

Solution: First arrange 3 women. 3 women can be arranged in 3 places in 3! ways. Now   W Blank W BlankW   we have to fill the two blanks with 2 men. We can arrange 2 persons in 2 places in 2! ways.   3! * 2! = 12 ways.   12 is the answer
Answer: A
Lerry, Michael, and Doug have five donuts to share. If any one of the men can be given any whole number of donuts from 0 to 5, in how many different ways can the donuts be distributed?  Select the correct option.
A) 21  B) 42  C) 120  D) 504  E) 5040

Solution: Lerry, Michael, and Doug have five donuts to share to get the answer, see how can we get sum5with 3 numbers.   1) 0,0,5 = 3 combinations or 3! /2!   2) 0,1,4 = 6 combinations or 3!   similarly   3) 0,2,3 = 6 combinations   4) 1,1,3 = 3 combination   5) 2,2,1 = 3 combination   total =21=21
Answer: A
A painting crew painted 80 houses. They painted the first y houses at a rate of x houses per week. Then more painters arrived and everyone worked together to paint the remaining houses at a rate of 4.25x houses per week. How many weeks did it take to paint all 80 houses, in terms of x and y? Select
A) (320 - y)/(5x)	B) (y +210)/(5x)	C) 5(80 - y)/(4x)	D) (y + 400)/(4x)	E) (4y + 320)/(5x)

Solution: Ans (y +210)/(5x)   Plug some numbers   Let y = 40 houses and x = 20   then they painted 20 houses per week   as painters were added to the group , the rate of the group increased to 4.25 x => 4.25 * 20= 
4.25 * 20 = 85
85 houses per week   total time they took= (40/20) + (40/85) = 2.5 weeks   Putting the values of x and y in equation (y +210)/(5x)   (y +210)/(5x) = (40+210)/5*20 = 250/100= 
250/100 = 5/2 = around 2.5
2.5
Answer: B
A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?  Choose the correct choice from the following answers.
A) 76 kmph B) 24 kmph C) 54 kmph D) 56 kmph E) 76 kmph

Solution: Distance from A and B be 'd'   Average Speed   = total distance/total time   Average Speed   = (2d)/[(d/20) + (d/30)]   = (2d)/[5d/60)   => 24 kmph.   Answer: 24 kmph
Answer: B
A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected at random and with replacement from the box. If the 3 numbers on the balls selected contain two odd and one even. What is the probability Z that the first ball picked up is odd numbered? Choose one.
A) 0	B) 1/3	C) 1/2	D) 2/3	E) 1

Solution: Answer-D   Selecting the balls either Even or Odd is having probability 50/100=1/2   We have already selected 3 balls with 2 odd numbers and 1 even number.   So we have 3 combinations OOE, OEO, EOO. We have 3 outcomes and 2 are favourable as in 2 cases 1st number is odd. So probability Z is 2/3.2/3
Answer: D