mathewhe/aqua_rat huggingface dataset:
Question: 1 + 9 + 8 = ? considering, 28 + 8 + 92 = 10
what is....?
(A) 7
(B) 8
(C) 9
(D) 6
(E) 10
Rationale: Equation 28 + 8 + 92 = 10 can be derived from
twenty eight(t) + eight(e) + ninetytwo (n) = ten => 10
Similarly for equation,
1 + 9 + 8
One (o) + nine (n) + eight (e) => one (1)
correct answer is E)10
Answer: (E) 10
Question: If nn is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?
(A) 2
(B) 4
(C) 5
(D) 8
(E) 9
Rationale: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.
Hence, n=2mn=2m, where mm is a positive integer. Then,
(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)
=4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8
Hence, the answer is (D).
Answer: (D) 8
Question: The ratio between the length and the breadth of a rectangular park is 1 : 2. If a man cycling along the boundary of the park at the speed of 6 km/hr completes one round in 6 min, then the area of the park (in sq. m) is?
(A) 600m
(B) 6000 m
(C) 20000 m
(D) 100 m
(E) 2000 m
Rationale: Perimeter = Distance covered in 6 min. = (6000 x 6)/60 m = 600 m.
Let length = 1x metres and breadth = 2x metres.
Then, 2(1x + 2x) = 600 or x = 100.
Length = 100 m and Breadth = 200 m.
Area = (100 x 200) m2 = 20000 m
C
Answer: (C) 20000 m
Question: A standard-sized cigarette can be rolled out of 6 standard-sized cigarette butts. How many cigarettes can be made and smoked from 36 butts?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 1
Rationale: D
No, 6 is not the answer! It is not correct, because after the 6 cigarettes have been smoked there will again be 6 butts which can be made into another cigarette.
The answer is 7
Answer: (D) 7
Question: The visitors of a modern art museum who watched a certain Picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it. According to the results of the survey, all 100 visitors who did not enjoy the painting also did not feel they had understood the painting, and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting. If 3/4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting, then how many visitors answered the questionnaire?
(A) 90
(B) 120
(C) 160
(D) 360
(E) 400
Rationale: If we exclude those cases and take the question at face value, then it seems straightforward.
Group #1 = (didn't like, didn't understand) = 100
Group #2 = (likeunderstood) = 3/4
(1/4)N = 100
N = 400
Answer =(E)
Answer: (E) 400
Question: A certain galaxy is known to comprise approximately 2x 10^11 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
(A) 800
(B) 1,250
(C) 8,000
(D) 4,000
(E) 80,000
Rationale: 2*10^11
50 mln = 5*10^7
we divide 10^11 by 10^7 and we get (10^4)*2 = 20,000 and divide by 5. the result is 4,000 (c)
D
Answer: (D) 4,000
Question: 3 singers will pick a song among a list of 3 songs. What is the probability that exactly one singer will pick a different song?
(A) 3!/3^3
(B) 1/3^3
(C) 3/3!
(D) 3/3^3
(E) 1/3!
Rationale: Each singer out of 3 has 3 options, hence total # of outcomes is 3^3;
Favorable outcomes will be 3!, which is # of ways to assign 3 different song to 3 singers.
P=favorable/total=3!/3^3
Answer: A.
Answer: (A) 3!/3^3
Question: If in a certain code "RANGE" is coded as 12345 and "RANDOM" is coded as 123678. Then the code for the word
"ROD" would be
(A) 156
(B) 174
(C) 176
(D) 180
(E) 182
Rationale: R-1
O-7
D-6
so for mango the code is 176
ANSWER:C
Answer: (C) 176
Question: x and y are positive integers of J. If 1/x + 1/y < 2, which of the following must be true?
(A)  x + y > 4
(B)  xy>1
(C)  x/y + y/x < 1
(D)  (x - y)^2 > 0
(E)  None of the above
Rationale: Answer is B:
1/X + 1/Y < 2
The maximum value of 1/X is 1 because if X equals any other number greater than one it will be a fraction. The same is true with 1/Y.
So 1/X and 1/Y will always be less than 2 as long as both X and Y are not both equal to one at the same time.
Another way of putting it is:
X*Y>1.B
Answer: (B)  xy>1
Question: Working alone at its constant rate, pump U pumped out ¼ of the water in a tank in 2 hours. Then pumps V and W started working and the three pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 3 hours. If pump V, working alone at its constant rate, would have taken 18 hours to pump out the rest of the water, how many hours would it have taken pump W, working alone at its constant rate, to pump out all of the water that was pumped out of the tank?
(A) 6
(B) 12
(C) 15
(D) 18
(E) 24
Rationale: Rate of pump U = 1/8
3 hours are required to pump out the remaining (3/4)ths of tank --> 1 hr to pump out 1/4
Rate of U + Rate of V + Rate of W = 1/4
Rate of V + Rate of W = 1/4 - 1/8 = 1/8
V takes 18 hours to pump out the remaining (3/4)ths of tank --> 6 hrs per (1/4)ths --> 24 hrs to pump out fully.
Rate of V = 1/24
1/24 + Rate of W = 1/8
Rate of W = 1/8 - 1/24 = 1/12
Time required to pump out all the water by W = 12 hrs
Answer: B
Answer: (B) 12
Question: A tourist does not have to pay tax on the first $600 of goods he purchases in Country B, but does have to pay a 7 percent tax on the portion of the total value that is in excess of $600. What tax must be paid by a tourist if he buys goods with a total value of $1720?
(A) $54.00
(B) $78.40
(C) $90.00
(D) $100.80
(E) $154.80
Rationale: Correct Answer: B
The tourist must pay tax on $1720 - $600 = $1120. Thus, the amount of tax he has to pay is 0.07 ($1120) = $78.40. The correct answer is B.
Answer: (B) $78.40
Question: The average age of an adult class is 40years. 12new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was theoriginal strength of class?
(A) 8
(B) 12
(C) 15
(D) 17
(E) 18
Rationale: Let original strength = y
Then , 40y + 12 x 32 = ( y + 12) x 36
⇒ 40y + 384 = 36y + 432
⇒ 4y = 48
∴ y = 12
B
Answer: (B) 12
Question: X is three times as fast as Y and working together, they can complete a work in 20 days. In how many days can Y alone complete the work?
(A) 11 days
(B) 80 days
(C) 13 days
(D) 15 days
(E) 19 days
Rationale: X = 3Y
X + Y = 3Y + Y = 4Y
These 4Y people together can do the work in 20 days, which means Y can alone do the work in 4*20 = 80 days.
Answer : B
Answer: (B) 80 days
Question: Find the area of circle whose radius is 9m?
(A) 138
(B) 154
(C) 254.6
(D) 280
(E) 371
Rationale: 22/7 * 9 * 9
= 254.6
Answer:C
Answer: (C) 254.6
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 50 paisa. If the share of Y is RS. 63, what is the total amount?
(A) 115
(B) 273
(C) 117
(D) 118
(E) 119
Rationale: x:y:z = 100:45:50
20:9:10
9 --- 63
39 --- ? => 273
ANSWER:B
Answer: (B) 273
Question: The salaries of A, B and C are of ratio 2:3:5. If the increments of 15%, 10% and 20% are done to their respective salaries, then find the new ratio of their salaries
(A) 20:33:60
(B) 21:33:60
(C) 22:33:60
(D) 23:33:60
(E) None of these
Rationale: Explanation:
Let A salary be 2k
B salary be 3k and C salary be 5k
A's new salary = 115/100∗2k=23/10k
B's new salary = 110/100∗3k=33/10k
C's new salary = 120/100∗5k=6k
New ratio = 23k/10: 33k/10: 6k=23:33:60
Option D
Answer: (D) 23:33:60
Question: When an amount was distributed among 14 boys, each of them got rs 80 more than the amount received by each boy when the same amount is distributed equally among 18 boys. What was the amount?
(A) 5040
(B) 5020
(C) 5010
(D) 5030
(E) 5070
Rationale: Let the total amount be Rs. X the,
x/14 - x/18 = 80<=> 2x/126 = 80 <=> x/63 =63 x 80 = 5040.
Hence the total amount is 5040.
Answer is A.
Answer: (A) 5040
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January?
(A) 3999
(B) 7867
(C) 4500
(D) 2789
(E) 3671
Rationale: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May = 4 * 8500 = 34000 ----(2)
(2)-(1) i.e. May - Jan = 2000
Salary of May is Rs.6500
Salary of January
= Rs.4500
Answer: C
Answer: (C) 4500
Question: A freelancer charges a fixed fee of $20 for his services. Any additional alterations costs 15% of the fixed fee per hour. If Tim hires this freelancer, and hires him again to make alterations which took 20 more hours. How much does Tim have to pay the freelancer in total?
(A) 15
(B) 23
(C) 100
(D) 20
(E) 80
Rationale: Fixed fee is $20
Additional hours is 0.15*20=$3
Total fee is (20*$3)+$20= $80.
Answer is E
Answer: (E) 80
Question: Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 55 kmph. In what time will they be completely clear of each other from the moment they meet?
(A) 7.19
(B) 7.17
(C) 7.62
(D) 7.15
(E) 7.11
Rationale: T = (121 + 165)/ (80 + 55) * 18/5
T = 7.62
Answer:C
Answer: (C) 7.62
Question: How many of the integers between 25 and 95 are even ?
(A) 35
(B) 90
(C) 11
(D) 10
(E) 9
Rationale: Number start between 25 to 95 is 70 numbers
half of them is even..which is 35
ANSWER:A
Answer: (A) 35
Question: A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 6 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
(A) 5.2 hrs
(B) 2.9 hrs
(C) 1.9 hrs
(D) 6 hrs
(E) 5 hrs
Rationale: Net part filled in 1 hour = (1/3 - 1/6) = 1/6
The cistern will be filled in 6/1 hrs i.e., 6 hrs.
Answer:D
Answer: (D) 6 hrs
Question: In a certain corporation, there are 300 male employees and 150 female employees. It is known that 20% of the male employees have advanced degrees and 40% of the females have advanced degrees. If one of the 450 employees is chosen at random, what is the probability this employee has an advanced degree or is female?
(A) 7/15
(B) 3/10
(C) 3/5
(D) 2/5
(E) 3/4
Rationale: P(female) = 150/450 = 1/3
P(male with advanced degree) = 0.2*300/450 = 60/450 = 2/15
The sum of the probabilities is 7/15
The answer is A.
Answer: (A) 7/15
Question: Find the value of y from (12)^3 x 6^ 4 ÷ 432 = y?
(A) 3456
(B) 4567
(C) 4789
(D) 5678
(E) y=5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72) 2 = 5184
432 12 x 62
E
Answer: (E) y=5184
Question: A car finishes a journey in nine hours at the speed of 80 km/hr. If the same distance is to be covered in six hours how much more speed does the car have to gain?
(A) 8 km/hr
(B) 40 km/hr
(C) 12 km/hr
(D) 16 km/hr
(E) None of these
Rationale: Distance covered by the car = 80 × 9 = 720 km
\ Speed = 720⁄6 = 120 km/hr
\ Speed gain = 120 – 80 = 40 km/hr
Answer B
Answer: (B) 40 km/hr
Question: How many times does the minute hand and the second hand make a straight line?
(A) 2844
(B) 2832
(C) 2855
(D) 2381
(E) 2831
Rationale: make a straight line 59 x 2 times = 118 times (both aligned, and in opposition) and there are 24 hours in a day, so in a day minutes and second hand make a straight line 24 x 118 times = 2832 times.
so answer is B
Answer: (B) 2832
Question: A used-book dealer sells paperback books at 3 times dealer's cost and hardback books at 4 times the dealer's cost. Last week, the dealer sold a total of 140 books, each of which had cost the dealer $1. If the gross profit (sales revenue minus the dealer's cost) on the sale of all of these books was $400, how many of the books sold were paperbacks?
(A) 20
(B) 40
(C) 60
(D) 80
(E) 100
Rationale: The dealer earns a profit of $2 per paperback and $3 per hardback.
If all 140 books were paperbacks, the dealer would earn a profit of $280.
Since the actual profit was $400, the dealer must have sold 120 hardbacks.
Then the number of paperbacks sold was 140-120 = 20.
The answer is A.
Answer: (A) 20
Question: In how many ways can a group of 4 men and 2 women be made out of a total of 7 men and 3 women?
(A) 100
(B) 102
(C) 105
(D) 107
(E) 101
Rationale: We need to select 4 men from 7 men and 2 women from 3 women.
Number of ways to do this
= 7C4 × 3C2
= 7C4 × 3C1 [∵ nCr = nC(n-r)]
= 105
Ans- C
Answer: (C) 105
Question: In a certain year, the population of a certain town was 9000. If in the next year the population of males increases by 4% and that of the females by 8% and the total population increases to 9600, then what was the ratio of population of males and females in that given year?
(A) 1 : 2
(B) 5 : 4
(C) 2 : 3
(D) Data inadequate
(E) None of these
Rationale: Let the population of males = x; then the population of females = 9000 – x
Now, 4% of x + 8% of (9000 – x)
= (9600 – 9000 ) = 600
or 0.04x + 720 – 0.08x = 600
or 720 – 600 = 0.08x – 0.04x
or, 120 = 0.04x
x = 3000
Reqd ratio of population of males and females
3000/9000−3000=3000/6000=1:2
Answer A
Answer: (A) 1 : 2
Question: Average of 7 results is 121. If the average of first three results is 115 and average of last three results is 120 Then find the fourth result?
(A) 142
(B) 150
(C) 126
(D) 185
(E) 165
Rationale: Option 'A'
Answer: (A) 142
Question: In an election between two candidates, 70% of the voters cast their votes, out of which 4% of the votes were declared invalid. A candidate got 6552 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
(A) 13000
(B) 12500
(C) 14000
(D) 12000
(E) None of these
Rationale: Explanation :
Solution: let the total number of votes enrolled be x. then, number of votes cast = 70% of x. valid votes = 96% of(70% of x). .'. 75% of(96% of (70% of of x)) = 6552.
(75/100 * 96/100 * 70/100 * x) = 6552.
=> x = (6552*100*100*100)/(75*96*70) = 13000
Answer : A
Answer: (A) 13000
Question: 100 oranges are bought at the rate of Rs. 350 and sold at the rate of 48 per dozen. The percentage of profit is
(A) 12 2/7%
(B) 13 2/7%
(C) 14 2/7%
(D) 15 2/7%
(E) 16 2/7%
Rationale: Explanation:
So before solving this question we will get the C.P. and S.P. of 1 article to get the gain percent.
C.P. of 1 orange = 350/100 = Rs 3.50
S.P. of one orange = 48/12 = Rs 4 [note: divided by 12 as 1 dozen contains 12 items]
Gain = 4 - 3.50 = Rs 0.50
Gain%=0.50/ 3.50∗100=100 /7%=14 2/7%
Option C
Answer: (C) 14 2/7%
Question: The Kiljaro Highway is marked with Milestones denoting the distance to the town of Kiljaro. Tommy left kiljaro and drove the highway, passing the 30 km milestone at 8:30. Some time afterwards, Tommy got a phone call asking him to return home, and he made a U-turn at the 160 km milestone. At 09:A0 Tommy passed the milestone marking 70 km to Kiljaro. The variable A represents the tens digit of the minutes in 09:A0. Assuming Tommy maintained the same constant speed during the entire drive, how many kilometers did Tommy travel in one minute?
(A) 220/(30+10A)
(B) 220/(30+60A)
(C) 220/36A
(D) 220/(30+10A)
(E) 220/40A
Rationale: Since we are dealing with the variables in the answer choices,the best possible method according to me would besubstitution.
Substitute A with 3.meaning tommy would have travelled a distance of ((160-30) + (160-70)) in 60 minutes.
220 Kms in 60 minutes ==> 3.6km/hr.
Substitute A with 3 in the answer options.
Option A
Answer: (A) 220/(30+10A)
Question: The compound ratio of 5:1, 3:1 and 2:5?
(A) 6:1
(B) 1:3
(C) 1:5
(D) 1:1
(E) 1:6
Rationale: 5/1 * 3/1 * 2/5 = 30/56:1Answer: A
Answer: (A) 6:1
Question: Mahesh can do a piece of work in 45days. He works at it for 20days and then Rajesh finished it in 30days. How long will Y take to complete the work?
(A) 54
(B) 25
(C) 37
(D) 41
(E) 30
Rationale: Work done by Mahesh in 45days = 20*1/45 = 4/9
Remaining work = 1 - 4/9 = 5/9
5/9 work is done by Rajesh in 30days
Whole work will be done by Rajesh is 30*9/5 = 54days
Answer is A
Answer: (A) 54
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 5/9 of the cups sold were small and the rest were large. If the large cups were sold for 12/11 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
(A) (a) 7/16
(B) (b) 7/15
(C) (c) 48/103
(D) (d) 17/35
(E) (e) 1/2
Rationale: A simpler way i guess would be to think that in total 9 cups were sold. Out of which 5 are small and 4 are large. Now let the small ones cost $11. so the large ones would cost $12.
So,
5*11=55 and 4*12=48.
Total revenue was 55+48=103
and Large cup sales as found above is 48
Therefore answer is 48/103
C
Answer: (C) (c) 48/103
Question: A square, with perimeter 80, is inscribed in a circle. What is the area of the circle?
(A) 400π
(B) 200π
(C) 250π
(D) 300π
(E) 150π
Rationale: Area of circuscribed circle = pi/2*area of square
Area of square = (80/4)^2 = 20^2= 400
Area of circle = pi/2*400=200pi
Answer : B
Answer: (B) 200π
Question: Ajit was driving down the country side when he saw a farmer tending his pigs and ducks in his yard. Ajit asked the farmer how many of each he had.The farmer replied that there were 60 eyes and 86 feet between them.How many ducks and how many pigs were there ?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: let the no of ducks be X and no of pigs be Y.
then,since there are 60 eyes in total and both ducks and pigs have 2 eyes we have : 2X+2Y=60 --(1)
and total no of legs are 86,ducks have 2 legs while a pig has four so.: 2X+4y=86 ---(2)
subtracting (1) from (2) ,we get
2Y=26. ie. Y =13
putting value in (1),
we get X=17
ANSWER:E
Answer: (E) 17
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
(A) 73
(B) 44
(C) 72
(D) 62
(E) 43
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer: Option B
Answer: (B) 44
Question: A car takes 6 hours to cover a distance of 630 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 60
(B) 50
(C) 40
(D) 70
(E) 65
Rationale: Time = 6
Distance = 630
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 630/9 = 70 Kmph
Answer D.
Answer: (D) 70
Question: In a forest 150 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 5 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
(A) 150
(B) 750
(C) 1,250
(D) 1,500
(E) 2,500
Rationale: Given 150 deers were caught and they are tagged in the first slot.
In the second slot , 50 were caught and 5 we tagged then 10% of them are tagged.
Given this 10% approximates the percentage of tagged deer in the forest..here number is 150..
then 100% is 1500.. is the number of deers population in the forest..
Answer: D is correct answer..
Answer: (D) 1,500
Question: At 9 am a car (A) began a journey from a point, traveling at 40 mph. At 10 am another car (B) started traveling from the same point at 60 mph in the same direction as car (A).
At what time will car B pass car A?
(A) 12 pm
(B) 1 pm
(C) 2 pm
(D) 3 pm
(E) 4 pm
Rationale: After t hours the distances D1 traveled by car A is given by
D1 = 40 t
Car B starts at 10 am and will therefore have spent one hour less than car A when it passes it. After (t - 1) hours, distance D2 traveled by car B is given by
D2 = 60 (t-1)
When car B passes car A, they are at the same distance from the starting point and therefore D1 = D2 which gives
40 t = 60 (t-1)
Solve the above equation for t to find
t = 3 hours
Car B passes car A at
9 + 3 = 12 pm
Answer A
Answer: (A) 12 pm
Question: The balance of a trader weighs 8% less than it should. Still the trader marks up his goods to get an overall profit of 20%. What is the mark up on the cost price?
(A) 40%
(B) 8%
(C) 10.4%
(D) 16.66%
(E) 9%
Rationale: The most natural way to deal with 'weights' questions is by assuming values.
Say the trader's balance shows 100 gms. It is actually 92 gms because it weighs 8% less. Say, the cost price is $92 ($1/gm). Since he gets a profit of 20%, the selling price must be 92+(20/100)*92 = $110.4
Since the cost price is actually supposed to be $100 (for 100 gms) and the selling price is $110.4, the mark up is simply 10.4%.
Ans : C
Answer: (C) 10.4%
Question: What are the unit's digits of 369, 6864, 4725 respectively ?
(A) 2
(B) 8
(C) 3
(D) 5
(E) 0
Rationale: Cyclicity of 3 is 4. 369 = (34)k.31(34)k.31 = (1)k.31(1)k.31 = 3
Power of 6 always gives units digit 6 only.
If power of 4 is odd, then we will get 4 as units digit, if power of 4 is even, then we get 6 as units digit.
Hence, Option 3 is correct.
Answer:C
Answer: (C) 3
Question: X and Y are positive two-digit integers such that the tens digit in X is the same as the units digit in Y, and the units digit in X is the same as the tens digit in Y. Which of the following can be the difference of X and Y ?
(A) 73
(B) 44
(C) 33
(D) 29
(E) 9
Rationale: X and Y are positive two-digit integers such that the tens digit in X is the same as the units digit in Y, and the units digit in X is the same as the tens digit in Y:
X = 10a + b
Y = 10a + b
X - Y = (10a + b) - (10a + b) = 9(a - b). As you can see the difference must be a multiple of 9. Only option E is a multiple of 9.
Answer: E.
Answer: (E) 9
Question: A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws,each ball being put back after it is drawn?
(A) 2/27
(B) 1/9
(C) 1/3
(D) 4/27
(E) 2/9
Rationale: P=2∗39∗29=427P=2∗39∗29=427
We are multiplying by 2 as there are two possible wining scenarios RW and WR.
Answer: D.
Answer: (D) 4/27
Question: In Kaya's teacher's desk there are 10 pink highlighters, 15 yellow highlighters, and 8 blue highlighters. How many highlighters are there in all?
(A) 11
(B) 22
(C) 77
(D) 33
(E) 88
Rationale: Add the numbers of highlighters.
10 + 15 + 8 =33.
Answer is D.
Answer: (D) 33
Question: If m is an integer such that (-2)^2m=2^(21-m) then m=?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 2m = 21-m
3m = 21
m = 7
The answer is C.
Answer: (C) 7
Question: In 1995, the Jossy spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Jossy cut back their water usage. By how much must the Jossy have reduce their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?
(A) a)	33 1/3 %
(B) b)	40 %
(C) c) 50 %
(D) d)	66 2/3 %
(E) e)	100 %
Rationale: Let x be the water usage and c be the cost waterof Jossy
We have
xc =800, c=800/x
Y(1.5c)=800 where Y is the water usage in 1996
Y= 800/ (1.5*800/x)= 1/1.5x=2/3x
Thus reduction will be x-2/3x=1/3x=A
Answer: (A) a)	33 1/3 %
Question: If 6 years are subtracted from the present age of Arun and the remainder is divided by 18, then the present age of his grandson Gokul is obtained.If Gokul is 2 years younger to Madan whose age is 5 years, then what is the age of Arun?
(A) 48
(B) 60
(C) 84
(D) 96
(E) 69
Rationale: arun age x.
(x-6)/18=y
y is gokul age which is 3
x=60
ANSWER:B
Answer: (B) 60