mathewhe/aqua_rat huggingface dataset:
Question: Company X sells a selection of products at various price points. Listed below are unit sales made for one particular day. How many unit sales on that day were greater than the mean sale price but less than the median sale price?
$50, $50, $97, $97, $97, $120, $125, $155, $155, $199, $199
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Taking the prices of products in ascending order(already arranged)
$50, $50, $97, $97, $97, $120, $125, $155, $199, $199, $199
we see that median value is the 6th value as there in total 11 values given
Arithmetic mean = total/number of entries = 1388/11 =126.1818
We are asked to find how many unit sales on that day were greater than the mean sale price but less than the median sale price
as we can clearly see that there is one value between $120 and $126.1818, answer is 1 unit
Correct Answer - B
Answer: (B) 1
Question: A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
(A) 50 Kmph
(B) 60 Kmph
(C) 70 Kmph
(D) 80 Kmph
(E) 90 Kmph
Rationale: Time = 6
Distance = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
B
Answer: (B) 60 Kmph
Question: In an examination, 30% of total students failed in Hindi, 35% failed in English and 35% in both. The percentage of these who passed in both the subjects is :
(A) 10%
(B) 20%
(C) 30%
(D) 70%
(E) 50%
Rationale: pass percentage = 100 - (30+35-35) = 100-30 = 70
ANSWER:D
Answer: (D) 70%
Question: Find the invalid no.from the following series 15 46 63 71 75 77 78
(A) 15
(B) 46
(C) 63
(D) 71
(E) 75
Rationale: In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on.
46
B
Answer: (B) 46
Question: At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ?
(A) 20
(B) 45
(C) 55
(D) 90
(E) 85
Rationale: Explanation:
Clearly, total number of handshakes = (9+ 8 + 7 + 6 + 5 + 4 + 3 + 2+1) = 45.
Answer: B
Answer: (B) 45
Question: The probability of having a girl is identical to the probability of having a boy. In a family with five children, what is the probability that all the children are of the same gender?
(A) 1/16
(B) 1/4
(C) 1/8
(D) 1/12
(E) 1/25
Rationale: There are two cases. All boys and all girls
case 1. all boys.
1/2*1/2*1/2*1/2*1/2= 1/32
case 2 .all girls.
1/2*1/2*1/2*1/2*1/2=1/32
We will add the cases to get 1/16
Answer: (A) 1/16
Question: In a school 50% of the students are younger than 10, 1/20 are 10 years old and 1/10 are older than 10 but younger than 12, the remaining 70 students are 12 years or older. How many students are 10 years old?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Solution
Let us write the fraction for each group of students
Group A: younger than 10: 50% = 50/100 = 1/2
Group B: 10 years old: 1/20
Group C: older that 10 but younger than 12: 1/10
Group D: 12 years or older: 70 students
The fraction for group A, B and C together is given by
1 / 2 + 1 / 20 + 1 / 10 = 10 / 20 + 1 / 20 + 2 / 20 , common denominator
= 13 / 20 , add numerators
The fraction for group D is given by
20 / 20 - 13 / 20 = 7 / 20 and corresponds to 70 students
If X is the total number of students, then
7 / 20 of X = 70
or (7 / 20) × X = 70
Solve for X
X = 70 × (20 / 7) = 200
Students who are 10 years old have a fraction of 1 / 20 of the total X and their number is equal to
(1 / 20) of 200 = 10 students
ANSWER IS B
Answer: (B) 10
Question: How many digits are in (8×10^10)(10×10^5)?
(A) 17
(B) 25
(C) 26
(D) 27
(E) 28
Rationale: The question simplfies to (8×10^10)(10^6)
=> 8*10^16
=> Will contain 16 zeros +1 digit 8
=>17
Ans A
Answer: (A) 17
Question: Set A is {1, 3, 5, 7, 9}
Set B is {16, 18, 20, 22, 24}
For the sets of numbers above, which of the following is true?
I. The mean of Set B is greater than the mean of Set A.
II. The median of Set B is greater than the median of Set A.
III. The standard deviation of Set B is greater than the standard deviation of Set A.
(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II, and III
Rationale: The mean and median of Set A is 5.
The mean and median of Set B is 20.
Thus statements I and II are both true.
The standard deviation is related to the distance from the mean.
Since the elements of both sets are spaced identically around the mean (+/- 2, +/- 4), the standard deviations of both sets are equal.
The answer is B.
Answer: (B) I and II only
Question: In the first half of the 20th century, the population of a particular country increased by 200 percent. In the second half of the century, the population increased by 300 percent. What was the percent increase for the 20th century as a whole?
(A) 500%
(B) 600%
(C) 800%
(D) 1100%
(E) 1200%
Rationale: Say initially population was 100.
What is 200% of 100? It is 200/100 * 100 = 200.
An increase of 200% means the new population became 100 + 200 = 300
What is 300% of 300? It is 300/100 * 300 = 900
An increase of 300% means the new population now is 300 + 900 = 1200
So from 100, the population increased to 1200 i.e. an increase of 1100.
1100 is what percent of 100?
1100 = x/100 * 100
i.e. it is 1100%
ANSWER:D
Answer: (D) 1100%
Question: A vendor bought Headphones at 5 for Rs 100.How many for Rs 100 must he sell to gain 50%?
(A) 8
(B) 3
(C) 5
(D) 6
(E) None
Rationale: C.P. of 9 Headphones= Rs100
S.P. of 9 Headphones = 150% of Rs 100 = Rs150
For Rs.150 , Headphones sold = 9.
For Rs. 100,Pens sold=(9/150)*100=6
Answer: Option D
Answer: (D) 6
Question: (500 + 200+100) Ã— 4 Ã— (3 + 4) = ?
(A) 52000
(B) 32400
(C) 22400
(D) 22800
(E) 24200
Rationale: (500 + 200+100) Ã— 4 Ã— (3 + 4) = ?
or, ? = 800 Ã— 4 Ã— 7 = 22400
Answer C
Answer: (C) 22400
Question: P is four times as old as Q, and Q is six years older than R. If R is z years old, what is P’s age in terms of z?
(A) 4z + 6
(B) 4z − 24
(C) 4z + 24
(D) (z + 6)/4
(E) (z − 6)/4
Rationale: P = 4Q
Q = R+6 = z+6
P = 4(z+6) = 4z + 24
The answer is C.
Answer: (C) 4z + 24
Question: By the how much is two-fifth of 400 greater than three -fifths of 150?
(A) 15
(B) 70
(C) 5
(D) 30
(E) None of these
Rationale: Reqd no. = 2â„5 Ã— 400 - 3â„5 Ã— 150
= 160 - 90 = 70
Answer B
Answer: (B) 70
Question: Two cars start from the opposite places of a main road, 150 km apart. First car runs for 30 km and takes a right turn and then runs 15 km. It then turns left and then runs for another 25 km and then takes the direction back to reach the main road. In the mean time, due to minor break down the other car has run only 35 km along the main road. What would be the distance between two cars at this point?
(A) 65
(B) 38
(C) 60
(D) 28
(E) 21
Rationale: Answer: C) 60 km
Answer: (C) 60
Question: The ratio, by volume, of soap to alcohol to water in a certain solution is 2:50:100. The solution will be altered so that the ratio of soap to alcohol is doubled while the ratio of soap to water is halved. If the altered solution will contain 100 cubic centimeters of alcohol, how many cubic centimeters of water will it contain?
(A) 50
(B) 200
(C) 400
(D) 625
(E) 800
Rationale: soap:alcohol
Initial ratio soap:alcohol: water --> 2:50:100
Initial soap:alcohol = 2/50 =2:50
after doubled soap:alcohol =2* 2/50 = 4:50
Initial soap:water = 2/100=2:100
after halved soap:water: 1/2 * 2/100 = 1/100 = 1:100= 4:400
After soap: alcohol:water --> 4:50:400
given alcohol 100 cumeter.
ratio is 8:100:800 (4:50:400)
For 100 cu meter of Alcohol ---800 cu m water is required
ANSWER:E
Answer: (E) 800
Question: If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 8400 ?
(A) 11
(B) 13
(C) 14
(D) 18
(E) 10
Rationale: Required difference = [3 ½ % of Rs.8400] – [3 1/3 % of Rs.8400]
= [(7/20-(10/3)]% of Rs.8400 =1/6 % of Rs.8400
= Rs. [(1/6)8(1/100)*8400] = Rs. 14.
Answer is C.
Answer: (C) 14
Question: P is four times as fast as Q and working together, they can complete a work in 12 days. In how many days can Q alone complete the work?
(A) 35 days
(B) 15 days
(C) 16 days
(D) 25 days
(E) 18 days
Rationale: P = 4Q
P + Q = 4Q + Q = 5Q
These 5Q people can do the work in 12 days, which means Q can do the work in 60 days.
Hence, P can do the work in 15 days.
ANSWER:B
Answer: (B) 15 days
Question: Find the average of the series : 150 , 160, 328, 147 and 120?
(A) 174
(B) 178
(C) 181
(D) 180
(E) 186
Rationale: Average = (150 + 160 + 328 + 147 + 120)/5
= 905/5
= 181
Answer: C
Answer: (C) 181
Question: Of the three numbers, second is twice the first and is also thrice the third.If the average of the three numbers is 44.Find the largest number.
(A) 42
(B) 48
(C) 72
(D) 67
(E) 54
Rationale: Sol: Let the third number be x.
Then second number = 3x.
First number=3x/2.
Therefore x+3x+(3x/2)=(44*3) or x=24
So largest number= 2nd number=3x=72
ANSWER :C
Answer: (C) 72
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team ?
(A) 11 year
(B) 12 year
(C) 23 year
(D) 25 year
(E) 27 year
Rationale: Let the average age of the whole team be x years.
11x - (26 + 29) = 9 (x - 1)
=> 11x - 9x = 46
=> 2x = 46
=> x = 23.
So, average age of the team is 23 years.
Answer: C
Answer: (C) 23 year
Question: The average of 9 observations was 7, that of the 1st of 5 being 10 and that of the last 5 being 8. What was the 5th observation?
(A) 27
(B) 12
(C) 15
(D) 17
(E) 18
Rationale: Explanation:
1 to 9 = 9 * 7 = 63
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 63 = 27
Option A
Answer: (A) 27
Question: In a hotel, 60% had vegetarian lunch while 30% had non-vegetarian lunch and 15% had both type of lunch. If 96 people were present, how many did not eat either type of lunch ?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: n(A)=(60/100 ∗96)=288/5
n(B)=(30/100 ∗96)=144/
n(A∩B)=(15/100 ∗96)=72/5
People who have either or both lunchn(A∪B)=288/5 +144/5 −72/5 =360/5 =72
So People who do no have either lunch were = 96 -72 = 24 ANSWER : D
Answer: (D) 24
Question: Which one of the following numbers is divisible by 99?
(A) 3572404
(B) 135792
(C) 913464
(D) 114345
(E) 114375
Rationale: Explanation:
The sum of all the digits of 114345 is 18.
The sum of all digits at even places and odd places are 9 and 9 respectively.
The difference between the sums is 0.
So, the number is divisible by both 9 and 11 and hence by 99.
Answer:D
Answer: (D) 114345
Question: In a circular track of length 100 m, three persons A, B and C start together. A and B start in the same direction at speeds of 10 m/s and 8 m/s respectively. While C runs in the opposite at 15 m/s. when will all the three meet for the first time after the start?
(A) 90
(B) 100
(C) 110
(D) 120
(E) 130
Rationale: A takes (100m) / (10m/s) = 10s to finish one complte round.
B takes (100m) / (8m/s) = 12.5s to finish one complte round.
C takes (100m) / (15m/s) = (20/3)s to finish one complte round.
For them to meet, the time will be LCM of above three times ie LCM(10,12.5,20/3)
= LCM(10/1,25/2,20/3)
= LCM(10,25,20)/GCD(1,2,3)
=100/1
=100
ANSWER:B
Answer: (B) 100
Question: Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.3. If VP Adams approves the proposal, then the probability that vice-president Baker will approve the proposal is 0.4. If VP Adams doesn’t approve the proposal, then the probability that vice-president Baker will approve the proposal is 0.3. What is the probability that at least one of the two VPs, approves Johnson’s proposal?
(A) 0.12
(B) 0.42
(C) 0.28
(D) 0.48
(E) 0.72
Rationale: (1at approves * second rejects ) + (1st rejects * 2nd approves ) + (both approves )
=0.3*0.2+0.4*0.3+0.6*0.4
= 0.06+0.12+0.24
=0.42
B
Answer: (B) 0.42
Question: A can do a piece of work in 16 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
(A) 10 2/5
(B) 10 2/0
(C) 12 1/6
(D) 10 2/1
(E) 12 2/3
Rationale: 2/16 + 4/15 + x/20 = 1
x = 73/6 = 12 1/6 Answer: C
Answer: (C) 12 1/6
Question: If the price of a computer were reduced by 12 percent, which of the following could not be the final price of the computer? (Assume initial price to be integer in cents)
(A) $844.10
(B) $895.40
(C) $1,053.80
(D) $1,135.20
(E) $1,262.80
Rationale: Let X be the initial price of computer without discount
then price (final) after discount should be=X(1-12/100)------->X(22/25)=A(say)
means X=A*(25/22).....
so initial price to be integer(As per stem) final price must be multiple of 22
if we check options all were divisible by 22 except option (A)..which is Ans.
Ans A
Answer: (A) $844.10
Question: Town M	Town N	Town O	Town P	Town Q	Town R ; Town A Town B Town C Town D Town E Town F In the table above, what is the least number of table entries that are needed to show the mileage between each Town and each of the other five Towns?
(A) 11
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: Easy way to go about this problem is we have 6*6 = 36 enteries in table the least number of enteries would be (36 - 6) /2 since 6 enteries represent the distances between same points .
Alternatively this can be solved as combination problem.
Correct Answer E
Answer: (E) 15
Question: 15 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
(A) 210
(B) 320
(C) 150
(D) 220
(E) 100
Rationale: we can go in any bus out of the 15 buses.
Hence He can go in 15 ways.
Since we can not come back in the same bus that he used for travelling,
we can return in 14 ways.
Total number of ways = 15 x 14 = 210
ANSWER:A
Answer: (A) 210
Question: The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 5th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year?
(A) 40
(B) 42
(C) 45
(D) 48
(E) 54
Rationale: 1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer))
2ndyear : 1-2 (age), we take age = 1
3rd year : 2-3 (age), we take age = 2
4th year : 3-4 (age), we take age = 3
5th year : 4-5 (age), we take age = 4
6th year : 5-6 (age), we take age = 5
Thus for the 5th year = 50,
6th year = 50-5 = 45.
The correct answer is C.
Answer: (C) 45
Question: An integer n between 1 and 100, inclusive, is to be chosen at random. What is the probability that n(n+1) will be divisible by 5 ?
(A) 1/9
(B) 1/3
(C) 1/2
(D) 2/3
(E) 2/5
Rationale: n(n+1) to be divisible by 3 either n or n+1 must be a multiples of 3.
In each following group of numbers: {1, 2, 3, 4, 5}, { 6, 7, 8, 9, 10}, ..., {96, 97, 98, 99,100} there is EXACTLY 1 numbers out of 5 satisfying the above condition. For example in {1, 2, 3, 4, 5} n can be: 4 or 5. Thus, the overall probability is 2/5.
Answer: D.
Answer: (E) 2/5
Question: In 1990 the budgets for projects Q and V were $500,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V ?
(A)  1992
(B)  1993
(C)  1994
(D)  1995
(E)  1997
Rationale: Let the no of years it takes is x.
500+30x = 780-10x --> 40x = 280 and x=7.
Thus, it happens in 1997.
E.
Answer: (E)  1997
Question: What is the average (arithmetic mean) of the numbers 16, 17, 18, 19 and 20?
(A)  14.2
(B)  16.5
(C)  17
(D)  17.5
(E)  18
Rationale: {16, 17, 18, 19, 20}={18-2,18-1, 18, 18+1,18+2} --> the average = 18.
Answer: E.
Answer: (E)  18
Question: On a certain test, Bill scored 20 more points than John, but half as many points as Sue. If the sum of the scores of the three students was 200 points, how many points did Bill receive?
(A) 30
(B) 40
(C) 50
(D) 55
(E) 100
Rationale: consider john's points as x
so bill's points are x +20
So sue's points are 2x +40
total of all three students is 4x +60, but this total is given as 200
x = 35
so bill's points = 35 +20 = 55
correct answer option D
Answer: (D) 55
Question: which number need to add to 859622 to get a number exactly divisible by 456?
(A) 547896
(B) 243545
(C) 445321
(D) 354568
(E) 859622
Rationale: Dividend = Quotient * Divisor + Reminder
859622 / 456 gives quotient = 1885 and reminder = 62.
So, the next number divisible by 456 is 456 places infront of 456 * 1885
Which means 456 – 62 = 394 should be added to 859622.
E
Answer: (E) 859622
Question: What is the total number of integers between 100 and 250 that are divisible by 5?
(A) 27
(B) 28
(C) 29
(D) 30
(E) 25
Rationale: 105, 110, 115, ..., 240,245
This is an equally spaced list; you can use the formula:
n = (largest - smallest) / ('space') + 1 = (245 - 105) / (5) + 1 = 140/5 + 1 = 28 + 1 = 29
Answer is C
Answer: (C) 29
Question: Evaluate permutation
4P4
(A) 22
(B) 23
(C) 24
(D) 25
(E) None of these
Rationale: Explanation:
nPn=n!
4P4=4∗3∗2∗1=24
Option C
Answer: (C) 24
Question: The ratio between the present ages of A and B is 5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
(A) 3:9
(B) 3:6
(C) 3:1
(D) 3:4
(E) 3:2
Rationale: Let the present ages of A and B be 5x and 3x years respectively.
Then, (5x - 4)/(3x + 4) = 1/1
2x = 8 => x = 4
Required ratio = (5x + 4):(3x - 4) = 24:8 = 3:1
Answer: C
Answer: (C) 3:1
Question: The ratio between the sale price and the cost price of an article is 10:7. What is the ratio between the profit and the cost price of that article?
(A) 2:9
(B) 2:5
(C) 3:7
(D) 2:0
(E) 2:1
Rationale: Let C.P. = Rs. 7x and S.P. = Rs. 10x.
Then, Gain = Rs. 3x
Required ratio =3x : 7x = 3:7
Answer:C
Answer: (C) 3:7
Question: A man purchases some eggs for Rs.500. 15% of the eggs break during transportation. What profit percentage should he take on the remaining to get an overall profit of 20%?
(A) 37.5
(B) 41.17
(C) 21.17
(D) 45.17
(E) 46.18
Rationale: Explanation:
The eggs remaining = 85%
CP of 85% eggs = 85x500/100 = Rs.425
Overall profit = 500 + 20% of 500 -CP of 85% eggs.
Rs.600 – Rs.425 = Rs.175.
:. Overall profit percent = 175x100/425 = 41.17%.
Answer: Option B
Answer: (B) 41.17
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) Rs. 150
(B) Rs. 300
(C) Rs. 250
(D) Rs. 200
(E) Rs. 220
Rationale: Explanation:
Let the amount paid to X per week =x
and the amount paid to Y per week =y
12y/10+y=550
22y/10=550
y=5500/22=500/2=250
ANSWER IS C
Answer: (C) Rs. 250
Question: How many three digit numbers X greater than 330 can be formed from the digits 1, 2, 3, 4, 5 and 6, if each digit can only be used once?
(A) 72
(B) 48
(C) 120
(D) 96
(E) 76
Rationale: Find the number of 3 digit numbers greater than 300, and then subtract from them the number of three digit numbers between 300 and 330 formed with the given 6 digits.
ABC three digit numbers greater than 300 - total of 4*5*4=80, because a must be greater than 2, so 4 possibilities left; B 5 remaining, and C 4 remaining possibilities to choose from.
Between 300 and 330 there are 1*2*4=8 numbers with the given property: A = 3, 1 possibility; B can be only 1 or 2 (ABC < 330), so two possibilities; C the remaining 4 possibilities after choosing A and B.
Total possible choice 80 - 8 =72=X
Answer: A.
Answer: (A) 72
Question: A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 30 seconds. What is the length of the goods train?
(A) 230 m
(B) 350 m
(C) 260 m
(D) 270 m
(E) None of these
Rationale: Explanation:
Speed =[ 72 x (5/18) ]m/sec= 20 m/sec.
Time = 30 sec.
Let the length of the train be x metres.
Then,[ (x+250)/30 ]= 20
=> x + 250 = 600
=> x = 350. Answer: B
Answer: (B) 350 m
Question: A 180 meter long train crosses a man standing on the platform in 6 sec. What is the speed of the train?
(A) 107 kmph
(B) 138 kmph
(C) 121 kmph
(D) 108 kmph
(E) 103 kmph
Rationale: D
108 kmph
S = 180/6 * 18/5 = 108 kmph
Answer: (D) 108 kmph
Question: An amount at compound interest sums to Rs.17640/- in 2 years and to Rs.19404/- in 3 years at the same rate of interest. Find the rate percentage?
(A) 5%
(B) 7%
(C) 9%
(D) 10%
(E) 12%
Rationale: Explanation:
The difference of two successive amounts must be the simple interest in 1 year on the lower amount of money.
S.I = 19404/- - 17640/- = Rs. 1764/-
Rate of interest = (1764/17640) × (100/1)
=>10%
Answer: Option D
Answer: (D) 10%
Question: How many digits 2^1000 has?
(A) 31
(B) 35
(C) 50
(D) 99
(E) 310
Rationale: 2^10 = 1.024 * 10^3 => 2^1000 = (1.024)^100 * 10^300
therefore 310 digits would be my best guess
E
Answer: (E) 310
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
(A) 10
(B) 18
(C) 36
(D) 72
(E) 84
Rationale: Explanation:
Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x =	(120 + 120) /12
2x = 20
x = 10.
Speed of each train = 10 m/sec = 10 x	18/5 km/hr = 36 km/hr.
ANSWER IS C
Answer: (C) 36
Question: To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 7/10 of its present?
(A) 61.5
(B) 60.5
(C) 63.5
(D) 35.71429
(E) 64.5
Rationale: Let capacity of 1 bucket = x
Capacity of the tank = 25x
New capacity of the bucket = 7x/10
Hence, number of buckets needed = 25x/(7x/10)=(25×10)/7=35.71429
Answer is D.
Answer: (D) 35.71429
Question: If p#q denotes the least common multiple of p and q, then E=((12#16)#(18#24)) = ?
(A)  216
(B)  180
(C)  144
(D)  108
(E)  72
Rationale: There are several ways to find the Least Common Multiple of two numbers. In this case, the most efficient method is to use the Greatest Common Factor: (A * B) / (GCF AB) = LCM AB
The greatest common factor of 12 and 16 is 4. So, 12#16 = 12*16/4 = 48.
The greatest common factor of 18 and 24 is 6. So, 18#24 = 18*24/6 = 72
Finally, the greatest common factor of 48 and 72 is 24. So, E=((12#16)#(18#24)) = 48#72 = (48*72)/24 = 2*72 = 144
The correct answer is C.
Answer: (C)  144
Question: One fourth of a solution that was 15% sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight?
(A) 34%
(B) 24%
(C) 22%
(D) 16%
(E) 8.5%
Rationale: Instead of using complex calculations and remembering formulae, why dont u directly get to weighted average.
3 parts of 15% + 1 part of x (unknown) % = 4 parts of 16%
=> x% = 64%-45% = 16%
ans D it is.
Answer: (D) 16%
Question: The 41 parents participating in the Smithville PTA have been assigned to at least 1 of 3 committees: festival planning, classroom aid, and teacher relations. 21 parents are assigned to the festival planning committee, 18 parents are assigned to the classroom aid committee, and 19 parents are assigned to the teacher relations committee. If 5 parents are assigned to all 3 committees, how many parents are assigned to exactly 2 committees?
(A) 4
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: The formula is Total = A+B+C - sum of exactly two + 2*all three + neither
21+18+19-x-2*5=41
solving for x you get 7
Answer B
Answer: (B) 7