mathewhe/aqua_rat huggingface dataset:
Question: Three competing juice makers conducted a blind taste test with mall shoppers. The shoppers could choose to taste any number of the three brands of juices but had to select at least one juice that they liked. If 100 shoppers liked brand J, 200 shoppers liked brand K, 700 shoppers liked brand L, 250 shoppers liked exactly 2 juices, and 50 shoppers liked all three juices, how many shoppers took the taste test?
(A) 1,300
(B) 1,000
(C) 900
(D) 700
(E) 650
Rationale: Given: Atleast 1 juice was liked by the participants. --> Neither = 0
Assume, I -->No overlap between the sets
II --> Overlap between 2 sets
III --> Overlap between 3 sets
I + 2*(II) + 3*(III) = 100 + 200 + 700
I + 2*(250) + 3*(50) = 1000
I = 350
Total number of shoppers who took the taste test = I + II + III = 350 + 250 + 50 = 650
Answer: E
Answer: (E) 650
Question: In a particular course, only two grades are given all semester: the midterm exam, which counts for 25% of the semester grade, and the final exam, which counts for the remainder. Lindsey's semester grade was 88%. If the highest possible score on either exam is 100%, what is the lowest possible score P that Lindsey could have received on her midterm exam?
(A) 52%
(B) 64%
(C) 72%
(D) 76%
(E) 80%
Rationale: If the midterm counts for 25% of the total grade, then the final exam must count for the remaining 75%, meaning that in this weighted average problem the final is weighted 3 times as much as the midterm. Using the weighted average mapping strategy, then, and maximizing her final exam score so that you minimize her midterm score, you have:
100-------------88----------------------------x
And you know that the ratio is 3:1. Since the final exam score of 100 is weighted heavier, then the difference of 12 between 100 and 88 is the1part of the ratio, meaning that 3(12) is the 3 portion. That equals 36, so the midterm score (x) is 36 less than the weighted average of 88. 88 - 36 = 52, sothe correct answer is 52%.
Answer: (A) 52%
Question: If three eighth of a number is 141. What will be the approximately value of 32.08% of this number?
(A) 90
(B) 120
(C) 160
(D) 60
(E) 100
Rationale: x * 3/8 = 141 => x= 376
376 * 32.08/100 = 120
ANSWER:B
Answer: (B) 120
Question: A searchlight on top of the watch-tower makes 1 revolutions per minute. What is the probability that a man appearing near the tower will stay in the dark for at least 20 seconds?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
Rationale: 1 revolutions per minute = 1 revolution every 60 seconds
So no matter what anybody appearing at the tower cannot stay in the dark for more than 60 seconds. This will be our total number of possibilities i.e the denominator.
P(man in dark for at least 20 seconds) = 1 - P (man in dark for max of 20 seconds) = 1 - 20/60 = 1 - 1/3 = 2/3
or the other way would be:
P(man in dark for at least 20 seconds) is like saying he can be in dark for 5,6,7...all the way to 60 seconds because that is the max. In this approach it would be 20/60 seconds = 1/3.
Answer is B
Answer: (B) 1/3
Question: 85% of a number is added to 24, the result is the same number. Find the number?
(A) 330
(B) 267
(C) 278
(D) 160
(E) 882
Rationale: (85/100) * X + 24 = X
3X = 480
X = 160
Answer:D
Answer: (D) 160
Question: 36 people {a1, a2… a36} meet and shake hands in a circular fashion. In other words, there are totally 36 handshakes involving the pairs, {a1, a2}, {a2, a3}, …, {a35, a36}, {a36, a1}. Then size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
(A) 76
(B) 55
(C) 44
(D) 12
(E) 91
Rationale: Ans: {a1, a2}, {a2, a3},{a3, a4}, {a4, a5},{a5, a6}, {a6, a7} …, {a35, a36}, {a36, a1}
From the above arrangement, If we separate a3, a6, a9, .....a36. Total 12 persons the reamining persons must have shaked hand with atleast one person. So answer is 12.
Answer:D
Answer: (D) 12
Question: IF
6= I
7= E
8= I
9= I
10=E
THEN 11=?
(A) I
(B) J
(C) K
(D) L
(E) M
Rationale: IF
6= I... Second letter of ONE.
7= E.... Second letter of TWO.
8= I
9= I
10= E
THEN 11=L... Second letter of Eleven
ANSWER:D
Answer: (D) L
Question: A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different colors r patterns can be floor be parqueted?
(A)  104
(B)  213
(C)  3^5
(D)  705
(E)  726
Rationale: Total number of squares we need to fill = 6
Number of colors we have r= 3
Therefore, total number of patterns = 3*3*3*3*3*3 = 729
However, this is considering that we can have a case in which all tiles are the same color. Since we are given that the quantity of each tile is 5 and the number of tiles required is 6, we know that this case cannot be possible. Therefore we must subtract the cases in which all tiles will be of the same color (3 cases since there are 3 colors).
Thus our answer should be :729 - 3 = 726
Answer : E
Answer: (E)  726
Question: We all know that square root of number 121 is 11.
But do you know what si the square root of the number "12345678987654321" ?
(A) 222222222
(B) 111111111
(C) 333333333
(D) 777777777
(E) 444444444
Rationale: B
It's a maths magical square root series as :
Square root of number 121 is 11
Square root of number 12321 is 111
Square root of number 1234321 is 1111
Square root of number 123454321 is 11111
Square root of number 12345654321 is 111111
Square root of number 1234567654321 is 1111111
Square root of number 123456787654321 is 11111111
Square root of number 12345678987654321 is 111111111 (answer)
Answer: (B) 111111111
Question: Joe went on a diet 3 months ago when he weighed 222 pounds. If he now weighs 198 pounds and continues to lose at the same average monthly rate, in approximately how many months will he weigh 170 pounds?
(A)  3
(B)  3.5
(C)  4
(D)  4.5
(E)  5
Rationale: 222 - 198 = 24 pounds lost in 3 months
24/3 = 8, so Joe is losing weight at a rate of 8 pounds per month.
...in approximately how many months will he weigh 170 pounds?
A simple approach is to just list the weights.
Now: 198 lbs
In 1 month: 190 lbs
In 2 months: 182 lbs
In 3 months: 174 lbs
In 4 months: 166 lbs
Since 170 pounds is halfway between 174 and 166, the correct answer must be 3.5 months.
Answer: B
Answer: (B)  3.5
Question: The average of first 10 even numbers is?
(A) 17
(B) 199
(C) 16
(D) 11
(E) 123
Rationale: Sum of 10 even numbers = 10 * 11 = 110
Average = 110/10 = 11
Answer:D
Answer: (D) 11
Question: There are 5 balls are in a bag; 2 are red balls and the other 3 are green balls. If 2 magazines are to be selected at random from the 5 balls, what is the probability that at least one of the green ball will be selected?
(A) 11/10
(B) 3/10
(C) 5/10
(D) 7/10
(E) 9/10
Rationale: Total probability=5C2=10
3C2 +3C1*2C1=3+6=9
therefore the probability that at least one of the green ball will be selected= 9/10
answer is E
Answer: (E) 9/10
Question: Look at this series: 23, 22, 24, 23, 25, 24, ... What number should come next?
(A) 20
(B) 26
(C) 28
(D) 21
(E) 22
Rationale: In this simple alternating subtraction and addition series; 1 is subtracted, then 2 is added, and so on.
23-1 = 22
22+2 = 24
24-1 = 23
23+2 = 25
25-1 = 24
24+2 = 26
Answer is B
Answer: (B) 26
Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, which A and B together can do it in 2 hours. How long will C alone take to do it?
(A) 12hours
(B) 10hours
(C) 6hours
(D) 8hours
(E) 4hours
Rationale: A's 1 hour work = 1/4;
(B + C)'s 1 hour work = 1/3;
(A + B)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12
C's 1 hour work = (7/12 - 1/2) = 1/12
C alone will take 12 hours to do the work.
Answer:A
Answer: (A) 12hours
Question: If the sum of three consecutive positive odd integers is A, then the sum of the next three consecutive odd integers in terms of A is:
(A) A+3
(B) A+9
(C) A+18
(D) 2A + 3
(E) 3A
Rationale: In Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median
I.e. Median = A/3 = Mean = Second Integer
First Integer = A/3 - 2
Second Integer = A/3
Third Integer = A/3 + 2
i.e.
Fourth Integer = A/3 + 4
Fifth Integer = A/3 + 6
Sixth Integer = A/3 + 8
Now Mean of next 3 Integers = Median = A/3 + 6
i.e. Sum of Next 3 integers = (A/3 + 6)*3 = A+18
Answer: option C
Answer: (C) A+18
Question: The average of 35 numbers is 25. If each number is multiplied by 5, find the new average?
(A) 125
(B) 777
(C) 255
(D) 199
(E) 261
Rationale: Sum of the 35 numbers = 35 * 25 = 875
If each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets multiplied by 5.
Thus, the new average = 25 * 5 = 125.Answer: A
Answer: (A) 125
Question: In an intercollegiate competition that lasted for 3 days, 175 students took part on day 1, 210 on day 2 and 150 on day 3. If 80 took part on day 1 and day 2 and 70 took part on day 2 and day 3 and 20 took part on all three days, how many students took part only on day 1?
(A) 25
(B) 45
(C) 55
(D) 70
(E) 30
Rationale: Day 1&2 = 80; Only Day 1&2 (80-20) = 60,
Day 2&3 = 70; Only Day 2&3 (70-20) = 50,
Only Day 1 = 175 - (60+50+20) = 45
Answer:B
Answer: (B) 45
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.200
(B) Rs.220
(C) Rs.250
(D) Rs.300
(E) Rs.350
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
C
Answer: (C) Rs.250
Question: The monthly incomes of A and B are in the ratio 5 : 2. B's monthly income is 12% more than C's monthly income. If C's monthly income is Rs. 16000, then find the annual income of A?
(A) Rs. 537600
(B) Rs. 180000
(C) Rs. 201600
(D) Rs. 504000
(E) None of these
Rationale: B's monthly income = 16000 * 112/100 = Rs. 17920
B's monthly income = 2 parts ----> Rs. 17920
A's monthly income = 5 parts = 5/2 * 17920 = Rs. 44800
A's annual income = Rs. 44800 * 12 = Rs. 537600
ANSWER:A
Answer: (A) Rs. 537600
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 4 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 15 a.m
(B) 10 a.m
(C) 7 a.m
(D) 02 a.m
(E) 05 a.m
Rationale: Suppose they meet x hours after 4 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 7 a.m.
Answer:C
Answer: (C) 7 a.m
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 25% profit by using a false weight. What weight does he substitute for a kilogram?
(A) 800 1/7 grams
(B) 800 grams
(C) 800 8/3 grams
(D) 883 1/3 grams
(E) 800 1/3 grams
Rationale: If the cost price is Rs.100, then to get a profit of 25%, the selling price should be Rs.125.
If 125kg are to be sold, and the dealer gives only 100kg, to get a profit of 25%.
How many grams he has to give instead of one kilogram(1000 gm).
125 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/125 =800 grams.
Answer:B
Answer: (B) 800 grams
Question: A man's speed with the current is 21 km/hr and the speed of the current is 4.3 km/hr. The man's speed against the current is
(A) 9.2
(B) 10.3
(C) 11.5
(D) 12.4
(E) 13
Rationale: Man's rate in still water = (21 - 4.3) km/hr = 16.7 km/hr.
Man's rate against the current = (16.7 - 4.3) km/hr = 12.4 km/hr.
Answer:D
Answer: (D) 12.4
Question: The sum of two numbers is 21 and the sum of their squares is 527. Find the product of the numbers.
(A) 48
(B) 41
(C) 46
(D) 43
(E) 96
Rationale: Let a and b be the two numbers(a+b)^2=a^2+2ab+b^2Given (a+b)=21 a^2+b^2=527So, 21^2=527+2ab2ab=527-4412ab=86ab=43Ans D
Answer: (D) 43
Question: If a, b, and c are consecutive positive integers and a > b > c, which of the following must be true?
I. c - a = 2
II. abc is an odd integer.
III. (a + b + c)/3 is an integer.
(A)  I only
(B)  II only
(C)  I and III only
(D)  II and III only
(E)  I, II, and III
Rationale: Since a, b, and c are consecutive positive integers and a < b < c, then c = a + 2, from which it follows that c - a = 2. So, I is true.
Next, out of 3 consecutive integers at least 1 must be even, thus abc=even. II is false.
Finally, since b = a + 1, and c = a + 2, then (a + b + c)/3 = (a + a + 1 + a + 2)/3 = a + 1 = integer. III is true as well.
Answer: C.
Answer: (C)  I and III only
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 96km/h, what is the circumference of the tire?
(A) 7 meters
(B) 9 meters
(C) 4 meters
(D) 5 meters
(E) 3 meters
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 96,000 m : C is the circumference
C = 4 meters
correct answer C
Answer: (C) 4 meters
Question: Approximately what percent of the employees with 5 or more years of employment are NOT taking either workshop?
(A) 86%
(B) 64%
(C) 50%
(D) 14%
(E) 7%
Rationale: Total = n(A) + n(B) - Both + None
None = Total - n(A) - n(B) + Both
Calculate "none" for each case
None(5+ yrs Line) = 200 - 50 - 40 + 30 = 140
None(5+ yrs Staff) = 160 - 40 - 50 + 20 = 90
Employees not taking either workshop/Total number of employees = (140 + 90)/(200 + 160) = 230/360 = About 64%
ANSWER:B
Answer: (B) 64%
Question: A and B undertake to do a piece of work for $600. A alone can do it in 6days while B alone can do it in 8days. With the help of C, they finish it in 3days. Find the share of A?
(A) $100
(B) $150
(C) $300
(D) $250
(E) $350
Rationale: C's 1day work = (1/3)-(1/6 + 1/8) = 1/24
A:B:C= 1/6 : 1/8: 1/24 = 4:3:1
A's share = 600*4/8 = $300
Answer is C
Answer: (C) $300
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 171.The amount of the bill is
(A) Rs. 1386
(B) Rs. 1764
(C) Rs. 1425
(D) Rs. 2268
(E) None of these
Rationale: Solution
32.5
Let P.W. be Rs. x.Then,S.I. on Rs.x at 16% for 9 months =Rs.171.
∴ x 16 x9/ 12x 1/100}= 171 or x = 1425.
∴ P.W. = Rs. 1425.
Answer C
Answer: (C) Rs. 1425
Question: If the two-digit integers P and N are positive and have the same digits, but in reverse order, which of the following CANNOT be the sum of P and N?
(A) 181
(B) 165
(C) 121
(D) 99
(E) 44
Rationale: Since the question asks for the answer that CANNOT be the sum of P and N, and the answers are numbers, we can use a combination of TESTing VALUES and TESTing THE ANSWERS to eliminate the possible values and find the answer to the question.
We're told that P and N are two-digit positive integers and have the SAME DIGITS but in REVERSE ORDER. We're asked which of the 5 answers CANNOT be the SUM of P and N.
Let's start with the 'easiest' answer first:
44. Can we get to 44 in the manner described?
Yes, if the numbers are 13 and 31.....13+31 = 44. Eliminate Answer E
Now let's work through the rest of the list....
Can we get to 99 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 18 and 81.....18+81 = 99. Eliminate Answer D
Can we get to 121 in the manner described?
Yes, there are several ways to do it. For example, if the numbers are 38 and 83.....38+83 = 121. Eliminate Answer C
Can we get to 165 in the manner described?
Yes, there are a couple of ways to do it. For example, if the numbers are 78 and 87.....78+87 = 165. Eliminate Answer B
There's only one answer left....
A
Answer: (A) 181
Question: a school has 9 English 7 history and 6 geography teachers each teacher can teach 2 subjects max what is he minimum number of teachers required
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Total subjects = 9+7+6=22
Max subjects by 1 teacher = 2
So, min of teachers required = 22/2 = 11
ANSWER:E
Answer: (E) 11
Question: If f(a)=a^2, what is the value of (f(a+b)−f(b))/b ?
(A) 2a+a^2
(B) b
(C) 2a
(D) 2a + b
(E) 2b - a
Rationale: start with f(a+b) before start calculations: f(a+b)=(a+b)^2= a^2+2ab+b^2
a^2+2ab+b^2 - b^2/b = (simplify a^2)
2ab+a^2/b = (cancel b's)
= 2a+a^2
Ans : A
Answer: (A) 2a+a^2
Question: A can run 22.5 m while B runs 25 m. In a kilometre race B beats A by:
(A) 120 meter
(B) 300 meter
(C) 100 meter
(D) 200 meter
(E) 500 meter
Rationale: when B runs 25 m, A runs 22.5 m
=> When B runs 1000 metre, A runs 22.5/25 x 1000 = 900m.
=> When B runs 1 kilometre, A runs 900 m
Hence, in a kilometre race, B beats A by
ANSWER:C
(1 kilometre - 900 metre) = (1000 metre - 900 metre) = 100 metre
Answer: (C) 100 meter
Question: The sum of the present ages of two persons A and B is 54. If the age of A is twice that of B, find the sum of their ages 5 years hence?
(A) 50
(B) 64
(C) 70
(D) 80
(E) 90
Rationale: A + B = 54, A = 2B
2B + B = 54 => B = 18 then A = 36.
5 years, their ages will be 41 and 23.
Sum of their ages = 41 + 23 = 64.
ANSWER:B
Answer: (B) 64
Question: If 7800 / 3.25 = 2400, then 780.0 / 32.5 is equal to ?
(A) 21
(B) 28
(C) 26
(D) 25
(E) 24
Rationale: Answer
Given expression 780.0 / 32.5 = 7800 / 325
= 7800 / (3.25 x 100)
= 2400 / 100
=24
Correct Option: E
Answer: (E) 24
Question: A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Explanation:
Relative speed = Speed of A + Speed of B (∴ they walk in opposite directions)
=2+3=5 rounds per hour
Therefore, they cross each other 5 times in 1 hour and 2 times in 12 hour
Time duration from 8 a.m. to 9.30 a.m. =1.5 hour
Hence they cross each other 7 times before 9.30 a.m.
ANSWER IS C
Answer: (C) 7
Question: Sam’s car was fined when he gave Joe and Peter a ride, so they decided to help Sam pay the fine. Joe paid $10 more than 1/4 of the fine and Peter paid $10 less than 1/3 of the fine, leaving pay $25 less than 1/2 the fine to complete the payment. What fraction of the fine did Sam pay?
(A) $120
(B) $125
(C) $130
(D) $135
(E) $140
Rationale: Call the fine F. Joe paid (1/4)F + 4 and Peter paid (1/3)F – 4, leaving (1/2)F – 5 left. If we add those three up, they should add up to F.
F = [(1/4)F + 10] + [(1/3)F – 10] + [(1/2)F – 25]
F = (1/4)F + (1/3)F + (1/2)F – 25
Multiply all terms by 12 to clear the fractions.
12F = 3F + 4F + 6F – 300
12F = 13 F – 300
–F = – 300
F = 300
Well, if the fine cost $300, then Sam paid the part not covered by Joe or Peter. Half the fine is $150, and Sam paid $25 less than this: $125
Answer = B
Answer: (B) $125
Question: Mary built a model ship. She spent 10 hours constructing the ship and 5 hours painting it, for what fraction of the total time did she spend painting the ship?
(A) 1/3
(B) 1/5
(C) 1/4
(D) 2/3
(E) 1/2
Rationale: We don't need to get into calculations for solving this question. We can use the concept of weighted averages.
The average time for the entire project is 15 hours; so, she spent a lesser duration of time painting the ship than constructing it.
5---(5---5)
This shows that you can divide the entire project into 3 equal parts. Thus, 1/3 of the journey was spent painting.
Answer: A
Answer: (A) 1/3
Question: A and B participate in a seven-person footrace on the basketball court during All-Star Weekend. If all seven contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which A defeats B ?
(A)  5040
(B)  2520
(C)  720
(D)  120
(E)  42
Rationale: PRINCETON REVIEW OFFICIAL SOLUTION:
A beats B? Carmelo beats B? No one said anything about specific results, especially not on a question that includes so many people.
Many questions on the GMAT can be overwhelming in appearance so first thing…Relax. This question looks nasty, but it’s pretty straightforward, requiring two things: the basic first calculation and then some additional work to solve the problem. It would be extremely painful to try to calculate this whole question in one fell swoop. So don’t.
Calculate out all possibilities first to get your bearings. That is, how many different arrangements, period? Since the order of arrangement again matters, this is another permutation. And since we’re placing all seven runners, this calculation is…
7 x 6 x 5 x 4 x 3 x 2 x 1, cash and prizes worth 5040 arrangements.
Now, what to do? Again, some nice deep breathing to control your nerves – relax and think. These 5040 arrangements are a comprehensive list; every possible seven-person order of finish has been counted. So, we have accounted for every time A beats B AND every time LeBron beats Carmelo. Doesn’t it make sense that, for every time Carmelo beats LeBron, there is exactly one other instance in which LeBron beats Carmelo? Or more simply, doesn’t it make sense that, if these 5040 represents everything, that Carmelo beats LeBron exactly 50% of the time and vice versa?
The thought takes time. You need to have the presence to recognize that grinding your way in, around, and through this question could take roughly forever. Stepping back and recognizing that this is simply a 50/50 proposition and applying that thought to the 5040 you cranked out gives you 2520. The answer is B.
Answer: (B)  2520
Question: Half of 3 percent written as decimal is
(A) 5
(B) 0.5
(C) 0.05
(D) 0.015
(E) None of these
Rationale: Explanation:
It will be 1/2(3%) = 1/2(3/100) = 3/200 = 0.015
Answer: Option D
Answer: (D) 0.015
Question: Jane and Thomas are among the 6 people from which a committee of 3 people is to be selected. How many different possible committees of 3 people can be selected from these 6 people if at least one of either Jane or Thomas is to be selected?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
Rationale: The total number of ways to choose 3 people from 6 is 6C3 = 20.
The number of committees without Jane or Thomas is 4C3 = 4.
There are 20-4 = 16 possible committees which include Jane and/or Thomas.
The answer is C.
Answer: (C) 16
Question: In a class of 37 students 26 play football and play 20 long tennis, if 17 play above, many play neither?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 14
Rationale: 26 + 20 - 17 = 29
37 - 29 = 8 play neither
Answer is B
Answer: (B) 8
Question: What is the area of square field whose side of length 25 m?
(A) 225 sq m
(B) 186 sq m
(C) 586 sq m
(D) 287 sq m
(E) 625 sq m
Rationale: 25 * 25
= 625 sq m
Answer: E
Answer: (E) 625 sq m
Question: P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 35 days to complete the same work. then Q alone can do it in
(A) 20
(B) 22
(C) 25
(D) 28
(E) 30
Rationale: Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/35
Work done by P, Q and R in 1 day = 1/10 + 1/35 =9/70
But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day Ã— 2 = 9/70
=> Work done by P in 1 day = 9/140
=> Work done by Q and R in 1 day = 9/140
Hence work done by Q in 1 day = 9/140â€“ 1/35 = 1/28
So Q alone can do the work in 28 days
Answer is D.
Answer: (D) 28
Question: 6 + 12 + 18 + 5 x 6^2 + 5 x 6^3 + 5 x 6^4 + 5 x 6^5 + 5 x 6^6 =
(A)  6^7
(B)  6^10
(C)  6^12
(D)  6^16
(E)  6^18
Rationale: Let's see that 6 + 12 + 18 is 36 or 6^2, then: 6^2 + 5 x 6^2 becomes 6 x 6^2 that is 6^3. So we follow with the next element: 6^3 + 5 x 6^3 is equal to 6 x 6^3 that is 6^4. Then is assumed right before 5 x 6^6: 6^6 + 5 x 6^6 becomes 6 x 6^6 that is 6^7. Thus, the correct answer is the option A, 6^7.
Answer: (A)  6^7
Question: A car takes 6 hours to cover a distance of 180 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) 20 Kmph
(C) 65 Kmph
(D) 70 Kmph
(E) None
Rationale: Time = 6
Distence = 180
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 180/9 = 60 Kmph
B)
Answer: (B) 20 Kmph
Question: How many positive integers less than 70 have a reminder 01 when divided by 3?
(A) 13
(B) 24
(C) 35
(D) 16
(E) 17
Rationale: 1 also gives the remainder of 1 when divided by 3. So, there are total of 24 numbers.
Answer: B.
Answer: (B) 24