mathewhe/aqua_rat huggingface dataset:
Question: What number continues the following sequence?
759, 675, 335, 165, ?
(A) 23
(B) 43
(C) 57
(D) 76
(E) 80
Rationale: E
80.
Each number is formed by multiplying the number formed by the first two digits of the previous number by its third digit. So, 16x5 = 80
Answer: (E) 80
Question: There are thirty-four lines that are tangent to a circle, and these lines create regions in the plane. Can you tell how many of these regions are not enclosed ?
(A) 50
(B) 74
(C) 37
(D) 77
(E) 68
Rationale: E
68
68 regions. Each new tangent increases the non-enclosed areas by two
Answer: (E) 68
Question: The average age 110 employees in a office is 40 years. Out of these, the average age of 65 employees is 45 years and that of the other 45 employees is 32 years. The age of the 110h employee is?
(A) 34
(B) 35
(C) 45
(D) 32
(E) 40
Rationale: Age of the 110th employee= 110*40- (65*45+45*32) = 4400-4365= 35 years
Answer is B
Answer: (B) 35
Question: Find the odd man out. 945, 725, 642, 481, 514, 835
(A) 945
(B) 725
(C) 642
(D) 481
(E) None of these
Rationale: Explanation :
In all numbers except 481, the difference of third and first digit is the middle digit. Answer : Option D
Answer: (D) 481
Question: Krisp cereal is 10% sugar by weight. Brano cereal is 2% sugar by weight. If you wanted to make the mixture 4% sugar by weight what should the ratio of Krisp to Brano.
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6
Rationale: w1 is the weight krisp, w2 is the weight of Brano
using weighted average formula w1/w2 = (c2 - avg) / (Avg-c1)
w1/w2 = 4-2 / 10-6 = 2/3
So Krisp and brano should be mixed in the ratio of 1/3.
ANSWER:B
Answer: (B) 1/3
Question: D is the set of all the multiples of 3 between 20 and 100. E is the set of all the factors of 200. Set D and Set E have how many numbers in common?
(A) 10
(B) 1
(C) 3
(D) 5
(E) 0
Rationale: D is a set of multiples of 3.
200 is NOT a multiple of 3, hence none of its factors is a multiple of 3.
Therefore, those two sets won't have any overlap.
Answer: E.
Answer: (E) 0
Question: In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
(A) 62%
(B) 57%
(C) 52%
(D) 22%
(E) 42%
Rationale: Total = 100
T= 40 NT= 60
40*(60/100)=24 60*(40/100)=24
24 + 24 = 48 => 100 - 48 = 52%
Answer:C
Answer: (C) 52%
Question: What is the greatest prime factor of 8^11 - 2^30?
(A) 2
(B) 3
(C) 5
(D) 7
(E) 11
Rationale: 8^11 - 2^30
=(2^3)^11 - 2^30
= 2^33 - 2^30
= 2^30 (2^3 -1)
= 2^30 * (8-1)
= 2^30 * 7
The greatest prime factor is 7.
The answer is D.
Answer: (D) 7
Question: The average of first 10 odd numbers is?
(A) 22
(B) 10
(C) 98
(D) 66
(E) 88
Rationale: Sum of 10 odd no. = 100
Average = 100/10 = 10
Answer:B
Answer: (B) 10
Question: Sarah had 13 pieces of candy. She ate several pieces of the candy and noticed that the number of remaining pieces was a prime number. Which of the choices is a possibility for the number of pieces left?
(A) 12 pieces
(B) 10 pieces
(C) 9 pieces
(D) 8 pieces
(E) 7 pieces
Rationale: Answer E, 7, is a prime number.
Answer: (E) 7 pieces
Question: Pavan travelled for 11 hours. He covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph. Find the distance travelled by Pavan.
(A) 208 km
(B) 637 km
(C) 342 km
(D) 300 km
(E) 543 km
Rationale: Let the distance travelled be x km.
Total time = (x/2)/30 + (x/2)/25 = 11
=> x/60 + x/50 = 11 => (5x + 6x)/300
= 11 => x = 300 km
Answer:D
Answer: (D) 300 km
Question: Numbers like 12345, 13542 and 21435 are some of the 120 different arrangements that can be made from the digits 1, 2 , 3, 4 and 5. If all 120 arrangements are placed in ascending manner, what will be the 87th number?
(A) 43255
(B) 53215
(C) 45215
(D) 43215
(E) 63215
Rationale: 1 _ _ _ _ =24
2 _ _ _ _ =24
3 _ _ _ _ =24
4 1 _ _ _ =6
4 2 _ _ _ =6
4 3 1 2 5 =85th
So, 87th = 43215
ANSWER:D
Answer: (D) 43215
Question: If 3/p=4 & 3/q=18 then p-q=?
(A) 5/24
(B) 7/12
(C) 7/24
(D) 8/24
(E) 9/24
Rationale: p=3/4 , q=3/18=>q=1/6
therefore
p-q=(3/4)-(1/6)=7/12
ANSWER:B
Answer: (B) 7/12
Question: An IT company wants to hire 500 candidate, and each candidate is either engineer, manager, or peon . If it wants to hire 300 more engineers than managers, and twice as many peons as managers. how many engineers does The company want to hire ?
(A) 310
(B) 320
(C) 330
(D) 340
(E) 350
Rationale: x = the number of engineers
y = the number of managers
z = the number of peons
From the first sentence we have
Equation #1: x + y + z = 500
...It wants to hire 300 more engineers than managers...
Equation #2: x = 300 + y
...twice as many peons as managers...
Equation #3: z = 2y
by reshuffling of equation #2 : x - y = 300
Now, we can replace z with y in Equation #1
equation #4 : x + y + 2y= 500
x+3y = 500
by adding equation #4 and equation #5 we get
y = 50
There are 50 managers.This is 300 less than the number of engineers, so x = 350. That's the answer. Just as a check, z = 100, and 350 + 50 + 100 = 500.
Answer = 350,(E)
Answer: (E) 350
Question: A boy buys 18 sharpners, (Brown/white) for Rs.100. For every white sharpener, he pays one rupee more than the brown sharpener. What is the cost of white sharpener and how much did he buy?
(A) 3.9
(B) 3,6
(C) 2,3
(D) 22,2
(E) 12,1
Rationale: C
Assume that he bought b, brown sharpeners and w, white sharpeners and the cost of brown sharpener is x and white sharpener is x + 1
So w(x+1) + bx = 100
w + b = 18
b = 18 - w
Substituting in equation 1, we get w(x+1) + (18 -w)x = 100 so w + 18 x = 100
Take option 1: If white sharpners are 13, x = (100 - 13) /18 = 4.833
Option 2, If white sharpeners are 10, x = (100 - 10)/18 = 5 So white sharpeners cost is 6.
Option 3 Satisfies this condition.
Answer:B
Answer: (B) 3,6
Question: In a certificate by mistake a candidate gave his height as 10% more than actual height. In the interview panel, he clarified that his height was 5 feet 5 nches. Find the % correction made by the candidate from his stated height to his actual height?
(A) 6.5
(B) 7
(C) 8
(D) 9
(E) 5
Rationale: His height was = 5 feet 5 inch = 5 + 60 = 65 inch. Required % correction =65*(1.10-1) = 6.5
A
Answer: (A) 6.5
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) 5991
(B) 4991
(C) 6001
(D) 7001
(E) 7999
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) - 34009 ]
= Rs. (39000 - 34009)
= Rs. 4991.
ANSWER B
Answer: (B) 4991
Question: The average of 50 numbers id 50. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is :
(A) 22
(B) 33
(C) 22
(D) 41
(E) 50
Rationale: Explanation:
Total of 50 numbers = (50×50)=2500
Total of 48 numbers =(2500-(45+55)]=2400
Required average = 2400/48=50
Answer:E
Answer: (E) 50
Question: What number is logically missing from the sequence below?
348269, 284315, ****, 8438, 4811
(A) 32456
(B) 84382
(C) 48114
(D) 28437
(E) 34826
Rationale: E
34826
Each number is the sum of the last two digits of the previous number, preceded by the remaining numbers in reverse.
Answer: (E) 34826
Question: If l is an integer, what is the greatest possible value for l that would still make the following statement true: 11*10^l < 1/10 ?
(A)  –4
(B)  –3
(C)  –2
(D)  –1
(E)  0
Rationale: Just putting values, the LHS becomes
l=0 --> 11
l=-1 --> 11/10
l=-2 --> 11/100
l=-3 --> 11/1000
Anything lower will be smaller than 11/1000. l=-2, equality does not hold but it does for n=-l.
Answer is B.
Answer: (B)  –3
Question: The average weight of 16 boys in a class is 50.25 kgs and that of the remaining 8 boys is 45.15 kgs. Find the average weight of all the boys in the class.
(A) 47.55 kgs
(B) 48 kgs
(C) 48.55 kgs
(D) 49.25 kgs
(E) None of these
Rationale: Solution
Required average =(50.25x16+45.15x8/16+8) =(804+361.20/24) =1165.20/24 =48.55 Answer C
Answer: (C) 48.55 kgs
Question: At a certain college there are three as many English majors as history majors and two times as many English majors as mathematics majors. What is the ratio of the number of mathematics majors to the number of history majors?
(A) 6 to 1
(B) 3 to 5
(C) 2 to 3
(D) 3 to 2
(E) 1 to 6
Rationale: This is how I translated the question:
At a certain college there are twice as many english majors as history majors
E = 3H
and three times as many english majors as mathematics majors.
E = 2M
What is the ratio of the number of history majors to the number of mathematics majors?
What is H:M?
Just set E equal to each other to get the ratio in terms of H and M.
2H = 3M
M/H = 3/2
The answer is 3:2
Answer : D
Answer: (D) 3 to 2
Question: The simple interest on a sum of money will be Rs.1400 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
(A) 2800
(B) 3799
(C) 1200
(D) 2693
(E) 1732
Rationale: P --- 10 ---- 1400
P --- 5 ----- 700
3P --- 5 ----- 2100
------
=> 2800
Answer: A
Answer: (A) 2800
Question: Find the average of all the numbers between 11 and 34 which are divisible by 5?
(A) 10
(B) 20
(C) 22
(D) 30
(E) 15
Rationale: Average = (15+20+25+30) 4 = 90/4 = 22
Answer is C
Answer: (C) 22
Question: A can finish a work in 72days, B in 9days and C in 2days, B and C start the work but are forced to leave after 3 days. The remaining work was done by A in?
(A) 30days
(B) 12days
(C) 6days
(D) 7days
(E) 8days
Rationale: B+C 1day work = 1/9 + 1/12 = 7/36
work done by B and C in 3days = 7/36 * 3 = 7/12
Remaining work = 1 - 7/12 = 5/12
1/24 work is done by A in 1day
5/12 work is done by A in 72*5/12 = 30days
Answer is A
Answer: (A) 30days
Question: The length of rectangle is thrice its breadth and its perimeter is 96 m, find the area of the rectangle?
(A) 432
(B) 876
(C) 297
(D) 200
(E) 267
Rationale: 2(3x + x) = 96
l = 36 b = 12
lb = 36 * 12 = 432
Answer:A
Answer: (A) 432
Question: Two trains each 190m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 65km/h while the other travels at 50km/h. how long will it take for them to pass each other completely.
(A) 10.7 sec
(B) 2.7 sec
(C) 11.9 sec
(D) 12.7 sec
(E) 25.7 sec
Rationale: Explanation:
D = 190 m + 190 m = 380 m
RS = 65 + 50 = 115 * 5/18 = 319/10
T = 380 * 10/319 = 11.9 sec
Answer: Option C
Answer: (C) 11.9 sec
Question: There are 5 periods in each working day of a school. In how many ways can one organize 4 subjects such that each subject is allowed at least one period?
(A) 240
(B) 250
(C) 260
(D) 280
(E) None of these
Rationale: 4 subjects can be arranged in 5 periods in 5P4 ways.
Remaining 1 period can be arranged in 4P1 ways.
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements = (5P4 x 4P1)/2! = 240
ANSWER:A
Answer: (A) 240
Question: A box contains 2 white balls, 3 black ball and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
(A) 32
(B) 48
(C) 64
(D) 96
(E) 54
Rationale: We may have ( 1 black and 2 non black) or (2 black and 1 non black)or(3 black)
=3c1 x 6c2 + 3c2 x 6c1 +3c3
=64
ANSWER C 64
Answer: (C) 64
Question: A shopkeeper sells 20% of his stock at 20% profit ans sells the remaining at a loss of 10%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
(A) 15500
(B) 16000
(C) 15000
(D) 17000
(E) 20000
Rationale: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 6/5 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.90 = 19x/25 = 36x/50
Total SP = 12x/50 + 36x/50 = 48x/50
Overall loss = x - 48x/50 = 2x/50
2x/50 = 600 => x = 15000
Answer:C
Answer: (C) 15000
Question: If it would take one machine 10 minutes to fill a large production order and another machine 18 minutes to fill the same order, how many minutes would it take both machines working together, at their respective rates, to fill the order?
(A) 4 1/60
(B) 5
(C) 5 5/11
(D) 6 3/7
(E) 11
Rationale: Since , Machine 1-M1 take 10 mins to fill the order
The work done by M1 in a min = 1/10
Machine 2- M2 take 18 mins to fill the same order
and work done by M2 in a min = 1/18
Total work done by M1 and M2 in a min = 1/10 + 1/18 = 14/90 = 7/45
Time needed for M1 and M2 to complete the order = 45/7 = 6 3/7
Answer D
Answer: (D) 6 3/7
Question: If the price of an item is decreased by 40% and then increased by 20%, the net effect on the price of the item is
(A) A decrease of 99%
(B) No change
(C) A decrease of 1%
(D) A increase of 1%
(E) A decrease of 28%
Rationale: initially assume 100 rupees
40% discount in 100 gives price of 60 rupees
then 20% raise in 60 is only 12 rupees.
therefore total price =72 rupees.
hence 28% is the loss
ANSWER:E
Answer: (E) A decrease of 28%
Question: If g,h,i,j represents the result gotten when the figure 8236.186 is rounded off to the nearest thousand, hundred ten and one, which of the following statements is correct?
(A) h<gh<j<i
(B) g<g<h<i
(C) g<h<j<i
(D) i<h<j<g
(E) g<i<j<h
Rationale: 8236.186..
Nearest thousand 8000..g
Nearest hundred 8200..h
Nearest ten 8300..i
Nearest one 8296..j
g<h<j<i
The correct option is C
Answer: (C) g<h<j<i
Question: what is the 50th term of term of the series 1,3,6,10,15,21?
(A) 1265
(B) 1270
(C) 1275
(D) 1280
(E) 1285
Rationale: The series is like 1,1+2,1+2+3,1+2+3+4,....
so 50th term wil be 1+2+3+4+....50
sum of n natural numbers =n*(n+1)/2 where n is 50
answer wil be 25*51=1275
ANSWER:C
Answer: (C) 1275
Question: A certain clock marks every hour by striking a number of times equal to the hour, and the time require for a stroke is exactly equal to the time interval between strokes. At 6:00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds. At 9:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
(A) 36
(B) 35
(C) 34
(D) 38
(E) 40
Rationale: at 6'o clock, there would be 6 strikes. First strike, then a short interval, the second strike, then a short interval and so on till the 6th strike. So there would be in all 5 intervals between 6 strikes. Similarly, between 9 strikes, there would be 8 intervals.
According to the question, the time spent in the strike and the interval is same.
At 6'o clock, the 6 strikes and the 5 intervals together take 22 sec so each strike and each interval takes 2 secs.
At 12'o clock, the 9 strikes and 8 intervals will take 2*(9+8) = 34 secs
C
Answer: (C) 34
Question: Given that 268 * 74 = 19832, find the values of 2.68 * 0.74.
(A) 1.9328
(B) 1.9832
(C) 1.9823
(D) 1.9382
(E) None of them
Rationale: Sum of decimal places = (2 + 2) = 4
2.68 * 0.74 = 1.9832.
Answer is B.
Answer: (B) 1.9832
Question: The average weight of 7 person's increases by 3.5 kg when a new person comes in place of one of them weighing 75 kg. What might be the weight of the new person?
(A) 74 kg
(B) 78.5 kg
(C) 99.5 kg
(D) Data inadequate
(E) None of these
Rationale: Total weight increased = (7 x 3.5) kg = 24.5 kg.
Weight of new person = (75 + 24.5) kg = 99.5 kg.
Answer: Option C
Answer: (C) 99.5 kg
Question: Peter invested a certain sum of money in a simple interest bond whose value grew to $100 at the end of 2 years and further to $200 at the end of another 4 years. What was the rate of interest in which he invested his sum?
(A) 50%
(B) 25%
(C) 10%
(D) 30%
(E) 18%
Rationale: Explanatory Answer
Initial amount invested = $ X
Amount at the end of year 2 = $ 100
Amount at the end of year 6 (another 4 years) = $ 200
Therefore, the interest earned for the 4 year period between the 2rd year and 6th year = $200 - $100 = $100
As the simple interest earned for a period of 4 years is $ 100, interest earned per year = $25.
Therefore, interest earned for 2 years = 2 * 25 = $ 50.
Hence, initial amount invested X = Amount after 2years - interest for 2 years
= 100 - 50 = $ 50.
Rate of interest = (interest per year/principal)*100 = 25/50*100 = 50%
correct choice is A
Answer: (A) 50%
Question: In how many different ways can the letters of the word 'SINGING' be arranged in such a way that the vowels always come together?
(A) A)360
(B) B)480
(C) C)720
(D) D)5040
(E) of these
Rationale: The word 'SINGING' has 7 different letters.
When the vowels II are always together, they can be supposed to form one letter.
Then, we have to arrange the letters SNGNG (II).
Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways.
The vowels (II) can be arranged among themselves in 1! = 1 way.
Required number of ways = (720 x 1) = 720.
ANSWER:C
Answer: (C) C)720
Question: In a dairy farm, 26 cows eat 26 bags of husk in 26 days. In how many days one cow will eat one bag of husk?
(A) 1
(B) 40
(C) 20
(D) 26
(E) 30
Rationale: Explanation :
One bag of husk = 26 cows per day
⇒ 26 × 1 × 26 = 1 × 26 × x
For one cow = 26 days
Answer : D
Answer: (D) 26
Question: A certain university will select 1 of 6 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?
(A) 42
(B) 270
(C) 140
(D) 165
(E) 315
Rationale: 1 of 6 will be chosen for the math
2 of 10 will be chosen for the computer
None of the 3 chosen people can be in more than one departments.
We can choose any of the 6 candidates for the math dep., which gives as 6 selections.
We can choose 2 of the 10 candidates for the computer dep., which gives us 2 selections and 8 rejections.
So, the way to find how many different selections of 2 candidates we can have for the computer dep., we do:
10! /2!*8!= (9*10) / 2 = 90 / 2 = 45.
We are multiplying our individual selections: 6*45 = 270
In the bolded part, we don't have to multiply all of the numbers, as those in 8! are included in 10!, so we simplify instead.
Ans B
Answer: (B) 270
Question: In a certain company, a third of the workers do not have a retirement plan. 50% of the workers who do not have a retirement plan are women, and 40% of the workers who do have a retirement plan are men. If 120 of the workers of that company are men, how many of the workers are women?
(A) 80
(B) 95
(C) 105
(D) 156
(E) 210
Rationale: Set up equation:
x = total number of workers
120 = 0,4 * 2/3 * x + 0,5 * 1/3 * x
120 = 13/30 x
x = 276
276 - 120 = 156
Answer D
Answer: (D) 156
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 130 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) 520
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) = 130
Group #2 = (like understood) = 3/4
(1/4)N = 130
N = 520
Answer =(E)
Answer: (E) 520
Question: Peter and Tom shared the driving on a certain trip. If Peter and Tom both drove for the same amount of time, but Peter only drove 3/5 of the total distance, what was the ratio of Peter's average speed to Tom's average speed?
(A) 1:5
(B) 3:2
(C) 1:2
(D) 3:5
(E) 2:3
Rationale: The answer is suppose to be B. 3:2. It's from the GMATPrep
Answer:option B
Answer: (B) 3:2
Question: P,Q and R together earn Rs.1620 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?
(A) Rs.40
(B) Rs.70
(C) Rs.90
(D) Rs.100
(E) Rs.120
Rationale: Explanation :
Amount Earned by P,Q and R in 1 day = 1620/9 = 180 ---(1)
Amount Earned by P and R in 1 day = 600/5 = 120	---(2)
Amount Earned by Q and R in 1 day = 910/7 = 130	---(3)
(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day
- Amount Earned by P,Q and R in 1 day = 120+130-180 = 70
=>Amount Earned by R in 1 day = 70
Answer : Option B
Answer: (B) Rs.70
Question: By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c?
(A) 28788
(B) 38000
(C) 27992
(D) 28872
(E) 29982
Rationale: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Answer: B
Answer: (B) 38000
Question: if length of a room is three times of its breadth and its area is 12 sq.m.what is perimeter of room?
(A) 14 m
(B) 18 m
(C) 24 m
(D) 16 m
(E) none of the above
Rationale: let breadth=x m. and length = 3x m.
x*3x=12,x^2=4,x=2.
length=6m,breadth = 2 m.
perimeter=2*(6+2)=16 m
answer D
Answer: (D) 16 m
Question: The curved surface of a sphere is 64 π cm2. Find its radius?
(A) 8
(B) 3
(C) 4
(D) 9
(E) 7
Rationale: Explanation:
4 πr2 = 64 => r = 4
Answer: Option C
Answer: (C) 4
Question: A train passes a station platform in 35 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 225
(B) 279
(C) 240
(D) 288
(E) 231
Rationale: Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x meters.
Then, x + 300 / 35 = 15
x + 300 = 525
x = 225 m. Answer:A
Answer: (A) 225
Question: A school’s annual budget for the purchase of student computers increased by 32% this year over last year. If the price of student computers increased by 20% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?
(A) 15%
(B) 5%
(C) 10%
(D) 12%
(E) 6%
Rationale: Lats year: budget = $100, price = $1 --> the number of computers purchased = 100/1 = 100;
This year: budget = $132, price = $1.2 --> the number of computers purchased = 132/1.2 = 110.
Increase in the number of computers purchased = 10%.
Answer: C
Answer: (C) 10%
Question: A can give B 60 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 148.94
(B) 148.13
(C) 148.22
(D) 111.0
(E) 111.12
Rationale: A runs 1000 m while B runs 940 m and C runs 800 m.
The number of meters that C runs when B runs 1000 m,
= (1000 * 800)/940
= 851.06 m.
B can give C = 1000 - 851.06
=148.94m.
Answer:A
Answer: (A) 148.94
Question: The respective ages of father and his son are 47 and 16 years. In how many years will the father be twice as old as his son ?
(A) 19 years
(B) 9 years
(C) 10 years
(D) 15 years
(E) 12 years
Rationale: Suppose x years later the father will be twice as old as his son.
x + 47 = 2 (x + 16)
x = 47 - 32 = 15 years
answer : D
Answer: (D) 15 years
Question: In how many ways a committee consisting of 3 men and 2 women can be formed from 4 men and 3 women?
(A) 10
(B) 15
(C) 20
(D) 18
(E) 21
Rationale: Required number of ways = 4C3*3C2 = 4*3 = 12
Answer is A
Answer: (A) 10
Question: What is the greatest positive integer x such that 7^x is a factor of 343^10?
(A) 5
(B) 9
(C) 10
(D) 20
(E) 30
Rationale: 343^10 = (7^3)^10 = 7^30
ANSWER:E
Answer: (E) 30
Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
(A) 5
(B) 10
(C) 50
(D) 40
(E) 30
Rationale: 20 + 24 + 8 * 2 = 60/2 = 30
Answer: E
Answer: (E) 30
Question: The speed of a boat in still water is 70kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 80,47 kmph
(B) 80,80 kmph
(C) 80,42 kmph
(D) 90,50 kmph
(E) 83,40 kmph
Rationale: Speed downstream = 70 + 20 = 90 kmph
Speed upstream = 70 - 20 = 50 kmph.Answer:D
Answer: (D) 90,50 kmph
Question: If x and y are non-zero integers, and 64x^4 – 4y^4 = 8x^2 + 2y^2, which of the following could be the value of x2 in terms of y?
(A) 2y^2
(B) 2y
(C) 2y^2/8
(D) 2y^2-1/8
(E) 2y^2+1/8
Rationale: 64x^4 – 4y^4 = 8x^2 + 2y^2
(8x^2 + 2y^2) (8x^2 - 2y^2) = 8x^2 + 2y^2
8x^2 - 2y^2 = 1
8x^2 = 2y^2+1
x^2 = 2y^2+1/8
Answer : E
Answer: (E) 2y^2+1/8