mathewhe/aqua_rat huggingface dataset:
Question: Two pipes A and B can separately fill a tank in 12 and 15 minutes respectively. A third pipe C can drain off 42 liters of water per minute. If all the pipes are opened, the tank can be filled in 15 minutes. What is the capacity of the tank?
(A) 542
(B) 504
(C) 548
(D) 829
(E) 279
Rationale: 1/12 + 1/15 - 1/x = 1/15
x = 12
12 * 42 = 504
Answer: B
Answer: (B) 504
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
(A) 12227
(B) 2787
(C) 2500
(D) 2778
(E) 2789
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500
Answer: C
Answer: (C) 2500
Question: In a sports club with 27 members, 17 play badminton and 19 play tennis and 2 do not play either. How many members play both badminton and tennis?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Let x play both badminton and tennis so 17-x play only badminton and 19-x play only tennis. 2 play none and there are total 30 students. hence,
(17-x)+(19-x)+x+2=27
38-2x+x=27
38-x=27
x=11
So 8 members play both badminton and tennis.
E
Answer: (E) 11
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
(A) 16 2/3%
(B) 30%
(C) 33 1/3%
(D) 33 1/6%
(E) 33 4/6%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
ANSWER:C
Answer: (C) 33 1/3%
Question: A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 30 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder?
(A)  $198
(B)  $216
(C)  $220
(D)  $230
(E)  $168
Rationale: Wholesale cost of video recorder = 200 $
Video recorder was priced at 20 percent above 200 = 240 $
% discount given by store employee = 30
Emlpoyee paid = .7 * 240 = 168 $
Answer E
Answer: (E)  $168
Question: There are 9 people in the room. There are two pairs of siblings within that group. If we choose two people, what is the probability that they will not be siblings?
(A) 12/18
(B) 17/18
(C) 2/9
(D) 1/18
(E) 4/18
Rationale: we have XXXXXBBCC
We have to take into the account when we have XX, XB, XC
So 5/9*4/8 5/9*2/8 and 5/9*2/8 note we need to multiply these by 2 (except the first) b/c we can have BX and CX.
20+20+20 --> 60/72 --> 30/36 --> 15/18
then next is
BC 2/9*2/8 --> 4/72 2/36 1/18 --> multiply this by 2 b/c of CB
so 2/18+15/18 --> 17/18
ANSWER:B
Answer: (B) 17/18
Question: Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
(A) Rs. 16500
(B) Rs. 15525
(C) Rs. 17000
(D) Rs. 17600
(E) None of these
Rationale: Price at which the TV set is bought = Rs. 12,500
Discount offered = 20%
Marked Price = 12500 * 100/80 = Rs. 15625
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100 = Rs. 17600
ANSWER:D
Answer: (D) Rs. 17600
Question: X starts a business with Rs.35000. Y joins in the business after 3 months with Rs.25000. What will be the ratio in which they should share the profit at the end of the year?
(A) 28:15
(B) 29:16
(C) 25:23
(D) 14:15
(E) None of these
Rationale: Explanation :
Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
= 35000 * 12: 25000 * 9
= 35 * 12: 25 * 9
= 7*4: 5 * 3
= 28:15. Answer : Option A
Answer: (A) 28:15
Question: A, B and C can do a piece of work in 7 days, 14 days and 28 days respectively. How long will they taken, if all the three work together?
(A) 4
(B) 3
(C) 5
(D) 6
(E) 2
Rationale: 1/7 + 1/14 + 1/28 = 7/28 = 1/4 => 4 days
ANSWER A
Answer: (A) 4
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is?
(A) 1/32
(B) 1/36
(C) 1/33
(D) 1/38
(E) 1/34
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216
= 1/36
Answer: B
Answer: (B) 1/36
Question: If 5 men and 2 boys working together, can do four times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time?
(A) 3:2
(B) 2:1
(C) 3:3
(D) 1:2
(E) 6:1
Rationale: B
2:1
5M + 2B = 4(1M + 1B)
5M + 2B = 4M + 4B
1M = 2B
The required ratio of work done by a man and a boy = 2:1
Answer: (B) 2:1
Question: A number x is multiplied by 7, and this product is then divided by 5. If the positive square root of the result of these two operations equals x, what is the value of x if x≠0 ?
(A) 25/9
(B) 9/5
(C) 5/3
(D) 7/5
(E) 9/25
Rationale: sqrt(7x/5) to be perfect square x has to 7/5
Ans: D
Answer: (D) 7/5
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
(A) 31.9
(B) 31.7
(C) 31.6
(D) 31.5
(E) 31.1
Rationale: 100*(80/100)*(90/100)*(95/100) = 68.4
100 - 68.4 = 31.6
Answer:C
Answer: (C) 31.6
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 120. If legs are counted, there are 580. The number of hares in the zoo is?
(A) 20
(B) 82
(C) 190
(D) 137
(E) 170
Rationale: 120*2 = 240
580
-----
340
1----2
?----340 =170
Answer:E
Answer: (E) 170
Question: At a small company, 58 percent of the employees are women, and 60 percent of the employees are married. If 2/3 of the men are single, what fraction of the women are married?
(A) 5/16
(B) 1/3
(C) 23/29
(D) 7/10
(E) 5/7
Rationale: Lets take total employees are 100.
Given that,Total Women= 58 and Total Married = 60.
Total Men = 100 - 58 = 42 and Single men = 2/3*42 = 28.
Married men = total men - single men = 42 - 28 = 14.
Married women= Total married - Married men = 60 - 14 = 46.
Fraction of women are married = Married women / Total Women = 46 / 58 = 23/29. ANS C
Answer: (C) 23/29
Question: Find the C.I. on a sum of Rs.10000 for 9 months at 20% per annum, interest being compounded quarterly?
(A) 2000
(B) 10025
(C) 1025
(D) 2015
(E) 2025
Rationale: C.I.= 10000(21/20)^3-10000
= 1025
Answer: C
Answer: (C) 1025
Question: What is theleast number should be added to 1056, so the sum of the number is completely divisible by 23?
(A) 1
(B) 2
(C) 4
(D) 5
(E) 6
Rationale: (1056 / 23) gives remainder 21
21 + 2 = 23, So we need to add 2
B
Answer: (B) 2
Question: A set consists of 20 numbers, all are even or multiple of 5. If 9 numbers are even and 12 numbers are multiple of 5, how many numbers is multiple of 10?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  5
Rationale: {Total} = {Even} + {Multiple of 5} - {Both} + {Nether}.
Since{Neither}=0(allare even or multiple of 5) then:
20 = 9 + 12 - {Both} + 0;
{Both}=1(so 1 number is both even AND multiple of 5, so it must be a multiple of 10).
Answer: B.
Answer: (B)  1
Question: Walking with 4/5 of my usual speed, I miss the bus by 4 minutes. What is my usual time?
(A) 16 min
(B) 26 min
(C) 34 min
(D) 20 min
(E) 12 min
Rationale: Speed Ratio = 1:4/5 = 5:4 Time Ratio
= 4:5 1 -------- 4 4 --------- ? è 16
Answer: A
Answer: (A) 16 min
Question: How many of the positive divisors of 720 are also multiples of 4 not including 720?
(A) 11
(B) 12
(C) 17
(D) 18
(E) 24
Rationale: 720 = 2^6 * 3 * 5 = (4) * 2^2 * 3^2 * 5
Besides (4), the exponents of 2, 3, and 5 are 2, 2, and 1.
There are (2+1)(2+1)(1+1) = 18 ways to make multiples of 4.
We must subtract 1 because one of these multiples is 720.
The answer is C.
Answer: (C) 17
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
(A) 12.6 kmph
(B) 17.5 kmph
(C) 12.8 kmph
(D) 12.5 kmph
(E) 14.5 kmph
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer: D
Answer: (D) 12.5 kmph
Question: Average expenditure of a person for the first 3 days of a week is Rs. 330 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is:
(A) 350
(B) 370
(C) 390
(D) 430
(E) None
Rationale: Explanation:
Assumed mean = Rs. 330
Total excess than assumed mean = 4 × (Rs. 420 - Rs. 350) = Rs. 280
Therefore, Increase in average expenditure = Rs. 280/7 = Rs. 40
Therefore, Average expenditure for 7 days = Rs. 330 + Rs. 40 = Rs. 370
Correct Option: B
Answer: (B) 370
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 8
(B) 7
(C) 6
(D) 4
(E) 9
Rationale: 80% --- 12
120% --- ?
80/120 * 12
= 8
Answer:A
Answer: (A) 8
Question: An article is bought for Rs.775 and sold for Rs.900, find the gain percent?
(A) 11.1%
(B) 12.1%
(C) 13.1%
(D) 15.1%
(E) 16.1%
Rationale: 775 ---- 125
100 ---- ? => 16.1%
Answer:E
Answer: (E) 16.1%
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs. 100 of money?
(A) 1500
(B) 6000
(C) 2500
(D) 1400
(E) 2000
Rationale: P = 100(100/10)2 => P = 2000
Answer: E
Answer: (E) 2000
Question: The area of a triangle is with base 10m and height 5m?
(A) 11
(B) 25
(C) 787
(D) 122
(E) 12
Rationale: 1/2 * 10 * 5 = 25 m2
Answer: B
Answer: (B) 25
Question: Two tains of equal lengths take 10 seconds and 12 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
(A) 12
(B) 14
(C) 10.9
(D) 20
(E) 18
Rationale: Sol.
Speed of the first train = [120 / 10] m/sec = 12 m/sec.
Speed of the second train = [120 / 12] m/sec = 10 m/sec.
Relative speed = (12 + 10) = m/sec = 22 m/sec.
∴ Required time = (120 + 120) / 22 secc = 10.9 sec.
Answer C
Answer: (C) 10.9
Question: On a Monday in a certain restaurant, 40 percent of the 180 customers ordered the daily special. On Tuesday, only 10 percent of the 120 customers ordered the special. For the two days combined, what percent of the customers ordered the daily special?
(A) 15%
(B) 16%
(C) 18%
(D) 28%
(E) 30%
Rationale: 40% of 180= 72
10% of 120=12
Total =84
percent for 2 days combined =84/300 =0.28. so it should be less than 0.28 so it is 28%
Answer:D
Answer: (D) 28%
Question: Sum of three numbers 292, If the first number be twice then second and third number be one third of the first, then the second number is
(A) A)80
(B) B)71
(C) C)72
(D) D)73
(E) E)74
Rationale: Explanation:
Let the second number is x, then first is 2x, and third is 1/3(2x)
=>2x+x+2x/3=292
<=>11x/3=292
=>x=80
Answer: Option A
Answer: (A) A)80
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
(A) 15 days
(B) 12 days
(C) 13 days
(D) 20 days
(E) 25 days
Rationale: A'S 2nd day work = (1/20 * 2) = 1/10
(A+B+C)'S 1 day's work = (1/20 + 1/30 + 1/60) = 1/10
work done in 3 days = 1/5
=> whole work will be done in (3*5) = 15 days
ANSWER A
Answer: (A) 15 days
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
(A) 277
(B) 267
(C) 120
(D) 110
(E) 112
Rationale: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
Answer:C
Answer: (C) 120
Question: The volume of a certain substance is always directly proportional to its weight. If 48 cubic inches of the substance weigh 112 ounces, what is the volume, in cubic inches, of 56 ounces of this substance?
(A) 27
(B) 36
(C) 42
(D) 24
(E) 147
Rationale: 112 ounces of a substance has a volume of 48 cubic inches
56 ounces of a substance has a volume of (48/112)*56 = 24 cubic inches
Answer D
Answer: (D) 24
Question: From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 36 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning
(A) 20
(B) 10
(C) 35
(D) 50
(E) 40
Rationale: Assume the number of boys at present = x
Then, the number of girls at present = 5x
Before the boys left, the number of boys were (x+36) and number of girls were 5x
Hence, 2(5x) = x + 36
=> 10x = x + 36
=> x = 4
Number of girls in the beginning = (5x + 15) = (5×4 + 15) = 35
Answer is C.
Answer: (C) 35
Question: A person decided to build a house in 100days. He employed 100men in the beginning and 100 more after 80 days and completed the construction in stipulated time. If he had not employed the additional men , how many days behind schedule would it have been finished?
(A) 40
(B) 80
(C) 70
(D) 60
(E) 50
Rationale: 200 men do the rest of the work in 100-80 = 20 days
100 men can do the rest of the work in 20*200/100 = 40days
Required number of days = 40-80 = 40 days
Answer is A
Answer: (A) 40
Question: Sales price is $44, gross profit is 120% of cost, what is the value of gross profit?
(A) 24
(B) 33
(C) 39
(D) 40
(E) 42
Rationale: Cost + Profit = Sales
Cost + (120/100)Cost = 44
Cost = 20
Profit = 44 - 20 = 24
Answer (A)
Answer: (A) 24
Question: Three medical experts, working together at the same constant rate, can write an anatomy textbook in 24 days. How many additional experts, working together at this same constant rate, are needed to write the textbook in 18 days?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Each expert can write 1/72 of the book per day.
To complete the book in 18 days, we need 72/18 = 4 experts, thus 1 more expert is needed.
The answer is A.
Answer: (A) 1
Question: If the average (arithmetic mean) of the four numbers K, 2K + 3, 3K – 5 and 5K + 1 is 30, what is the value of K?
(A)  11
(B)  15 3/4
(C)  22
(D)  23
(E)  25 3/10
Rationale: K + 2K +3 + 3K - 5 + 5K +1 = 11K -1
(11K -1)/4 = 30
11K = 30 * 4 +1 = 120 +1 = 121
K = 121 / 11 = 11.
Answer A.
Answer: (A)  11
Question: A father is twice as old as his son. 20 years ago, the age of the father was 12 times the age of the son. The present age of the father (in years) is
(A) 11
(B) 22
(C) 44
(D) 55
(E) 66
Rationale: Explanation:
Let sons age = x. Then, fathers age = 2x.
12(x—2O) = (2x - 20) so x = 22
Fathers present age = 44 years
Option C
Answer: (C) 44
Question: What is the area of an equilateral triangle whose one side length is 80?
(A) 800√3
(B) 1000√3
(C) 1200√3
(D) 1400√3
(E) 1600√3
Rationale: -> The area of an equilateral triangle with one side length of a is √3a2/4. Thus, √3(80^2)/4=1600√3 and the answer is E.
Answer: (E) 1600√3
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?
(A) 16.5
(B) 16.0
(C) 16.3
(D) 16.8
(E) 16.1
Rationale: D = 110 + 170 = 280 m
S = 60 * 5/18 = 50/3
T = 280 * 3/50 = 16.8 sec.
Answer: D
Answer: (D) 16.8
Question: How many odd, positive divisors does 540 have?
(A) 6
(B) 8
(C) 12
(D) 15
(E) 24
Rationale: Make a prime factorization of a number: 540=2^2*3^3*5 --> get rid of powers of 2 as they give even factors --> you'll have 3^3*5 which has (3+1)(1+1)=8 factors.
Another example: 60=2^2*3*5 it has (2+1)(1+1)(1+1)=12 factors out of which (1+1)(1+1)=4 are odd: 1, 3, 5 and 15 the same # of odd factors as 60/2^2=15 has.
Answer: B.
Answer: (B) 8
Question: it is a small town railway station and there are 25 stations on that line.at each of the 25 stations the passengers can get tickets for any other 24 stations.how many different kind of tickets do you think the booking clerk has to keep?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
Rationale: 600 different kind of tickets booking clerk has to keep.
24 type of tickets are to be issued from each originating station.
Therefore, 25*24 = 600 tickets
ANSWER:A
Answer: (A) 24
Question: In a 60 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners?
(A) 29
(B) 13
(C) 25
(D) 23
(E) 21
Rationale: Solution simple
Out of 60 20% are male i.e 12 and 25% are female i.e 15 , so total homeowner is 27.
Now min number homeowner is 12 and max is 27 so question ask us to find least and 13 has least value among all option.
So ans is 13.
Answer : B
Answer: (B) 13
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 227 m
(B) 287 m
(C) 245 m
(D) 186 m
(E) 177 m
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.
Answer:C
Answer: (C) 245 m
Question: Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
(A) 1261
(B) 8981
(C) 2379
(D) 2893
(E) 2721
Rationale: A = 8000(21/20)3
= 9261
= 8000
---------
1261
Answer: A
Answer: (A) 1261
Question: In how many ways can the letters D, I, G, I, T be arranged so that the two I's are not next to each other?
(A) 36
(B) 48
(C) 72
(D) 96
(E) 128
Rationale: total number of ways to arrange all the letters = 5!/2!
this includes when both I's are together and not together.
now consider both I's are combined together and arranged, then total number = 4!
these are the arrangements when both the I's are together.
so number of ways when both I's are not together = 5!/2! - 4! = 60-24 = 36
Answer:A
Answer: (A) 36
Question: A,B,C can complete a piece of work in 21,6,12 days. Working together, they complete the same work in how many days?
(A) 2
(B) 4/5
(C) 7/9
(D) 10
(E) 84/25
Rationale: A+B+C 1day work = 1/21 + 1/6 + 1/12 = 25/84
A,B,C together will complete the job in 84/25 days
Answer is E
Answer: (E) 84/25
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
(A) 5/21
(B) 5/27
(C) 5/25
(D) 5/24
(E) 5/22
Rationale: Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)
As remaining person can be any one among three couples left.
Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅
= (10 * 6)/252
= 5/21
Answer: A
Answer: (A) 5/21
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 18 kmph?
(A) 80 sec
(B) 20 sec
(C) 40 sec
(D) 50 sec
(E) 60 sec
Rationale: D = 100 + 150 = 250
S = 18 * 5/18 = 5 mps
T = 250/5 = 50 sec
D) 50 sec
Answer: (D) 50 sec
Question: A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 96 cookies, what is the minimum number of chocolate chip cookies he makes?
(A) 7
(B) 14
(C) 21
(D) 28
(E) 42
Rationale: 7C+6P=96
We need to maximize P to minimize C so that the eq is also satisfied
Try substitution for CP to solve so that eqn is satisfied
The least value of C for which equation gets satisfied is 5
i.e. 7*6+6*9=42+54=96
Hence E is the answer
Answer: (E) 42
Question: A truck covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33kms in 45minutes. The ratio of their speeds is?
(A) 1:2
(B) 3:4
(C) 2:5
(D) 3:7
(E) 1:3
Rationale: Ratio of speeds = (550/60) 18/5 : 60*33/45 = 33:44 = 3:4
Answer is B
Answer: (B) 3:4
Question: What is remainder of the division (1225*1227*1229)/12?
(A) 1
(B) 0
(C) 3
(D) 2
(E) 4
Rationale: remainder will be number/ 100 here as the divisor is two digit number = 12.
hence checking for the last two digits = 5*7*9 = 15
Thus remainder = 3.
Answer : C
Answer: (C) 3
Question: Jolene entered an 14-month investment contract that guarantees to pay 2 percent interest at the end of 6 months, another 3 percent interest at the end of 12 months, and 4 percent interest at the end of the 18 month contract. If each interest payment is reinvested in the contract, and Jolene invested $10,000 initially, what will be the total amount of interest paid during the 18-month contract?
(A) $506.00
(B) $726.24
(C) $900.00
(D) $920.24
(E) $926.24
Rationale: If interest were not compounded in every six months (so if interest were not earned on interest) then we would have (2+3+4)=9% simple interest earned on $10,000, which is $900. So, you can rule out A, B and C right away.
Interest earned after the first time interval: $10,000*2%=$200;
Interest earned after the second time interval: ($10,000+$200)*3%=$300+$6=$306;
Interest earned after the third time interval: ($10,000+$200+$306)*4%=$400+$8+(~$12)=~$420;
Total: 200+306+(~420)=~$506.00
Answer: A.
Answer: (A) $506.00
Question: If X is the sum of first 40 positive even integers and Y is the sum of first 40 positive odd integers, what is the value of x-y?
Please try to explain your answers
(A) 0
(B) 25
(C) 40
(D) 75
(E) 100
Rationale: First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
We can see the patterns here, so the sum of first 40 positive even integers minus the sum of first 40 positive odd integers will be 40.
Answer: C.
Answer: (C) 40
Question: In how many ways can the integer 120 be expressed as a product of two different positive integers?
(A) 10
(B) 8
(C) 5
(D) 4
(E) 2
Rationale: 120=(2^3)*3*5
Since 120 is not a perfect square, no of ways=5
Answer C
Answer: (C) 5
Question: The cost of 8 dozen pencil and 2 dozen note book is 520 rupee. If cost of 3 pencil and 4 note book is 60 rupee, then sum of the cost of 1 pencil and 1 note book will be (in rupee)
(A) rs 13.51
(B) rs 15.51
(C) rs 16.51
(D) rs 14.51
(E) rs 17.51
Rationale: let cost of pencil=rs x
cost of notebook= rs y
cost of 8 dozen pencils are 96x
cost of 2 dozen pencils are 24y
cost of 3 pencils are 3x
cost of 4 notebooks are 4y
equations are
96x + 24y = 520-----1
3x +4y = 60-----2
multiplying 6 with equation (2) and then subtracting eqn (1)-eqn (2),we get
96x + 24y = 520
18x + 24y = 360
after solving the equations,we get
x=2.05
y=13.46
cost of 1 pencil and 1 notebook is 2.05+13.46=rs 15.51
ANSWER:B
Answer: (B) rs 15.51
Question: If x is divisible by 2, 14, and 35, which of the following must be the least multiple of x?
(A) 308
(B) 154
(C) 70
(D) 44
(E) 35
Rationale: We are looking for the LCM (which is not 0) of 2, 35 = 7*5, 14 = 2*7:
2 * 5 * 7 = 70
The answer is C.
Answer: (C) 70
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
(A) 320 m
(B) 350 m
(C) 650 m
(D) 700 m
(E) 750 m
Rationale: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 50/3
3x + 900 = 1950 => x = 350 m.
ANSWER B
Answer: (B) 350 m
Question: A baseball card decreased in value 50% in its first year and 10% in its second year. What was the total percent decrease of the card's value over the two years?
(A) 28%
(B) 55%
(C) 32%
(D) 36%
(E) 72%
Rationale: Let the initial value of baseball card = 100
After first year , value of baseball card = (1- 50/100)* 100 = 50
After second year , value of baseball card =(1 - 10/100)* 50 = 45
total percent decrease of the card's value over the two years = (100-45)/100 *100%
=55%
Answer B
Answer: (B) 55%
Question: There are 2 kinds of staff members in a IT company, PART TIME AND FULL TIME. 25 percent of the total members are PART TIME members others are FULL TIME members. The work time of part time members is 3/5 of the full time members. Wage per hour is same. What is the ratio of total wage of part time members to total wage of all members.
(A) A.1/4
(B) B.1/5
(C) 1/6
(D) 1/7
(E) 1/8
Rationale: Just plug in
Assuming there are 100 employees
25% are PT = 25
75% FT = 75
Assume that the total number of hrs FT employees have to work = 10
PT will work = 3/5*10 = 6
since the wages are same , there will no affect on ratios
total number of hrs FT employees work = 75*10 = 750
PT = 25*6 = 150
now the ratio is 150/900 = 1/6 answer is C
Answer: (C) 1/6
Question: Three cubes of metal whose edges are 9, 12 and 21 cm respectively, are melted and one new cube is made. Find the edge of the new cube?
(A) 28
(B) 22.7
(C) 66
(D) 18
(E) 99
Rationale: 93 + 123 + 213 = a3 => a
= 22.7
Answer: B
Answer: (B) 22.7