mathewhe/aqua_rat huggingface dataset:
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 3
(B) 5
(C) 6
(D) 4
(E) 9
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4. Answer: D
Answer: (D) 4
Question: How many ways to draw 3 balls from 16 balls pool.(balls are numbered as 1 to 16 and are distinct)
(A) 460
(B) 560
(C) 660
(D) 760
(E) 860
Rationale: 16C3=(16*15*14)/(3*2*1)=3360/6=560
ANSWER:B
Answer: (B) 560
Question: A welder received an order to make a 1 million liter cube-shaped tank. If he has only 4x2 meter sheets of metal that can be cut, how many metal sheets will be required for this orderT? (1 cubic meter = 1,000 liters)
(A) 92
(B) 90
(C) 82
(D) 78
(E) 75
Rationale: I get 75. A cube with 1 million liters cube would be a cube with the dimensions of 100*100*100. 4*2 covers 8 sq liters so 100/8 = 12.5.
T=12.5*6 = 75.E
Answer: (E) 75
Question: A trader sells 5 pineapples per rupee, calculate the profit loss percentage if the trader bought the pineapples at 6 per rupee.
(A) 10 %
(B) 20 %
(C) 30 %
(D) 50 %
(E) 40 %
Rationale: Let he total number of pineapples bought by the shopkeeper be 12.
If he buys 6 a rupee, his CP = 5
He selling at 5 a rupee, his SP = 6
Profit = SP - CP = 6 - 5 = 1
Profit Percent = 1/5 * 100 = 20 %
Answer: B
Answer: (B) 20 %
Question: If 40% of a number is 20, then the number is
(A) number is 50
(B) number is 70
(C) number is 90
(D) number is 80
(E) None of these
Rationale: Solution:
Let "a" be the number we seek. We get
40% × a = 20
2 × 40% × a = 2 × 20 = 40
80% × a = 40
10% × a = 40 : 8 = 5
100% × a = 5 × 10 = 50
a = 50
Answer A
Answer: (A) number is 50
Question: if Juan takes 15 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
(A) 11x/y
(B) 11y/x
(C) 15x/y
(D) 11/xy
(E) xy/11
Rationale: Answer is C.
The rate of running hards: 15 minutes per y hards.
Thus the time for running x hards = x hards * 15 minutes/y hards = 15x/y
Answer: (C) 15x/y
Question: If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 6 m of the same rod?
(A) 22.8 kg
(B) 25.6 kg
(C) 28 kg
(D) 26.5 kg
(E) None of these
Rationale: Explanation :
Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion)
=> 11.25 : 6 :: 42.75 : x
=> 11.25 x x = 6 x 42.75
=> x = (6 x 42.75) / 11.25
=> x = 22.8
Answer : A
Answer: (A) 22.8 kg
Question: 12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job to complete the remaining work, if it so to be completed in 3 days?
(A) 15 women
(B) 85 women
(C) 75 women
(D) 65 women
(E) 35 women
Rationale: 1 man's 1 day work = 1/48; 1 woman's 1 day work = 1/60.
6 men's 2 day's work = 6/48 * 2 = 1/4.
Remaining work = (1 - 1/4) = 3/4
Now, 1/60 work is done in 1 day by 1 woman.
So, 3/4 work will be done in 3 days by (60 * 3/4 * 1/3) = 15 women.
Answer:A
Answer: (A) 15 women
Question: John sold an item for Rs.4900/- and incurred a loss of 30%. At what price should he have sold the item to have gained a profit of 30%?
(A) 8800
(B) 8900
(C) 9000
(D) 9100
(E) 9200
Rationale: Explanation:
30% loss means SP = 70% of CP
:. CP = Rs.4900x100/70 = Rs.7000.
The SP for a gain of 30% = 7000+30% of 3000 = 7000+2100 =Rs9100.
Answer: Option D
Answer: (D) 9100
Question: How long does a train 110 meters long running at the speed of 72 km/hour take to cross a bridge 132 meters in length ?
(A) 15 seconds
(B) 12.1 seconds
(C) 10 seconds
(D) 8.1 seconds
(E) None of these
Rationale: Explanation:
Speed = 72 km/hour = 72*(5/18) m/sec
= 20 m/sec
Total distance to be covered = 110+132 = 142 meters
Time = Distance/Speed
= 242/20 = 12.1 seconds
Option B
Answer: (B) 12.1 seconds
Question: Dustin's Pizza Shop sells Bread Sticks in orders of 2 and 8. A party of 12 guests would like to have at least 2 Bread Sticks a piece. Which of the following combinations would NOT be possible.
(A) 3 Orders of 8
(B) 2 Orders of 2, and 1 order of 8
(C) 4 orders of 2, and 2 orders of 8
(D) 3 orders of 2, and 3 orders of 8
(E) 13 orders of 2
Rationale: The correct answer would not allow each of the 12 guests to have AT LEAST 2 bread sticks a piece.
A=24 (24 divided by 12 is exactly 2 a piece)
B=12 (12 divided by 12 would only allow for 1 bread stick a piece) *Correct Answer*
C=24 (Same as Answer A)
D=30 (30 divided by 12 allows for each guest to have 2 bread sticks with 6 leftover)
E=26 (26 divided by 12 allows for each guest to have 2 bread sticks with 2 leftover)
The Correct Answer is B
Answer: (B) 2 Orders of 2, and 1 order of 8
Question: P and Q start a business with Rs.7000 and Rs.28000 respectively. Hoe should they share their profits at the end of one year?
(A) 1:3
(B) 1:4
(C) 1:5
(D) 1:6
(E) 4:1
Rationale: Explanation:
They should share the profits in the ratio of their investments.
The ratio of the investments made by P and Q =
7000 : 28000 => 1:4
Answer:B
Answer: (B) 1:4
Question: Complete the series:5, 20, 24, 6, 2, 8, ?
(A) 12
(B) 22
(C) 32
(D) 42
(E) 16
Rationale: The series is *4, +4, /4, -4, *4,....
That is 5*4 = 20, 20+4 = 24, 24/4 = 6, 6-4 = 2, and again 2*4 = 8 constructing the series 20,24,6,2,8,...so obviously the next operation will be +4, so 8+4 = 12 ANSWER:A
Answer: (A) 12
Question: How many numbers of 5 digits can be formed with the digits 0, 1, 2, 3, 4, 6 & 8 with no digit being repeated in the same number?
(A) 2170
(B) 2160
(C) 4396
(D) 4500
(E) 3500
Rationale: As we have 5 digits.. and having no repeation..
For the first digit can't be "0".. so, possibilities are 6..
for the second digit the possibilities are 6 including "0" also..
for the third digit there are 5 possibilities
for the fourth digit 4 possibilities
for the fifth digit 3 possibilities..
so, total no.of numbers can form is 6*6*5*4*3=2160
ANSWER:B
Answer: (B) 2160
Question: From a pack of 52 cards, two cards are drawn together at random. What is the probability of one is a spade and one is a heart?
(A) 102/102
(B) 5/102
(C) 1/102
(D) 8/102
(E) 13/102
Rationale: Solution
Let S be the sample space. Then,
n(S) = 52C2	= (52×51)/(2×1)
= 1326.
Let E = event of getting 1 spade and 1 heart.
n(E) = number of ways of choosing 1 spade out of 13 and 1 heart out of 13
=(13C1*13C1)=169.
P(E) = n(E) / n(S)	= 169 / 1326
= 13/102.
Answer E
Answer: (E) 13/102
Question: Of a certain group of 100 people, 40 graduated from High School A, 65 graduated from College Y, and 30 live in City Z. What is the greatest possible number of people in this group who did not graduate from High School A, did not graduate from College Y, and do not live in City Z ?
(A)  5
(B)  15
(C)  35
(D)  65
(E)  85
Rationale: 1. a+y+z+ay+yz+az+ayz+ none=100. Fornoneto be maximum others have to be minimum
2. We know the underlined portions sum to 65 and that is the minimum value of others
3. Maximumnone= 100-65=35=C
Answer: (C)  35
Question: There are 15 teams in a certain league and each team plays each of the other teams exactly twice. If each game is played by 2 teams, what is the total number of games played?
(A) 15
(B) 16
(C) 28
(D) 56
(E) 210
Rationale: Every team plays with 14 teams...so total no of matches = 15 x 14 = 210.
Now, each match is played twice => 210 x 2
But 2 teams play a match => 210 x 2 /2 = 210.
Answer: E
Answer: (E) 210
Question: A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The rate of the stream is:
(A) 2 km/hr
(B) 1 km/hr
(C) 4 km/hr
(D) 6 km/hr
(E) 5 km/hr
Rationale: Explanation:
Assume that he moves 4 km downstream in x hours.
Then, speed downstream = distance/time = 4/x km/hr
Given that he can row 4 km with the stream in the same time as 3 km against the stream
i.e., speed upstream = 3/4 of speed downstream
=> speed upstream = 3/x km/hr
He rows to a place 48 km distant and comes back in 14 hours
⇒48/(4/x)+48/(3/x)=14
⇒12x+16x=14
⇒6x+8x=7
⇒14x=7
⇒x=1/2
Hence, speed downstream =4x=4(12) = 8 km/hr
speed upstream = 3x=3(12) = 6 km/hr
Now we can use the below formula to find the rate of the stream
Let the speed downstream be a km/hr and the speed upstream be b km/hr, then
Speed in still water = 1/2(a+b) km/hr
Rate of stream = 1/2(a−b) km/hr
Hence, rate of the stream = 1/2(8−6)= 1 km/hr
Answer: Option B
Answer: (B) 1 km/hr
Question: Three candidates contested an election and received 80020, 22908 and 45000 votes respectively. What percentage of the total votes did the winning candidate get ?
(A) 57.20%
(B) 54.09
(C) 45.10%
(D) 64.10%
(E) 55.10%
Rationale: Explanation :
Total number of votes polled = (80020+22908+45000)
= 147928.
Required percentage = (80020/147928) X 100%
= 54.09%.
Answer :B
Answer: (B) 54.09
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
(A) 1350
(B) 8837
(C) 2377
(D) 3772
(E) 3881
Rationale: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 2 = Rs.1350 Answer: A
Answer: (A) 1350
Question: In a division sum, the quotient is 40, the divisor 72 and the remainder 64, find the dividend?
(A) 2674
(B) 2944
(C) 2464
(D) 2924
(E) 2994
Rationale: Explanation:
40 * 72 + 64 = 2944
Answer : B
Answer: (B) 2944
Question: A man walking at a rate of 15km/hr crosses a bridge in 20 minutes. The length of the bridge is?
(A) 1250m
(B) 1110m
(C) 950m
(D) 1000m
(E) 1300m
Rationale: Speed = 15*5/18 = 15/18 m/sec
Distance covered in 20minutes = 15/18 *20 *60 = 1000m
Answer is D
Answer: (D) 1000m
Question: Kamal obtained 81, 68, 82, 69 and 90 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 65
(B) 69
(C) 72
(D) 75
(E) NOne
Rationale: Sol.
Average
= 81 + 68 + 82 + 69 + 90 / 5)
= (390 / 5)
= 78.
Answer E
Answer: (E) NOne
Question: f a < b < c , which of the following must be true?
(I) a < b^2
(II) b − a < c
(III) a^2 < b^2 < c^2
(A) None
(B) I only
(C) II only
(D) III only
(E) II and III
Rationale: (I) a < b^2. Not necessarily true fractions: try a=1/3 and b=1/2.
(II) b − a < c. Not necessarily true: try a=-1, b=0, and c=1.
(III) a^2 < b^2 < c^2. Not necessarily true: try a=-1, b=0, and c=1.
None of the options must be true.
Answer: A.
Answer: (A) None
Question: In a college, the ratio of the number of boys to girls is 8 : 4. If there are 200 girls, the total number of students in the college is
(A) 420
(B) 520
(C) 600
(D) 720
(E) 820
Rationale: Explanation:
Let the boy are 8x and Girls are 4x
=> 4x = 200
=> x = 50
Total students = 8x+4x = 12x = 12(50) = 600
Option C
Answer: (C) 600
Question: If x is real, find the maximum value of the expression -2x^2 + 3x + 5.
(A) 2.145
(B) 6.125
(C) 8.725
(D) 11.885
(E) 13.485
Rationale: This is an equation of a downward facing parabola.
The maximum value is the top point of the parabola.
-2x^2+3x+5 = (-2x+5)(x+1)
The roots are 5/2 and -1.
The maximum value must be when x is halfway between these two points.
x = 0.75
The maximum value is -2(0.75)^2+3(0.75)+5 = 6.125
The answer is B.
Answer: (B) 6.125
Question: find value for x from below equation? x + 1 = -3
(A) 1
(B) -4
(C) -1
(D) 2
(E) 3
Rationale: 1. Subtract 1 from both sides:
x + 1 - 1 = -3 - 1
2. Simplify both sides:
x = -4
B
Answer: (B) -4
Question: 0.007 x 0.45=?
(A) 0.00315
(B) 0.0315
(C) 0.315
(D) 0.0351
(E) None of them
Rationale: 7 x 45 = 315
Sum of decimal places =5
Therefore, 0.007 x 0.45 = 0.00315
Answer is A.
Answer: (A) 0.00315
Question: Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?
(A) 432 miles
(B) 651 miles
(C) 387 miles
(D) 954 miles
(E) 556 miles
Rationale: The number of miles to drive to finish his journey is given by
1200 - 768 = 432 miles
correct answer A
Answer: (A) 432 miles
Question: On Monday morning, Chris receives tickets to a baseball game that will be played at 7pm on the next evening that it does not rain. However, Chris is only in town until Wednesday morning, at which point he must fly to another city. If there is a 66% chance of rain each of the next two evenings, what is the probability that Chris will be able to attend the game?
(A)  56.44%
(B)  60%
(C)  66%
(D)  80%
(E)  84%
Rationale: Chris won't be able to attend the game if it be raining on Monday eveningandTuesday evening. The probability of that is 0.66*0.66 = 0.4356. So, the probability that he will be able to attend is 1 - 0.4356 = 0.5644.
Answer: A.
Answer: (A)  56.44%
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) 2277
(B) 38000
(C) 26688
(D) 26666
(E) 19871
Rationale: CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Answer: B
Answer: (B) 38000
Question: If the radius of a cylinder is doubled and height 4 times, what is the new volume of the cylinder divided by the old one?
(A) 8.
(B) 2.
(C) 6.
(D) 4.
(E) 16.
Rationale: let v and v' be the original and the changed volume
now
v=pir^2h
v'=pi(2r)^2(4h)
v'=16v
E) 16
Answer: (E) 16.
Question: The mean of 15 observations was 25. It was found later that an observation 40 was wrongly taken as 25. The corrected new mean is
(A) 20
(B) 30
(C) 15
(D) 18
(E) 26
Rationale: Explanation:
Correct Sum = (25* 15 + 40 - 25) = 390
Correct mean = = 390/15 = 26
Answer: E
Answer: (E) 26
Question: A present value of a machine is $128000. Its value depletiation rate is 20% per annum then find the machine value after 3 years?
(A) A)$54000
(B) B)$48000
(C) C)$9216
(D) D)$32450
(E) E)$42500
Rationale: P= $128000
R = 20%
T = 3 years
Machine value after 3years = P/(1-R/100)^T
=128000*3/5* 3/5 * 3/5
=$9216
Answer is C
Answer: (C) C)$9216
Question: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 1 at its maximum rate ?
(A) 2hrs, 48mins
(B) 6hrs, 32mins
(C) 1hrs, 38mins
(D) 13hrs, 4mins
(E) 14hrs, 24mins
Rationale: The rate of pump 1 = 4x job/minute.
The rate of pump 2 = 2x job/minute.
The rate of pump 3 = x job/minute.
Given that x+2x+4x=1/56 --> x=1/392 --> (time) = (reciprocal of rate) = 392 minutes x/4= 1 hours and 38 minutes.
Answer: C
Answer: (C) 1hrs, 38mins
Question: A car dealership has 40 cars on the lot, 10% of which are silver. If the dealership receives a new shipment of 80 cars, 25% of which are not silver, what percentage of total number of cars are silver?
(A) 15%
(B) 18%
(C) 20%
(D) 21%
(E) 22%
Rationale: The number of silver cars is 0.1*40 + 0.25*80 = 24
The percentage of cars which are silver is 24/120 = 20%
The answer is C.
Answer: (C) 20%
Question: David and ANDREW can finish the work 12 days if they work together. They worked together for 8 days and then ANDREW left. David finished the remaining work in another 8 days. In how many days David alone can finish the work?
(A) 30 days
(B) 60 days
(C) 70 days
(D) 80 days
(E) 24 days
Rationale: Amount of work done by David and ANDREW in 1 day = 1/12
Amount of work done by David and ANDREW in 8 days = 8 Ã— (1/12) = 2/3
Remaining work â€“ 1 â€“ 2/3 = 1/3
David completes 1/3 work in 8 days
Amount of work David can do in 1 day = (1/3)/8 = 1/24
=> David can complete the work in 24 days
Answer : E
Answer: (E) 24 days
Question: In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number R and the smallest possible number of students that could have taken both geometry and biology?
(A) 144
(B) 119
(C) 113
(D) 88
(E) 31
Rationale: OFFICIAL SOLUTION:
First of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119.
{Total} = {geometry} + {biology} - {both} + {neither};
232 = 144 + 119 - {both} + {neither};
{both} = 31 + {neither}.
{both} is minimized when {neither} is 0. In this case {both} = 31.
The greatest possible number R of students that could have taken both geometry and biology, is 119.
Thus, the answer is 119 - 31 = 88.
Answer: D.
Answer: (D) 88
Question: The largest 3 digit number exactly divisible by 88 is?
(A) A)9944
(B) B)9954
(C) C)9967
(D) D)9969
(E) E)9970
Rationale: Largest 4-digit number = 999
88) 999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (999 - 55)
= 9944.
A)
Answer: (A) A)9944
Question: Donald duck can can swim his pool downstream(with the pool current helping time) in exact 40 seconds and upstream(against the pool current) in a pool in exact 60 seconds. The length of pool is 2 kilometers.
How long Donald duck can cover distance of one side at a still pool (with no current).
(A) 40 minutes
(B) 45 minutes
(C) 38 minutes
(D) 48 minutes
(E) 30 minutes
Rationale: D
48 minutes.
Donald duck's speed = X km/seconds
pool current speed = Y km/seconds
2/(X+Y) = 40
2/(X-Y) = 60
Solving the simultaneous equations gives X = 1/24
Therefore, to cover 2km will take 2/X = 48 seconds
Answer: (D) 48 minutes
Question: find the number, difference between number and its 3/5 is 56.
(A) 140
(B) 143
(C) 144
(D) 145
(E) 150
Rationale: Explanation:
Let the number = x,
Then, x-(3/5)x = 56,
=> (2/5)x = 56 => 2x = 56*5,
=> x = 140
Answer: Option A
Answer: (A) 140
Question: Given that 268x74= 19832, find the value of 2.68x.74.
(A) 1.9832
(B) 1.0025
(C) 1.5693
(D) 1.0266
(E) None
Rationale: Solution
Sum of decimals places	=(2+2)
= 4.
Therefore,	= 2.68×.74
= 1.9832
Answer A
Answer: (A) 1.9832
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 90 kmph. In how much time will the trains cross each other?
(A) 6
(B) 7
(C) 9
(D) 2
(E) 10
Rationale: Relative speed = (54 + 90)* 5/18 = 40 mps.
The time required = d/s = (100 + 100 + 200)/40
= 400/40= 10 sec.
Answer:E
Answer: (E) 10
Question: The product of digit is a Factor of a two digit number. Number of such digit are:
(A) 33
(B) 18
(C) 19
(D) 17
(E) 11
Rationale: Let the number be xy. So 10x+yxy=k10x+yxy=k. Here k is some interzer.
⇒⇒ 10x + y = kxy
⇒⇒ x(10 - ky) = - y
⇒⇒ x(ky - 10) = y
So x is a factor of y. The possibilities are,
11, 1×1=1; 12 , 1×2=2; 15 ,1×5=5; 24 ,2×4=8; 36 , 3×6=18
Answer:B
Answer: (B) 18
Question: Sita and Sinu together can do a work in 50 days. With the help of Smitha, they completed the work in 6 days and earn Rs.250. What is the share of Sinu if Sita alone can do the work in 100 days?
(A) Rs.15
(B) Rs.18
(C) Rs.20
(D) Rs.25
(E) Rs.35
Rationale: Sinu’s one day’s work = 1/50 - 1/100
= (2-1)/100
= 1/100
Sinu’s 6 day’s work = 6/100* 1 = 3/50
Sinu completed 3/50 th of total work.
So, Sinu’s share= 3*250/50 = Rs. 15
ANSWER:A
Answer: (A) Rs.15
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
(A) 767 cm
(B) 800 cm
(C) 266 cm
(D) 181 cm
(E) 188 cm
Rationale: Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200 = 800 cm.
Answer: B
Answer: (B) 800 cm
Question: The ratio of money with Ram and Gopal is 7 : 17 and that with Gopal and Krishan is 7: 17. If Ram has Rs. 637, Krishan has ?
(A) s. 2890
(B) s. 2330
(C) s. 3757
(D) s. 1620
(E) s. 2680
Rationale: Ram : Gopal = 7 : 17 = 49 : 119
Gopal : Krishan = 7 : 17 = 119 : 289
Ram : Gopal : Krishan = 49 : 119 : 289
Ram : Krishan = 49 : 289
Thus, 49 : 289 = 637 : N
&there N = 289 x 637 / 49
= Rs. 3757
Answer :C
Answer: (C) s. 3757
Question: A fruit drink is made of orange, watermelon, and grape juice, where 15 percent of the drink is orange juice and 60 percent is watermelon juice. If the drink is made with 30 ounces of grape juice, how many ounces is the drink total?
(A) 120
(B) 160
(C) 190
(D) 200
(E) 400
Rationale: Let the total number of ounces in the drink be x.
% of orange = 15%
% of watermelon = 60%
% of grape = 100% - 75% = 25%
0.25x = 30
x = 120
Therefore there are a total of 120 ounces in the drink.
The answer is A.
Answer: (A) 120
Question: It takes 40 identical printing presses 15 hours to print 500,000 papers. How many hours would it take 30 of these printing presses to print 500,000 papers?
(A) 16
(B) 18
(C) 20
(D) 21
(E) 24
Rationale: 40 printing presses can do 1/15 of the job each hour.
30 printing presses can do 3/4*1/15 = 1/20 of the job each hour.
The answer is C.
Answer: (C) 20
Question: If n is a natural number, then (6n^2 + 6n) is always divisible by
(A) 6 only
(B) 6 and 12 both
(C) 12 only
(D) 18 only
(E) 12 and 18 both
Rationale: (6n^2 + 6n) = 6n(n + 1), which is divisible by both 6 and 12, since n(n+1) is always even.
Answer B.
Answer: (B) 6 and 12 both
Question: If 5% more is gained by selling an article for Rs. 600 than by selling it for Rs. 580, the cost of the article is?
(A) 127
(B) 688
(C) 400
(D) 121
(E) 123
Rationale: Let C.P. be Rs. x.
Then, 5% of x = 600 - 580 = 20
x/20 = 20 => x = 400
Answer: C
Answer: (C) 400
Question: The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 24. Which of the following integers is the higher of the remaining two integers?
(A) 32
(B) 86
(C) 84
(D) 22
(E) 55
Rationale: Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)
A = 93, D = 39 and B - C = 24
(1) => B + C = 276 - (A + D) = 276 - 132 = 144.
B + B -24 = 144
B = (144 + 24)/2 = 84
Answer:Option C
Answer: (C) 84
Question: A committee of two students has to be formed. There are five candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options?
Your approach: total 10 options, 5c3.
Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together.
This gives us 10-3-3=4 as the answer.
Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE, BDE
B
Answer: (B) 4
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 8 seconds. What is the length of the fast train ?
(A) 27 7/9
(B) 44 4/9
(C) 29 7/9
(D) 30 7/9
(E) None of these
Rationale: Explanation:
As Trains are moving in same direction,
So, Relative Speed = 40-20 = 20 kmph
= 20*(5/18) = 50/9 m/sec
Length of Train= Speed * Time
Length=50/9âˆ—8
=400/9
=44 4/9
Option B
Answer: (B) 44 4/9
Question: In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of B is
(A) 27
(B) 66
(C) 39
(D) 28
(E) 21
Rationale: Let B's present age = x years. Then, A's present age = (x + 9) years.
(x + 9) + 10 = 2(x - 10)
=> x + 19 = 2x - 20
=> x =39.
Answer: C
Answer: (C) 39
Question: The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
(A) 35 years
(B) 45 years
(C) 51 years
(D) 54 years
(E) None of these
Rationale: Explanation:
Age of the teacher = (37 * 15 - 36 * 14) years = 51 years. Answer: C
Answer: (C) 51 years
Question: When positive integer A is divided by positive integer B, the result is 9.44. Which of the following could be the reminder when A is divided by B?
(A)  11
(B)  14
(C)  15
(D)  24
(E)  19
Rationale: the remainder will be obtained from the decimal part when A is divided by B i.e. 0.44
0.44 = 44/100 = 11/25 so possible remainders are 11,22,33,44.
Only option A-11 satisfies this
for remainder 11,
Ans - A
Answer: (A)  11