mathewhe/aqua_rat huggingface dataset:
Question: Bacteria reproduce in such a manner that every hour their number
doubles In a controlled experiment that started with a certain number of
bacteria in a jar at 12noon on Tuesday ,30 million were found at 12noon on
Wednesday .At what time were there 15 million bacteria ?
(A) Midnight ,Tuesday
(B) 6 a.m on Wednesday
(C) 10 a.m Wednesday
(D) 9 a.m Wednesday
(E) None of these
Rationale: at 12 pm ,bacteria was 30 million ,plus it is also given that quantity of bacteria gets double after every 1 hour
if 12pm(wednesday) bacteria was 30 million;
then at 11 am(wednesday) bacteria was 15 million
so answer is none of these
ANSWER:E
Answer: (E) None of these
Question: One side of a rectangular field is 15 m and one of its diagonals is 17 m. Find the area of the field.
(A) 100 m^2
(B) 110 m^2
(C) 120 m^2
(D) 130 m^2
(E) 140 m^2
Rationale: Other side = ((17) 2- (15)2)(1/2)
= (289- 225)(1/2)
= (64)(1/2)
= 8 m.
Area = (15 x 8) m2 = 120 m2.
Option C
Answer: (C) 120 m^2
Question: Circular gears L and R start to rotate at the same time at the same rate. Gear L makes 20 complete revolutions per minute and gear R makes 60 revolutions per minute. How many seconds after the gears start to rotate will gear R have made exactly 8 more revolutions than gear L?
(A) a) 6
(B) b) 8
(C) c) 10
(D) d) 14
(E) e) 12
Rationale: Gear L -- 20 rotations per 60 seconds -- 2 rotation per 6 seconds.
Gear R -- 60 rotations per 60 seconds -- 6 rotations per 6 seconds.
First 6 seconds -- Gear L makes 1 rotation. -- Gear R makes 4 rotations -- Net difference -- 4 rotations
Hence every 6 seconds the difference between the number of rotations of R and L gear is 4 units.
Required net difference should be 8 rotations => 2 (6 seconds later) ==> 12 seconds.
Answer: E
Answer: (E) e) 12
Question: 248:3::328:?
(A) 7
(B) 5
(C) 4
(D) 6
(E) none of the above
Rationale: 248----24/8...3
328---32/8...4
answer C
Answer: (C) 4
Question: A starts business with Rs.3500 and after 6 months, B joins with A as his partner. After a year, the profit is divided in the ratio 2 : 3. What is Bâ€™s contribution in the Capital ?
(A) 24887
(B) 20778
(C) 23788
(D) 10500
(E) 2811
Rationale: Explanation:
A invested Rs.3500 for 12 months.
Let B joined with investment x. And he invested for 12 - 6 = 6 months.
So there profit ratio = (3500 Ã— 12) : (6x) = 2 : 3
â‡’ x = 10500
Answer: D
Answer: (D) 10500
Question: In the x-y plane, point (x, y) is a lattice point if both x and y are integers. A square has a center at (0, 0) and side = 4. Some points, such as the center (0, 0), are inside the square, but a point such as (0, 2) is on the square but not in the square. How many lattice points are in the square?
(A) 10
(B) 9
(C) 8
(D) 5
(E) 12
Rationale: The lattice points that are in the square, that lie on the x and y axes, are (0, 0), (0, 1), (1, 0), (0, -1), and (-1, 0).The lattice points in the square and not on the x and y axes are (1, 1), (-1, 1), (1, -1), and (-1, -1).
There are a total of 9 lattice points in the square.
Answer: B
Answer: (B) 9
Question: In how many ways can 6 boys and 4 girls sit around a table in such a way that no two girls sit together?
(A) 43200
(B) 41100
(C) 48500
(D) 46500
(E) 49600
Rationale: The 6 boys can be seated around a table in 5! Ways. In between them there are 6 places.
The 4 girls can be placed in the 6 places in 6P4 ways.
Therefore, Required number of ways= 5!* 6P4
=120*360
=43200
ANSWER:A
Answer: (A) 43200
Question: A sum of Rs. 125000 amounts to Rs. 15000 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 3%
(B) 4%
(C) 5%
(D) 6%
(E) 7%
Rationale: S.I. = (15000 - 12500) = Rs. 2500\
Rate = (100 * 2500) / (12500 * 4) = 5%
ANSWER:C
Answer: (C) 5%
Question: A man saves 10% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 10%, he is only able to save Rs. 200 per month. What is his monthly salary?
(A) Rs.22,000
(B) Rs.21,000
(C) Rs.20,000
(D) Rs.23,000
(E) Rs.24,000
Rationale: Income = Rs. 100
Expenditure = Rs. 90
Savings = Rs. 10
Present Expenditure 90+90*(10/100) = Rs.99
Present Savings = 100 – 99 =Rs. 1
If savings is Rs. 1, salary = Rs. 100
If savings is Rs.200, salary = 100/1*200 = 20000
Answer : C
Answer: (C) Rs.20,000
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) 2888
(B) 2777
(C) 2500
(D) 2999
(E) 2771
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: Farm A had an average output of 300 kgs of wheat per acre. Farm B had an average output of 350 kgs of wheat per acre. It is known that Farm B's area is 20 acres less than Farm A's. It is also known that Farm B in total harvested 2000 kgs of wheat more than Farm A. What is the area of Farm A?
(A)  130 acres
(B)  135 acres
(C)  145 acres
(D)  160 acres
(E)  180 acres
Rationale: The area of Farm A = x acres;
The area of Farm B = x-20 acres.
Total output of Farm A = 300x kgs;
Total output of Farm B = 350(x-20) kgs.
Farm B in total harvested 2000 kgs of wheat more than Farm A: 300x+2000=350(x-20) --> x=180 acres.
Answer: E.
Answer: (E)  180 acres
Question: If n is a natural number, t hen 6n^2 + 6n is always divisible by?
(A) 6 only
(B) 6 and 12
(C) 12 only
(D) 18 only
(E) 20 only
Rationale: 6n^2 + 6n = 6n(n+1), which is always divisible by 6 and 12 both, since n(n+1) is always even.
Answer is B
Answer: (B) 6 and 12
Question: If a cube has a volume of 125, what is the surface area of one side?
(A) 5
(B) 25
(C) 50
(D) 150
(E) 625
Rationale: volume of a cube = side^3
125 = side^3
so side = 5
area of one side of the cube = side^2 = 5^2 = 25
correct answer - B
Answer: (B) 25
Question: What is the value of 10^7 - 6^5?
(A) 99,91,223
(B) 99,92,224
(C) 99,94,265
(D) 99,95,300
(E) 99,96,307
Rationale: As 10^n will always have last digit as 0 AND 6^n will always as last digit 6.. hence difference of such sum should always be ending with 4 and there is only on option ..
Answer B
Answer: (B) 99,92,224
Question: A man on tour travels first 160 km at 64 km/he and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is?
(A) 71.61 km/hr
(B) 71.11 km/hr
(C) 71.18 km/hr
(D) 77.11 km/hr
(E) 21.11 km/hr
Rationale: Total time taken = (160/64 + 160/8) = 9/2 hrs.
Average speed = 320 * 2/9
=71.11 km/hr.
Answer:B
Answer: (B) 71.11 km/hr
Question: When the bus started from the first bus stop, the number of male passengers to the number of female passengers was 1 : 3. At the first stop, 16 passengers got down and 6 more female passengers got in. The ratio of the male to female passengers now became 1: 2. What was the total number of passengers in the bus when it started from the first stop?
(A) 64
(B) 48
(C) 54
(D) 46
(E) Cannot be determined
Rationale: Let, initially the number of males and females in the bus be ’x’ and ’3x’ respectively.
At the first stop, suppose ’m’ males and ’f’ females left the bus.
Therefore at the first stop the number of males is ’x - m’ and the number of females is ’(3x - f) + 6’
Therefore (x - m)/[(3x - f) + 6] = 1/2
=> 2x - 2m = 3x - f + 6
Also m + f = 16
x = 26 - f
As we have 3 variable and 2 equations, a definite value cannot be determined.
ANSWER:E
Answer: (E) Cannot be determined
Question: The amount of electrical current that flows through a wire is inversely proportional to the resistance in that wire. A wire originally carries 4 amperes of electrical current. Then the resistance is reduced to one-fifth of its original value. How many amperes of electrical current will flow through the wire?
(A) 0.8
(B) 5
(C) 12
(D) 20
(E) 24
Rationale: Given that, I∝1/R, I*R is a constant value.
I1*R1 = I2*R2
I1*R1 = I2*R1/5
I2 = 5*I1 = 20 amperes
The answer is D.
Answer: (D) 20
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8800. If his salary for the month of May is Rs.6500, find his salary for the month of January?
(A) s.3300
(B) s.4570
(C) s.4500
(D) s.4550
(E) s.2500
Rationale: Sum of the salaries of the person for the months of January, February, March and April
= 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May
= 4 * 8800
= 35200 ----(2)
(2)-(1) i.e. May - Jan = 3200
Salary of May is Rs.6500
Salary of January = Rs.3300
Answer:A
Answer: (A) s.3300
Question: A boat can travel with a speed of 10 km/hr in still water. If the speed of the stream is 8 km/hr, find the time taken by the boat to go 54 km downstream.
(A) 4.25 hr
(B) 5.25 hr
(C) 3 hr
(D) 2.25 hr
(E) 2.50 hr
Rationale: speed of boat in still water = 10 km/hr
speed of the stream = 8 km/hr
Speed downstream = (10+8) = 18 km/hr
Time taken to travel 68 km downstream = 54â„18 = 17â„4 = 3 hours
Answer is C
Answer: (C) 3 hr
Question: The second of two numbers is two less than three times the first. Find the numbers if there sum is
74.
(A) 7-19
(B) 8-20
(C) 10-16
(D) 15-9
(E) 19-55
Rationale: We are looking for two numbers.
#1 - x
#2 - 3x â€“ 2
The sum is 74. #1 + #2 = 74
Substituting x + 3x â€“ 2 = 74
4x â€“ 2 =74
4x = 76
x = 19
The first number is 19, the second number is two less than three times 19 or 55.
correct answer E
Answer: (E) 19-55
Question: A, B and C are partners in a business. A contributes Rs. 4000, B Rs.5000 and C Rs.9000. If B receives Rs. 800 as his share of profit at the end of one year, find the total profit .
(A) Rs.2880
(B) Rs.2780
(C) Rs.2990
(D) Rs.2480
(E) Rs.2380
Rationale: Total capital =4000+5000+9000 =Rs.18000 For the capital of Rs.5000 B's profit =Rs.800 For the capital Rs.18000 total profit =800/5000*18000 =Rs.2880 Answer :A
Answer: (A) Rs.2880
Question: If 12 men or 20 women can do a piece of work in 54 days, then in how many days can 9 men and 12 women together do the work?
(A) 30 days
(B) 40 days
(C) 50 days
(D) 70 days
(E) 80 days
Rationale: B
40 days
Given that 12m = 20w => 3m = 5w
9 men + 12 women = 15 women + 12 women = 27 women
20 women can do the work in 54 days. So, 27 women can do it in (20 * 54) /27 = 40 days.
Answer: (B) 40 days
Question: Rates for having a manuscript typed at a certain typing service are $6 per page for the first time a page is typed and $4 per page each time a page is revised. If a certain manuscript has 100 pages, of which 40 were revised only once, 10 were revised twice, and the rest required no revisions, what was the total cost of having the manuscript typed?
(A) $850
(B) $840
(C) $860
(D) $870
(E) $880
Rationale: 50 pages typed 1x
40 pages typed 2x (original + one revision)
10 pages typed 3x (original + two revisions)
50(6)+40(6+4)+10(6+4+4)=300+400+140=840
Answer - B
Answer: (B) $840
Question: A “palindromic integer” is an integer that remains the same when its digits are reversed. So, for example, 43334 and 516615 are both examples of palindromic integers. How many 6-digit palindromic integers are both even and greater than 300,000?
(A) 200
(B) 216
(C) 300
(D) 400
(E) 2,500
Rationale: The first digit and last digit are the same so the 3 possibilities are 4, 6, or 8.
The second and third digits can be any digit from 0 to 9.
The total number of palindromic integers is 3*10*10 = 300
The answer is C.
Answer: (C) 300
Question: The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.5. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?
(A) 1/5
(B) 7/10
(C) 3/5
(D) 4/5
(E) 12/25
Rationale: p(m) =0.2
p(r) =0.5
p(m intersection r) = 0 (If events M and R cannot both occur)
p(m or r) = 0.2+0.5 =0.7
Corrected !!
Answer B
Answer: (B) 7/10
Question: In a 100-mile trip, the first 20 miles were completed at 40 mph. If the average speed for the whole trip was 50 mph, what was the average speed in the last 80 miles?
(A) 155/3 mph
(B) 160/3 mph
(C) 165/3 mph
(D) 170/3 mph
(E) 175/5 mph
Rationale: The time to complete the first 20 miles was (20 miles / 40 mph) = (1/2) hours.
The time to complete the whole trip was (100 miles / 50 mph) = (2) hours.
The time to complete the last 80 miles was (2) - (1/2) = (3/2) hours.
The average speed in the last 80 miles was (80 miles / (3/2) hours) = 160/3 mph.
The answer is B.
Answer: (B) 160/3 mph
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is?
(A) 17/29
(B) 17/21
(C) 17/22
(D) 17/29
(E) 17/25
Rationale: The number of exhaustive events = 50C1 = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50
= 17/25.
Answer: E
Answer: (E) 17/25
Question: Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
(A) 11
(B) 15
(C) 16
(D) 28 min
(E) 19
Rationale: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 --------- ? è 28 m
Answer: D
Answer: (D) 28 min
Question: A baker sold all of his donuts for a total amount of 216 pounds. If on each donut the baker made a profit of 8% of the cost, how much did it cost the baker to make all the donuts?
(A) 210.
(B) 200
(C) 190
(D) 180
(E) 170
Rationale: Cost of donuts = X
Profit on one donut = 8%
Profit on all donuts is also =8%
X+8% of X =216
1.08X=218
X=218/1.08
X=200
ANSWER:B
Answer: (B) 200
Question: Find the unit's digit in 264^102+264^103
(A) 0
(B) 1
(C) 2
(D) 4
(E) 5
Rationale: Required unit's digit = unit's digit in 4102+4103.4102+4103.
Now, 4242 gives unit digit 6.
⇒ 41024102 gives unit digit 6.
⇒ 41034103 gives unit digit of the product 6×46×4 i.e., 4.
Hence, unit's digit in 264102+264103264102+264103
= unit's digit in (6+4)=0
A
Answer: (A) 0
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 18 years. The present age of the husband is
(A) 35 years
(B) 44 years
(C) 50 years
(D) 55 years
(E) None
Rationale: Solution
Sum of the present ages of husband, wife and child	= (27x3+3x3) years
= 90 years.
Sum of the present ages of wife and child	= (18x2+5x2) years
= 46 years.
âˆ´ Husband's present age	= (90 - 46) years
= 44 years.
Answer B
Answer: (B) 44 years
Question: What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?
(A) 8000
(B) 9179
(C) 2789
(D) 2686
(E) 9087
Rationale: 8820 ---- 441
100 ---- ? => 5%
x *105/100 * 105/100 = 8820
x*1.1025=8820
x=8820/1.1025 => 8000
Answer:A
Answer: (A) 8000
Question: In how many way the letter of the word "RUMOUR" can be arranged
(A) 2520
(B) 480
(C) 360
(D) 180
(E) 470
Rationale: Explanation:
In above word, there are 2 "R" and 2 "U"
So Required number will be
=6!/2!∗2!=6∗5∗4∗3∗2∗1/4=180
Option D
Answer: (D) 180
Question: Both Robert and Alice leave from the same location at 7:00 a.m. driving in the same direction, but in separate cars. Robert drives 40 miles per hour while Alice drives 60 miles per hour. After 6 hours, Alice’s car stops. At what time will Robert’s car reach Alice’s car?
(A) 1 p.m.
(B) 3 p.m.
(C) 4 p.m.
(D) 8 p.m.
(E) 9 p.m.
Rationale: 7:00 am so 6 hours later is 1:00 pm
In six hours, Robert will have driven 6*40 = 240 miles
In six hours, Alive will have driven 6*60 = 360 miles
So Robert needs 360-240 = 120 miles do catch Alice up.
So at 40 mph, he will need 3 hours
1:00 pm + 3 hours = 4:00 pm
ANS : C
Answer: (C) 4 p.m.
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 10:00, how many seconds elapse between the beginning of the first stroke and the end of the last stroke?
(A) 42
(B) 36
(C) 46
(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 10 strikes, there would be 9 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 10 strikes and 9 intervals will take 2*(10+9) = 38 secs
D
D
Answer: (D) 38
Question: Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/3, 1/2 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?
(A) 1/16
(B) 7/8
(C) 9/64
(D) 5/64
(E) 3/64
Rationale: P(Xavier will solve)=1/3
P(Yvonne will solve)=1/2
P(Zelda will NOT solve) = 1- 5/8 = 3/8.
Now, we need to multiply all this Ps to find an answer:
p= (1/3)*(1/2)*(3/8) = 1/16.
Ans. A.
Answer: (A) 1/16
Question: Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $20 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year?
(A)  $752
(B)  $755
(C)  $765
(D)  $773
(E)  $775
Rationale: = (750*6+ 770 *20)/26
= 765
Answer is C.
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Answer: (C)  $765
Question: Truck P and Truck Q drive on the highway in the same direction at respective rates of 70 kph and 75 kph. If Truck Q is 4 km behind Truck P, by how much does Truck P need to increase the speed to catch up with Truck P in 20 minutes?
(A) 4 kph
(B) 5 kph
(C) 6 kph
(D) 7 kph
(E) 8 kph
Rationale: Truck Q needs to gain 4 km in 20 minutes.
The relative speed difference needs to be 4 km / 20 minutes = 12 km/hour
Truck Q needs to increase up to 82 kph, thus an increase in 7 kph.
The answer is D.
Answer: (D) 7 kph
Question: Two trains are moving at 45kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
(A) 40/6 sec
(B) 43/6 sec
(C) 47/6 sec
(D) 40/3 sec
(E) 40/7 sec
Rationale: 70 + 45 = 115 * 5/18 = 575/18 mps
D = 150 + 100 = 250 m
T = 250 * 18/575 = 15/2 = 47/6 sec
Answer:C
Answer: (C) 47/6 sec
Question: At present, the ratio between the ages of Shekhar and Shobha is
4:3. After 6 years, Shekhar's age will be 26 years. Find out the age of Shobha at present?
(A) 15 Years
(B) 14 years
(C) 13 years
(D) 12 years
(E) 20 years
Rationale: After 6 years shekhar's age will be 26 yrs
therefore present age of shekhar = 26-6=20
let present age of shobha = x
then 20/x = 4/3
x=20*3/4 = 15
ANSWER A
Answer: (A) 15 Years
Question: A wire can be bent in the form of a circle of radius 56cm. If it is bent in the form of a square, then its area will be?
(A) 7744
(B) 2388
(C) 2279
(D) 1287
(E) 1100
Rationale: length of wire =2 \Pi r}= 2 *(22/7 )*56 = 352 cm
side of the square = 352/4 = 88cm
area of the square = 88*88 = 7744sq cm
Answer: A
Answer: (A) 7744
Question: A merchant sells an item at a 20 percent discount. but still makes a gross profit of 20 percent of the cost.What percent of cost would be gross profit on the item have been if it had been sold without the discount?
(A) 20%
(B) 40%
(C) 50%
(D) 60%
(E) 66.6%
Rationale: Let the S.P. be 100 Rs.
on giving 20 % discount,,S.p. will be 80Rs.
Profit %=profit*100/C.P.
20=profit*100/C.P.
C.P.=5*profit
C.p.=5*(s.p.-c.p.)
c.p.=5*(80-c.p.)
(c.p./5)+c.p.=80
c.p.=66.66Rs
At no discount,S.P.=100Rs.
C.P.=66.66Rs.
Profit=33.34
Profit%=profit*100/c.p
=33.34*100/66/66
Profit%=50
ANSWER:C
Answer: (C) 50%
Question: A person borrows 7000 for 3 years at 6% p.a. simple interest. He immediately lends it to another person at 31 % p.a. for 3 years. Find his gain in the transaction per year.
(A) 1600
(B) 1700
(C) 1550
(D) 1650
(E) 1750
Rationale: Gain in 3 years
= [(7000Ã—31Ã—3/100)âˆ’(7000Ã—6Ã—3/100)]
= (6510 â€“ 1260) = 5250.
âˆ´ Gain in 1 year = (5250â„3) = 1750
Answer E
Answer: (E) 1750
Question: In one hour, a boat goes 15 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is:
(A) 2
(B) 4
(C) 10
(D) 12
(E) 15
Rationale: Sol.
Speed in still water = 1/2 (15+5) kmph = 10 kmph.
Answer C
Answer: (C) 10
Question: In the coordinate plane, points (x, 5) and (7, y) are on line k. If line k passes through the origin and has slope 5/7, then x + y =
(A) 13
(B) 14
(C) 9
(D) 10
(E) 12
Rationale: Line k passes through the origin and has slope 5/7 means that its equation is y=5/7*x.
Thus: (x, 5)=(7,5) and (7, y) = (7,5) --> x+y=7+5=12.
Answer: E
Answer: (E) 12
Question: A batsman makes a score of 64 runs in the 16th innings and thus increased his average by 3. Find his average after the 16th inning?
(A) 12
(B) 17
(C) 15
(D) 19
(E) 26
Rationale: Let the average after the 16th inning be P.
So, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 64 = 16P => P
= 19
Answer:D
Answer: (D) 19
Question: Two dogsled teams raced across a 300 mile course in Wyoming. Team A finished the course in 3 fewer hours than team R. If team A's average speed was 5 mph greater than team R's, what was team R's average mph?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 25
Rationale: This is a very specific format that has appeared in a handful of real GMAT questions, and you may wish to learn to recognize it: here we have a *fixed* distance, and we are given the difference between the times and speeds of two things that have traveled that distance. This is one of the very small number of question formats where backsolving is typically easier than solving directly, since the direct approach normally produces a quadratic equation.
Say Team R's speed was s. Then Team R's time is 300/s.
Team A's speed was then s+5, and Team A's time was then 300/(s+5).
We need to find an answer choice for s so that the time of Team A is 3 less than the time of Team R. That is, we need an answer choice so that 300/(s+5) = (300/s) - 3. You can now immediately use number properties to zero in on promising answer choices: the times in these questions will always work out to be integers, and we need to divide 300 by s, and by s+5. So we want an answer choice s which is a factor of 300, and for which s+5 is also a factor of 300. So you can rule out answers A and C immediately, since s+5 won't be a divisor of 300 in those cases (sometimes using number properties you get to the correct answer without doing any other work, but unfortunately that's not the case here). Testing the other answer choices, if you try answer D, you find the time for Team R is 15 hours, and for Team A is 12 hours, and since these differ by 3, as desired, D is correct.
Answer: (D) 20
Question: In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
(A) 8490
(B) 50400
(C) 9003
(D) 490
(E) 7493
Rationale: In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
A.	810
B.	1440
C.	2880
D.	50400
E.	5760
Answer: Option D
Explanation:
In the word 'CORPORATION', we treat the vowels OOAIO as one letter.
Thus, we have CRPRTN (OOAIO).
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Number of ways arranging these letters =	7!/2!	= 2520.
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
in	5!/3!	= 20 ways.
Required number of ways = (2520 x 20) = 50400.
Answer:B
Answer: (B) 50400
Question: Pointing to a gentleman, Deepak said, "His only brother is the father of my daughter's father." How the gentleman related to Deepak ?
(A) Actuate
(B) Accumulate
(C) Acquit
(D) Uncle
(E) 2433
Rationale: Explanation:
Father of Deepak's daughter's father — Deepak's father.
So, the man's brother is Deepak's father or the man is the brother of Deepak's father i.e., Deepak's uncle.
Answer: D
Answer: (D) Uncle
Question: The average weight of A, B and C is 46 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
(A) 17 kg
(B) 20 kg
(C) 26 kg
(D) 31 kg
(E) 22 kg
Rationale: let d sum of a, b, c is 3*46=144
and sum of a and b s 2*40=80
sum of b and c is 3 *43=86
hence 80+86-144=22
ans=22
ANSWER:E
Answer: (E) 22 kg