divelab/Sys2Bench huggingface dataset:
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?
Options:
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
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?
Options:
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
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.
Options:
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
Question: The second of two numbers is two less than three times the first. Find the numbers if there sum is
74.
Options:
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
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 .
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is?
Options:
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
Question: Walking 7/6 of his usual rate, a boy reaches his school 4 min early. Find his usual time to reach the school?
Options:
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
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?
Options:
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
Question: Find the unit's digit in 264^102+264^103
Options:
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
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
Options:
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
Question: What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?
Options:
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
Question: In how many way the letter of the word "RUMOUR" can be arranged
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
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?
Options:
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
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.
Options:
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
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:
Options:
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
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 =
Options:
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
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?
Options:
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
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?
Options:
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
Question: In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?
Options:
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
Question: Pointing to a gentleman, Deepak said, "His only brother is the father of my daughter's father." How the gentleman related to Deepak ?
Options:
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
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:
Options:
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
Question: Calculate the number of bricks, each measuring 25 cm * 15 cm * 8 cm required to construct a wall of dimensions 10 m * 4 m * 5 m when 10% of its volume is occupied by mortar?
Options:
A)1787
B)6000
C)8648
D)7000
E)7300
Rationale: 10 * 4/100 * 5 * 90/100 = 25/100 * 15/100 * 8/100 * x
10 * 20 * 90
= 15 * 2 * x => x
= 6000
Answer: B
Answer: B
Question: On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor
Options:
A)12
B)14
C)18
D)22
E)24
Rationale: d = (D-R)/Q
= (109 - 1)/9
= 108/9 = 12
A)
Answer: A
Question: Two trains 135 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
Options:
A)7.45
B)7.16
C)7.12
D)7.15
E)7.11
Rationale: T = (135 + 165)/ (80 + 65) * 18/5
T = 7.45
Answer: A
Answer: A
Question: Which of the following is equal to 3.14 x 106 ?
Options:
A)314
B)3140
C)3140000
D)31400000
E)none of the above
Rationale: 3.14 x 10^6 = 3.14 x 1000000 = 3140000.
Answer = C
Answer: C
Question: 252 can be expressed as a product of primes as :
Options:
A)2 x 2 x 3 x 3 x 7
B)2 x 2 x 2 x 3 x 7
C)3 x 3 x 3 x 3 x 7
D)2 x 3 x 3 x 3 x 7
E)2 x 3 x 7 x 3 x 2
Rationale: 252 = 2 x 2 x 3 x 3 x 7.
answer :A
Answer: A
Question: When Greenville State University decided to move its fine arts collection to a new library, it had to package the collection in 20-inch by 20-inch by 15-inch boxes. If the university pays $1.30 for every box, and if the university needs 3.06 million cubic inches to package the collection, what is the minimum amount the university must spend on boxes?
Options:
A)$255
B)$275
C)$510
D)$1,250
E)$663
Rationale: Total no. Of boxes = 3060000/(20×20×15) = 510
Total cost = 510×$1.30=$663
Answer E
Answer: E
Question: The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?
Options:
A)1289
B)2799
C)1000
D)2792
E)2912
Rationale: 2 * 22/7 * 1.75 * x
= 11000
x = 1000
Answer:C
Answer: C
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)120 m
B)240 m
C)300 m
D)400 m
E)450 m
Rationale: Answer: Option B
Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: B
Question: Rs.900 is divided among Maya, Annie, Saiji so that Maya receives half as much as Annie and Annie half as much as Saiji. Then Saiji’s share is :
Options:
A)Rs.200
B)Rs.300
C)Rs.400
D)Rs.600
E)Rs.500
Rationale: Let Saiji = x. Then, Annie = x/2 and Maya = x/4.
Therefore, Maya : Annie : Saiji = x/4 : x/2 : x = 1 : 2 : 4.
Therefore, Saiji’s share = Rs. 900 * 4/9
= Rs.400.
ANSWER:C
Answer: C
Question: A train 136 m long pass a telegraph pole in 6 seconds. Find the speed of the train
Options:
A)66 km/hr
B)68.4 km/hr
C)82.8 km/hr
D)79.2 km/hr
E)None
Rationale: Sol.
Speed = [136/6] m/sec = [23 * 18/5] km/hr = 82.8 km/hr.
Answer C
Answer: C
Question: A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m. ?
Options:
A)7
B)5
C)9
D)2
E)8
Rationale: A
7
Relative speed = 2 + 3 = 5 rounds per hour.
So, they cross each other 5 times in an hour and 2 times in half an hour.
Hence, they cross each other 7 times before 9.30 a.m.
Answer: A
Question: A man walking at a rate of 15km/hr crosses a bridge in 30 minutes. The length of the bridge is?
Options:
A)1250m
B)1110m
C)950m
D)1500m
E)1300m
Rationale: Speed = 15*5/18 = 15/18 m/sec
Distance covered in 30 minutes = 15/18 *30 *60 = 1500 m
Answer is D
Answer: D
Question: Given a circular wheel of 3.62 m radius how many revolutions will the will make to travel a distance of 1 km?
Options:
A)22754.3
B)22254.2
C)25754.2
D)22753.2
E)22254.2
Rationale: 2 * 22/7 * 3.62 * x = 22754.3
x = 1000
Answer: A
Answer: A
Question: Which of the following is equal to 1(2/5)%?
Options:
A)0.012/100
B)1.4/100
C)1.2/100
D)12/100
E)12/10
Rationale: This notation may be confusing for some, since it looks like we're multiplying 1 and 2/5
How about adding a space:Which of the following is equal to (1 2/5)%
(1 2/5)% = 1.4% = 1.4/100
Answer:
B
Answer: B
Question: There are 2 red chips and 3 blue ones. When arranged in a row, they form a certain color pattern, for example RBRRB. How many color patterns?
Options:
A)A)10
B)B)12
C)C)24
D)D)60
E)E)100
Rationale: Using anagram method:
5_4_3_2_1
R_R_R_B_B
so..
5!/Number of repeated letters (2!)(3!) = 10
ANS:E
Answer: E
Question: If the sides of a triangle are 30 cm, 40 cm and 50 cm, what is its area?
Options:
A)400
B)500
C)550
D)600
E)700
Rationale: The triangle with sides 30 cm, 40 cm and 50 cm is right angled, where the hypotenuse is 50 cm.
Area of the triangle = 1/2 * 40 * 30 = 600 cm2
Answer: Option D
Answer: D
Question: From (1, 2, 3, 4, 5, 6), one number is picked out and replaced and one number is picked out again. If the sum of the 2 numbers is 10, what is the probability that the 2 numbers included the number 5?
Options:
A)1/5
B)2/5
C)3/10
D)3/5
E)1/3
Rationale: We know that the sum of two numbers picked was 10. So, there could be the following cases:
(4, 6);
(6, 4);
(5, 5);
Total of 3 cases out of which 1 have 5, thus the probability is 1/3.
Ans E
Answer: E
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 50 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)12 sec
B)24 sec
C)45 sec
D)60 sec
E)62 sec
Rationale: Relative speed = 50 + 30 = 80 km/hr.
80 * 5/18 = 200/9 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 9/200 = 45 sec.
ANSWER:C
Answer: C
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.9 the sixth number is?
Options:
A)11.4
B)14.5
C)11.8
D)11.5
E)11.1
Rationale: 1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.9 = 71.4
63 + 71.4 = 134.4 – 119.9 = 14.5
6th number = 11.5
Answer: B
Answer: B
Question: F is a positive integer and 225 and 216 are both divisors of F. If F=(2^a)*(3^b)*(5^c), where a, b and c are positive integers, what is the least possible value of a+ b+ c?
Options:
A)4
B)5
C)8
D)7
E)6
Rationale: Lets make factorization of 225 and 216 ..
225 = 5 X 5 X 3 X 3 X 3
216 = 2 X 2 X 2 X 3 X 3 X 3
F would have to have 3 two's , 225 has 3 threes and and so does 216 but they can be the same three threes so we count them only once ... 225 has 2 fives ... So we had them together and we get 3 + 3 + 2 = 8(C) (answer) ...
Answer: C
Question: Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day S on which the buses leave at the same time.
Options:
A)S=Tuesday
B)Wednesday
C)Thursday
D)Sunday
E)S=The busses will never leave at the same time
Rationale: The answer is E.
I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers would always end in a 1 or 6. So you can see they'd never coincide.
Alternatively, you could see that if they left at the same time, they'd coincide every 30 hours, but since C is one hour ahead of B, every 30 hours C will still be one hour ahead of B.E
Answer: E