divelab/Sys2Bench huggingface dataset:
Question: Walking at 70% of his usual speed a man takes 24 minutes more to cover a distance. What is his usual time to cover this distance?
Options:
A)30
B)36
C)42
D)48
E)56
Rationale: speed is inversly proprtional to time
walking at 70% of speed meand 7/10s takes 10/7t.
It takes 24 minutes extra to cover the distance. then
10/7t=t+24
10t=7t+168
3t=168
t=56.
Option E is correct
Answer: E
Question: Twelve identical machines, running continuously at the same constant rate, take 9 days to complete a shipment. How many additional machines, each running at the same constant rate, would be needed to reduce the time required to complete a shipment by three days?
Options:
A)2
B)3
C)4
D)6
E)9
Rationale: From the question you know that 12R = 1/9. The question asks you (partially) to make the rate from 1/9 to 1/6 (drop from 9 day to 6). So the only thing that you need to do is to find the magic number than can convert 1/9 to 1/6.
So 1/9 * x = 1/6 (1 equation with one unknown). So by solving this you get x = 9/6 or 3/2. Thats it then! Take the magic number 4/3 and multiply BOTH sides of the original equation and you have:
12*(3/2)*R = (3/2) * 1/9
6 * 3 * R = 1/6, Hence 18R = 1/6, therefore 6 more machines!
D
Answer: D
Question: The security gate at a storage facility requires a five-digit lock code. If the lock code must consist only of digits from 1 through 6, inclusive, with no repeated digits, and the first and last digits of the code must be even, how many lock codes are possible?
Options:
A)144
B)240
C)360
D)720
E)1440
Rationale: X-X-X-X-X --> there are 3 even digits from 1 to 6, inclusive thus options for the first and the last X's are: 3-X-X-X-2. Other X's can take following values: 3-4-3-2-2 --> 3*4*3*2*2=144..
Answer: A.
Answer: A
Question: It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
Options:
A)Sunday
B)Saturday
C)Friday
D)Wednesday
E)None
Rationale: EXPLANATION
On 31st December, 2005 it was Saturday.
Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days.
On 31st December 2009, it was Thursday.
Thus, on 1st Jan, 2010 it is Friday.
Answer C
Answer: C
Question: Consider the word ROTOR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5-letter palindromes?
Options:
A)56678
B)16789
C)17576
D)35142
E)None of these
Rationale: Explanation :
The first letter from the right can be chosen in 26 ways because there are 26 alphabets.Having chosen this, the second letter can be chosen in 26 ways.=> The first two letters can be chosen in 26*26=676 waysHaving chosen the first two letters, the third letter can be chosen in 26 ways.=> All the three letters can be chosen in 676*26=17576 ways.It implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
Answer : C
Answer: C
Question: There are cats got together and decided to kill the mice of 999984. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats?
Options:
A)941,1009
B)991,1001
C)996,1004
D)791,1009
E)931,1009
Rationale: 999984 can be written as 1000000 â€“ 16
= 10002 â€“ 42 ie of the form a2-b2=(a+b)(a-b)
=(1000+4)*(1000-4)
= (1004)*(996)
Given that number of cats is less than number if mice.
So number of cats is 996 and number of mice were 1004
Answer C
Answer: C
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 45 kmph. When and at what distance from Mumbai do the two trains meet?
Options:
A)287
B)279
C)270
D)278
E)379
Rationale: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 40 / (45 -40) = 8 hours
So, the two trains meet at 6 p.m. The two trains meet 6 * 45 = 270 km away from Mumbai.
Answer:C
Answer: C
Question: Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cistern when fill?
Options:
A)1/4
B)1/7
C)2/4
D)2/3
E)1/3
Rationale: 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
ANSWER:E
Answer: E
Question: A can do a piece of work in 4 days. B can do it in 8 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
Options:
A)87 days
B)20 days
C)8 days
D)19 days
E)36 days
Rationale: C = 1/2 - 1/4 - 1/8 = 1/8
=> 8 days
Answer:C
Answer: C
Question: A soccer team plays games only against the other five teams in its league and always in the following order: Gary, Howard, Robin, Fred and Jackie. If the team’s final game of the season is against Fred, which of the following could be the number of games in the team’s schedule?
Options:
A)24
B)66
C)56
D)72
E)81
Rationale: IMO 'A' is the answer.
Matches will be in multiples of 5x+4. The answer that satisfies this condition is A
Answer: A
Question: A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is?
Options:
A)7/17
B)7/12
C)7/19
D)7/11
E)7/15
Rationale: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = ⁷C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂
= 7/15
Answer:E
Answer: E
Question: The standard serial numbers for medical licence are 3 letters followed by 5 digits. How many different medical licenses are possible if letters and digits can be repeated?
Options:
A)26 × × 3 × 5
B)26³ × 10 000
C)26³ x 100 000
D)26 × 25 × 24 × 10 × 9 × 8 × 7
E)26³ × 10 000 x 15
Rationale: OFFICIAL SOLUTION:
(C) The formula for permutations of events is the product of the number of ways each event can occur. There are 26 letters and 10 digits. So there are 26 × 26 × 26 options for the three letters, and 10 × 10 × 10 × 10 x 10 for the five digits. The number of different Medical license is 26 × 26 × 26 × 10 × 10 × 10 × 10 x 10= 26³ × 100 000.
The correct answer is choice (C).
Answer: C
Question: Speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph. A man rows to a place at a distance of 7740 km and comes back to the starting point. The total time taken by him is:
Options:
A)914.2 hours
B)900 hours
C)915 hours
D)982.9 hours
E)915 hours
Rationale: Explanation:
Speed downstream = (16 + 2) = 18 kmph
Speed upstream = (16 - 2) = 14 kmph
Total time taken = 7740/18 + 7740/14 = 430 + 552.9 = 982.9 hours
Answer: Option D
Answer: D
Question: The average of 10 numbers was calculated as 18. It is discovered later on that while calculating the average, one number, namely 66, was incorrectly read as 26. What is the correct average?
Options:
A)20
B)21
C)22
D)23
E)24
Rationale: 10*18 - 26 + 66 = 220
220 / 10 = 22
The answer is C.
Answer: C
Question: How many positive integers less than 90 are multiples of 6 but NOT multiples of 9?
Options:
A)4
B)6
C)8
D)10
E)12
Rationale: The LCM of 6 and 9 is 18.
If x <90 and x is divisible by 6 not by 9 --> x is NOT divisible by 18.
From 1--> 90, we have 5 numbers which is divisible by 18: 18, 36, 54, 72, 90.
From 1-->90, we have (90-6)/6 +1 = 15 numbers divisible by 6.
Therefore, our answer is 15-5 = 10 numbers.
D
Answer: D
Question: If |z|/w = 4,which of the following must be true?
Options:
A)z = -4w
B)z = 4w
C)z^2 = 16w^2
D)z^2 = 16w^3
E)z^3 = 64w^3
Rationale: |z|/w = 4.
|z| = 4w.
Then z = 4w or -4w and so z^2 = 16w^2.
The answer is C.
Answer: C
Question: A total of 50 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 20 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? [Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)]
Options:
A)1/4
B)7/12
C)2/3
D)7/8
E)8/7
Rationale: Let' take the Number of geese to be 100.
Male = 50. Female = 50.
Now the second part of the Q, Let's take the Number migrated to be 20.
So we have 20 geese that migrated and out of that 20% are male i.e 20/100 *20 = 4 Geese (Males)
And now we know out of the total 20 geese , 4 are male , then 16 have to be female.
Now the ratio part , Male Geese Ratios = 4/50 = 2/25. - A
Female Geese Ratios =16/50=8/25 - B
Cross Multiply Equations A and B and you get =1/4 .
Ans A
Answer: A
Question: 2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 32 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A?
Options:
A)15 km/hr
B)24 km/hr
C)17 km/hr
D)18.75 km/hr
E)None of these
Rationale: Explanation :
Total distance covered by B=32*6=192kmTotal time taken by A to cover same distance=2+6=8 hrsaverage speed of A=192/8=24 km/hr
Answer : B
Answer: B
Question: A train 1000 m long can cross an electric pole in 200 sec and then find the speed of the train?
Options:
A)12
B)14
C)16
D)18
E)20
Rationale: Length = Speed * time
Speed = L/T
S = 1000/200
S = 5 M/Sec
Speed= 5*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 18 Kmph
Answer:D
Answer: D
Question: For all integers a and b, a%b = (a + b)(a - b). If 4%x = 12, then which of the following could be a value of x?
Options:
A)-4
B)-3
C)2
D)3
E)6
Rationale: 4%x = (4+x)(4-x)
16-x^2 = 12
x^2 = 4
x=-2,2
Ans: C
Answer: C
Question: A man is 24 years older than his son. In three years, his age will be twice the age of his son. The present age of the son is
Options:
A)14 years
B)18 years
C)20 years
D)21 years
E)None
Rationale: Solution
Let the son's present age be x years .Then, man's present age	= (x+24)years.
Then	â€¹=â€º(x+24)+3= 2(x+3)
â€¹=â€ºx+27=2x+6
x= 21.
Answer D
Answer: D
Question: Kiran has 85 currency notes in all, some of which were of Rs. 100 denomination and the remaining of Rs. 50 denomination. The total amount of all these currency notes was Rs.5000. How much amount did she have in the denomination of Rs. 50?
Options:
A)1900
B)3500
C)4000
D)4200
E)4450
Rationale: Let the number of 50 – rupee notes be x.
Then, the number of 100-rupee notes = (85 – x)
50x + 100(85 – x) = 5000
= x + 2 (85 – x) = 100
= x =70
So, required amount = Rs. (50 x 70) = Rs. 3500
Answer: Option B
Answer: B
Question: In a bag there are a certain number of red balls and blue balls. The probability of picking up exactly 1 blue ball when 2 balls are randomly drawn, is 1/2. Which of the following is the ratio of the number of red balls to blue balls in the bag
Options:
A)5:1
B)1:6
C)1:4
D)1:46
E)1:1
Rationale: since the probability of drawing a blue ball out of two picks is 1/2.
the ratio of the blue ball to red balls should be 1:1
Answer : E
Answer: E
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 6000. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Options:
A)s. 375
B)s. 400
C)s. 600
D)s. 750
E)s. 850
Rationale: C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24
A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4: 3 : 1
C's share (for 3 days) = Rs.	(3 * 1/24 * 6000) =Rs.750
Answer = D
Answer: D
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
Options:
A)29
B)32
C)19
D)77
E)99
Rationale: A/8 = 8 * 8 => A = 8 * 8 * 8
x * 2x = 8 * 8 * 8
x = 16 => 2x = 32
Answer:B
Answer: B
Question: If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 18. By how much do the two digits differ?
Options:
A) 2
B) 4
C) 5
D) 6
E) 7
Rationale: Given that (10a + b) - (10b + a) = 18 --> 9a - 9b =18 --> a - b = 2.
Answer: A.
Answer: A
Question: In a certain pond, 40 fish were caught, tagged, and returned to the pond. A few days later, 40 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what`s the approximate number of fish in the pond?
Options:
A)400
B)800
C)1250
D)2500
E)10 000
Rationale: The percent of tagged fish in the second catch is 2/40*100 = 5%.
We are told that 5% approximates the percent of tagged fish in the pond. Since there are 40 tagged fish, then we have 0.05x = 40 --> x = 800.
Answer: B.
Answer: B
Question: What is the cost of leveling the field in the form of parallelogram at the rate of Rs.40/10 sq.metre, whose base & perpendicular distance from the other side being 24m & 34m respectively?
Options:
A)s. 600
B)s. 630
C)s. 640
D)s. 648
E)s. 816
Rationale: Area of the parallelogram = Length of the base * Perpendicular height
= 24 * 34 = 816 m.
Total cost of levelling = Rs.816
E
Answer: E
Question: Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 3 percent and the mobile phone at a profit of 10 percent. Overall he make a.
Options:
A)228
B)350
C)27
D)200
E)881
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 3/100) = 15000 - 450
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -450 + 800 = Rs. 350
As this is positive, an overall profit of Rs. 350 was made.Answer:B
Answer: B
Question: There are 12 students in a class. On the day the test was given, Ella was absent. The other 11 students took the test and their average was 74. The next day, Ella took the test, and with this grade included, the new average was 75. What was Ella's grade on the test?
Options:
A)82
B)83
C)84
D)85
E)86
Rationale: 11*74+Ella's grade=12*75
Ella's grade is 12*75-11*74=86.
The answer is E.
Answer: E
Question: At a casino in Mumbai, there are 3 tables A, B and C. The payoffs at A is 10 : 1, at B is 20 : 1 and C is 30 :1. If a man bets Rs. 200 at each table and win at two of the tables, what is the maximum and minimum difference between his earnings can be ?
Options:
A)Rs. 4000
B)Rs. 4500
C)Rs. 2500
D)Rs. 2000
E)None of these
Rationale: Solution: Maximum earning will be only possible when he will won on the maximum yielding table.
A → 10 :1
B → 20 :1
C → 30 :1
i.e., he won B and C but lost on A,
20 *200 +30 *200 - 1 *200 = 9800
Minimum earnings will be when he won on table A and B and lose on table 3.
10 *200 + 20 *200 - 1 *200 = 5800
Therefore, difference = 9800-5800 = Rs. 4000.
Alternatively,
The difference,
= [(30 +20 -1) - (10 +20 -1)] * 200
= Rs. 4000.
Answer: Option A
Answer: A
Question: Can you find the smallest non fractional number such that
If the number gets divided by 3 , we get the remainder of 1;
If the number gets divided by 4 , we get the remainder of 2
If the number gets divided by 5 , we get the remainder of 3;
If the number gets divided by 6 , we get the remainder of 4.
Options:
A)55
B)60
C)58
D)44
E)72
Rationale: C
58.
As we know LCM of the numbers 3 4 5 & 6 is 60.
So if i divide 60 by any of the four number , it gives remainder as 0.
Now to get reminder as desired, is should be 2 short of 60. (3-1,4-2,5-3,6-4 )
Answer: C
Question: A car is traveling 45 kilometers per hour. How many meters does the car travel in one minute?
Options:
A)750 meters / minute
B)850 meters / minute
C)950 meters / minute
D)550 meters / minute
E)650 meters / minute
Rationale: Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
45 kilometers per hour = 45 km/hr
= (45 * 1000 meters) / (60 minutes) = 750 meters / minute
correct answer A
Answer: A
Question: The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units?
Options:
A)140 sq.units
B)176 sq.units
C)178 sq.units
D)189 sq.units
E)678 sq.units
Rationale: Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
Answer:A
Answer: A
Question: Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?
Options:
A)1887 ways
B)1440 ways
C)1657 ways
D)1652 ways
E)6745 ways
Rationale: In the word, "MATERIAL" there are three vowels A, I, E.
If all the vowels are together, the arrangement is MTRL'AAEI'.
Consider AAEI as one unit. The arrangement is as follows.
M T R L A A E I
The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.
Number of required ways of arranging the above letters = 5! * 4!/2!
= (120 * 24)/2
=1440 ways.
Answer:B
Answer: B
Question: A worker can load one truck in 5 hours. A second worker can load the same truck in 4 hours. If both workers load one truck simultaneously while maintaining their constant rates, approximately how long, in hours, will it take them to fill one truck?
Options:
A)1.8
B)2.0
C)2.2
D)2.4
E)2.6
Rationale: The workers fill the truck at a rate of 1/5 + 1/4 = 9/20 of the truck per hour.
Then the time to fill one truck is 20/9 which is about 2.2 hours.
The answer is C.
Answer: C
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
Options:
A)1/3
B)1/7
C)1/4
D)1/2
E)1/9
Rationale: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3
Answer: a
Answer: A
Question: The arithmetic mean of the set S = {5, K, 4, 10, M, 5} is 6. If K and M are integers, and K ≠ M, what is the median of the numbers in the set?
Options:
A)4
B)4.5
C)5
D)5.5
E)6
Rationale: The sum of the numbers is 6*6 = 36
K+M = 36 - 10 - 5 - 5 - 4 = 12
Since K ≠ M, K and M do not equal 6.
Thus one of the two numbers is 5 or less and one is 7 or more.
Then middle two numbers in the set are 5 and 5.
The median is 5.
The answer is C.
Answer: C
Question: An ice cream store received shipments of ingredients on Tuesday and Wednesday. Tuesday's shipment had 6 different packages, with an average (arithmetic mean) of 11 and 2/3 pounds. Wednesday's shipment included 14 packages, weighing an average of 9 and 3/7 pounds. What was the average package weight, in pounds, of the shipments received on both days?
Options:
A)9 and 6/7 pounds
B)10 and 1/10 pounds
C)10 and 2/5 pounds
D)11 pounds
E)11 and 1/7 pounds
Rationale: Solution: Average weight = Total weight/number of packages. The total weight on Tuesday was 6 * (11 and 2/3 pounds), or 70 pounds. The total weight on Wednesday was 14 * (9 and 3/7 pounds), or 132 pounds. The sum of the weights for both days is 132 + 70, or 202 pounds. The average is 202 pounds/20 packages, or 10 and 1/10 pounds per package.
Correct answer: B
Answer: B
Question: The area of the largest circle that can be drawn inside a square of side 42 Cm in length is:
Options:
A)1200
B)1428
C)1420
D)1356
E)1386
Rationale: Radius of required circle = 21 Cm
its area = 22/7 × 21 × 21
66 × 21= 1386 Cm(power)2
Answer is E.
Answer: E
Question: Six computers, each working at the same constant rate, together can process a certain amount of data in 6 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 4 days?
Options:
A)3
B)5
C)6
D)9
E)12
Rationale: Explanation: If six computers require 6 days to process the data, thats
a total of 36 computer-days the product of 6 and 6. If you change the number
of computers or the number of days, 36 will have to remain the product, whether
that means 36 days of one computer or one day with 36 computers.
In 4 days, the number of computers is:
4c = 36
c = 9
9 computers is 3 more than the 6 that it took to do the job in 6 days, so
the correct choice is (A).
Answer: A
Question: he ratio between the sale price and the cost price of an article is 5:1. What is the ratio between the profit and the cost price of that article?
Options:
A)2:6
B)2:9
C)2:4
D)2:1
E)2:5
Rationale: Let C.P. = Rs. x and S.P. = Rs. 5x.
Then, Gain = Rs. 4x
Required ratio = 2x : x = 2:1
Answer:D
Answer: D
Question: Maggie has to buy 50 toys from a toy shop. She buys 13 hoola hoops, 15 beach balls, and 12 baseball bats. What percentage of Toys has she not bought ?
Options:
A)26 %
B)34 %
C)30 %
D)20 %
E)38 %
Rationale: Explanation :
Toys not bought = 50 - 13 - 15 - 12 = 10
Toys not bought percentage (10/50 x 100) %
Answer : D
Answer: D
Question: 20 men can dig a tunnel in 30 days. If after 10 days, 20 more men are deployed to dig the tunnel, how many more days it will take to dig the whole tunnel?
Options:
A)10
B)15
C)20
D)25
E)30
Rationale: A
Remaining work can be completed by 20 men in 30-10 = 20 days.
If 20 men can do X work in 20 days, and let us say 40 men take N days to do the same work.
Now, more men, less number of days (inversely proportion)
20 : 40 :: N : 20
N = 20 X 20 / 40 = 10 days.
Answer: A
Question: A car traveling at a certain constant speed takes 20 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 36 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
Options:
A)24
B)26
C)28
D)30
E)32
Rationale: 36 * T = 1 km => T = 1/36 km/h
V*(T+20/3600) = 1
V (1/36 + 20/3600) = 1
V (120/3600) = 1
V = 30 km/h
The answer is D.
Answer: D
Question: A cycle is bought for Rs.900 and sold for Rs.1170, find the gain percent?
Options:
A)30%
B)20%
C)23%
D)74%
E)83%
Rationale: 900 ---- 270
100 ---- ? =>
30%
Answer:A
Answer: A
Question: Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours. C is closed A and B can fill the remaining par in 7 hours. The number of hours taken by C alone to fill the tank is?
Options:
A)17 hours
B)18 hours
C)14 hours
D)19 hours
E)16 hours
Rationale: Part filled in 2 hours = 2/6 = 1/3.
Remaining part = 1 - 1/3 = 2/3
(A + B)'s 1 hour work = 2/21
C's 1 hour work = [(A + B + C)'s 1 hour work - (A + B)'s 1 hour work]
= (1/6 - 2/21) = 1/14
C alone can fill the tank in 14 hours.
Answer:C
Answer: C
Question: A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank?
Options:
A)28
B)24
C)22
D)20
E)30
Rationale: 1/A + 1/B + 1/C = 1/8 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/8
=> (1 + 2 + 4)/2B = 1/8
=> 2B/7 = 8
=> B = 28 hours.
ANSWER A
Answer: A
Question: In a certain town, there are six times as many people who were born in the town’s state as there are people who were born in another state or country. The ratio of those residents born in the town’s state to the town’s total population is
Options:
A)1 to 4
B)1 to 3
C)1 to 2
D)3 to 4
E)6 to 7
Rationale: Town state: 6 times the whole town or country
then ratio will be 6(times)/7 total(times)
So the answer is 6/7.
E
Answer: E
Question: The simple form of the ratio 7/6:2/5 is?
Options:
A)10:6
B)10:3
C)15:3
D)25:3
E)35:12
Rationale: 7/6 : 2/5 = 35:12
ANSWER:E
Answer: E
Question: A bus can hold 60 passengers. If there are 12 rows of seats on the bus, how many seats are in each row?
Options:
A)6
B)5
C)3
D)2
E)12
Rationale: No. of seats = 60/12 = 5
There are 5 seats in each row
Answer : B
Answer: B