divelab/Sys2Bench huggingface dataset:
Question: Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:
Options:
A)15
B)16
C)18
D)25
E)28
Rationale: Work done by Sakshi in 1 day = 1/20
Since Tanya is 25% efficient than Sakshi, she completes 25% more work in a day than Sakshi.
=> Tanya's 1 day work = 120 + 120 * 25100 = 116
So time taken by Tanya to finish the work = 16 days answer B
Answer: B
Question: The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly four elements each?
Options:
A)126
B)120
C)110
D)100
E)118
Rationale: nC2 = 36
=> n*(n-1)/2 = 36 by middle term factor n can not be negative
=> n = 9
nC3 = 9C4 = 126
So, Answer is A.
Answer: A
Question: Victor's job requires him to complete a series of identical jobs. If Victor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish a total of 36 jobs. How long W would it take Victor to complete 10 jobs without any supervision?
Options:
A)34
B)52
C)60
D)70
E)92
Rationale: Rate when supervised = (job)/(time) = 1/t.
Rate when unsupervised = (job)/(time) = 1/(t+3).
For 144/2=72 days he is supervised and for 144/2=72 days he is unsupervised and does 36 jobs:
72/t + 72/(t+3) = 36 --> t=3 days --> t+3 = 6 days.
Victor to complete 10 jobs without any supervision will need W 10(t + 3) = 60 days.
Answer: C.
Answer: C
Question: A box measuring 90 inches long by 45 inches wide by 9 inches deep is to be filled entirely with identical cubes. No space is to be left unfilled. What is the smallest number of cubes that can accomplish this objective?
Options:
A)17
B)18
C)50
D)108
E)864
Rationale: least number of cubes will be required when the cubes that could fit in are biggest.
9 is the biggest number that could divide all three, 90, 45 and 9.
Thus side of cube must be 9, and total number of cubes = 90/9 * 45/9*9/9 = 50
Ans C it is.
Answer: C
Question: A car travels at a speed of 65 miles per hour. How far will it travel in 6 hours?
Options:
A)125 miles
B)225 miles
C)390 miles
D)425 miles
E)525 miles
Rationale: During each hour, the car travels 65 miles. For 6 hours it will travel
65 + 65 + 65 + 65 + 65+ 65 = 6 × 65 = 390 miles
correct answer is C) 390 miles
Answer: C
Question: A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs $ 2 per gallon, how long will it take for the truck owner to refuel his vehicle with $ 50 worth of diesel fuel?
Options:
A)50 seconds
B)1 minute
C)1 minute 20 seconds
D)20 minutes
E)1 hour 20 minutes
Rationale: 2 gal / 5 sec
$2 / gal
$40/$2 = 20 gal
2 gal / 5 sec with 20 gal = 50 sec
A. 50 seconds
Answer: A
Question: Exactly 12% of the reporters for a certain wire service cover local politics in Country X. If 40% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics?
Options:
A)20%
B)42%
C)44%
D)80%
E)84%
Rationale: Let's assume there are 100 reporters --> 12 reporters cover local politics.
Now, as 40% of the reporters who cover all politics do not cover local politics then the rest 60% of the reporters who cover politics do cover local politics, so if there are x reporters who cover politics then 60% of them equal to 12 (# of reporters who cover local politics): 0.6x=12 --> x=20, hence 20 reporters cover politics and the rest 100-20=80 reporters do not cover politics at all.
Answer: D.
Answer: D
Question: When two dice are rolled, what is the probability that the sum is either 7 or 11?
Options:
A)1/4
B)1/9
C)4/3
D)3/9
E)2/9
Rationale: Total number of outcomes possible=36
Probability of getting sum of 7=6/36
Probability of getting sum of 11=2/36
probability that the sum is either 7 or 11=6/36+2/36=2/9
ANSWER:E
Answer: E
Question: A mixture contains alcohol and water in the ratio 4 : 3. If 9 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture
Options:
A)15 litres
B)10 litres
C)30 litres
D)22 litres
E)18 litres
Rationale: Let the quantity of alcohol and water be 4x litres and 3x litres respectively
4x/(3x+9)=4/5
20x=4(3x+9)
8x=36
x=4.5
Quantity of alcohol = (4 x 4.5) litres = 18 litres.
Answer is E
Answer: E
Question: If a^x = b^4y, then
Options:
A)log a/b= x/y
B)log a/ log b = x/y
C)log a/ log b = 4y/x
D)log b/a = x/y
E)log b/a = y/x
Rationale: a^x = b^4y => log a^x = log b^4y => x log a = 4y log b
=> log a/ log b = 4y/x
ANSWER:C
Answer: C
Question: A women purchased 3 towels @ Rs.100 each, 5 towels @ Rs.150 each and two towels at a certain rate which is now slipped off from his memory. But she remembers that the average price of the towels was Rs.150. Find the unknown rate of two towels?
Options:
A)400
B)450
C)500
D)550
E)600
Rationale: 10 * 150 = 1500
3 * 100 + 5 * 150 = 1050
1500 – 1050 = 450
B
Answer: B
Question: The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder S of Y divided by 5?
Options:
A)S=1.
B)S=2.
C)S=3.
D)4.
E)5.
Rationale: X divided by 10 gives reminder of 2. X can be 2/12/22....
X+Y divided by 5 is 4. X+Y can be 4/ 9/ 19....
If X+Y= 4 and X is 2 then Y = 2 and Y/5 will give a reminder of 2
Similarly, if X+Y= 9 and X = 2, then y/5 will give a reminder of 2
Hence the answer must be 2 (B)
Also....
x+y=5m+4 and x=10K+2
hence 10k+2+y=5m+4 or y=5(m-2k)+2, m-2k being a constant remainder is 2 hence answer is B
Answer: B
Question: A baker makes chocolate cookies and peanut cookies. His recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6. If he makes exactly 98 cookies, what is the minimum number of chocolate chip cookies he makes?
Options:
A)7
B)14
C)21
D)28
E)56
Rationale: 7C+6P=98
We need to maximize P to minimize C so that the eq is also satisfied
Try substitution for CP to solve so that eqn is satisfied
The least value of C for which equation gets satisfied is 5
i.e. 7*2+6*14=14+84=98
Hence B is the answer
Answer: B
Question: Lagaan is levied on the 60% of the cultivated land. The revenue department collected total Rs. 3,84,000 through the lagaan from the village of Sukhiya. Sukhiya, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Sukhiya over the total taxable land of the village is:
Options:
A)0.20887
B)0.3887
C)0.33487
D)0.20833
E)0.38222
Rationale: Explanation:
Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 384000x
\therefore Required percentage = \inline \frac{800x}{384000}\times 100 = 0.20833
Answer: D
Answer: D
Question: Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are 1/4, 1/3 and 5/8, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?
Options:
A)1/32
B)7/8
C)9/64
D)5/64
E)3/64
Rationale: P(Xavier will solve)=1/4
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= (1/4)*(1/3)*(3/8) = 1/32.
Ans. A.
Answer: A
Question: The ratio between the length and the breadth of a rectangular plot is 7 : 5. If the perimeter of the plot is 72 metres, what is its area?
Options:
A)315 sq.metres
B)260 sq.metres
C)280 sq.metres
D)380 sq.metres
E)None of these
Rationale: Let the length and breadth be 7x and 5x respectively.
Then, P = 2(7x + 5x) = 72 â‡’ x = 3
Area = 7 Ã— 3 Ã— 5 Ã— 3 = 315 sq.m.
Answer A
Answer: A
Question: If the area of circle is 616 sq cm then its circumference?
Options:
A)21
B)88
C)66
D)16
E)12
Rationale: 22/7 r2 = 616 => r = 14
2 * 22/7 * 14 = 88
Answer: B
Answer: B
Question: A man is 22 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
Options:
A)20
B)25
C)27
D)22
E)91
Rationale: Let the son's present age be x years.
Then, man's present age = (x + 22) years.
(x + 22) + 2 = 2(x + 2) x + 24 = 2x + 4 => x = 20.
Answer: A
Answer: A
Question: Albert invested Rs. 8000 in a scheme for 2 years at compound interest rate 5% p.a. How much amount will Albert get on maturity of the fixed deposit?
Options:
A)Rs. 8600
B)Rs. 8620
C)Rs. 8800
D)Rs. 8840
E)None of these
Rationale: Amount = [8000 * (1 + 5/100)2]
= 8000 * 21/20 * 21/20
= Rs. 8820
ANSWER:E
Answer: E
Question: 1/2 + [(2/3 * 3/4)/4] - 9/16 =
Options:
A) 1/16
B) 19/16
C) 15/16
D) 9/13
E) 0
Rationale: We need to simplify the expression using PEMDAS.
Parentheses
Exponents
Multiplication andDivision
Addition andSubtraction
The calculation of an equation or expression must be carried out in the following order:
1) Operations within parentheses (or absolute value bars or radicals)
2) Exponents
3) Multiplication and division from left to right
4) Addition and subtraction from left to right
The answer is A.
Answer: A
Question: If x is to be chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {3,4,5}, what`s the probability that xy will be even?
Options:
A)1/6
B)2/3
C)1/2
D)1/3
E)5/6
Rationale: The product to be even either one or both must be even, so:
P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3;
Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1.
Answer: B.
Answer: B
Question: A man spends 75% of his income.If his income increases by 20%,then what will be his new expenditure?
Options:
A)61.5%
B)62.5%
C)63.5%
D)64.5%
E)65.5%
Rationale: Let Rs 100 be the income
Expenditure=Rs75
Increased income=Rs120
Expenditure in amount is same.
So, expenditure % =75/120 *100=62.5%
ANSWER:B
Answer: B
Question: Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 5 muffins remained. How many guests did Monica plan on?
Options:
A)3.
B)4.
C)5.
D)6.
E)7.
Rationale: Let x be the number of guests.
Number of muffins prepared = 5x + 2
Number of muffins eaten + Number of muffins remaining = Number of muffins prepared
6(x - 1) + 3 = 5x + 2
6x - 5 = 5x + 2
x = 7
Answer: E
Answer: E
Question: The perimeter of one square is 48 cm and that of another is 20 cm. Find the perimeter and the diagonal of a square which is equal in area to these two combined?
Options:
A)13√2
B)15
C)48
D)75
E)23
Rationale: xplanation:
4a = 48 4a = 20
a = 12 a = 5
a2 = 144 a2 = 25
Combined area = a2 = 169 => a = 13
d = 13√2
Answer: A
Answer: A
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 12 sec, then the speed of each train is?
Options:
A)22
B)77
C)36
D)88
E)21
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/12 => x = 10
Speed of each train = 10 m/sec.
= 10 * 18/5 =- 36 km/hr.
Answer: C
Answer: C
Question: The simple interest on a sum of money is Rs. 50. What is the sum?
I.The interest rate is 10% p.a.
II.The sum earned simple interest in 10 years.
Options:
A)I alone sufficient while II alone not sufficient to answer
B)II alone sufficient while I alone not sufficient to answer
C)Either I or II alone sufficient to answer
D)Both I and II are not sufficient to answer
E)Both I and II are necessary to answer
Rationale: EXPLANATION
Explanation:
Given : S.I. = Rs. 50.
I gives, R = 10% p.a.
II gives, T = 10 years.
Sum =(100 x S.I/ T x R) = Rs. (100x50/10x10) = Rs.50
Thus, I and II together give the answer.
answer is (E).
Answer: E
Question: Kant and Jaya started a business by investing a certain amount, Jaya’s share is Rs.1400, out of annual profit of Rs.3800, then what is the ratio of investments of Kant and Jaya respectively ?
Options:
A)3:4
B)18:21
C)12:7
D)6:11
E)4:3
Rationale: otal profit = Rs.3800.
Jaya share = Rs.1400.
Kant share = Rs.3800 - Rs.1400 = Rs.2400.
Kant : Jaya = 2400 : 1400 => 12 : 7
Option C
Answer: C
Question: Two pipes A and B can fill a tank in 4 and 5 hours respectively. If they are turned up alternately for one hour each, the time taken to fill the tank is?
Options:
A)4 hrs 29 min
B)4 hrs 24 min
C)4 hrs 84 min
D)3 hrs 24 min
E)7 hrs 24 min
Rationale: 1/4 + 1/5 = 9/20
20/9 = 2 2/9
9/20 * 2 = 9/10 ---- 4 hours
WR = 1 - 9/10 = 1/10
1 h ---- 1/4
? ----- 1/10
2/5 * 60 = 24 = 4 hrs 24 min
Answer:B
Answer: B
Question: The sum of 3 consecutive numbers is definitely:
Options:
A)Positive
B)Divisible by 2.
C)Divisible by 3
D)Divisible by 4.
E)Divisible by 5
Rationale: If 1st term is x:
x+(x+1)+(x+2)=3x+3--->Always divisible by 3
If 2nd term is x:
(x-1)+x+(x+1)=3x--->Always divisible by 3
If 3rd term is x:
(x-2)+(x-1)+x=3x-3--->Always divisible by 3
Answer: C
Answer: C
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ?
Options:
A)5/5
B)5/9
C)5/3
D)5/8
E)5/1
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216
= 5/9.
Answer:B
Answer: B
Question: Which of the following options must be true given the equation p=-q^6
I. If q is negative then p is negative.
II. q is negative.
III. q is non-negative.
Options:
A)I only
B)II only
C)III only
D)II and III only
E)I and III only
Rationale: I. p is negative --> not necessarily true, if q=0 then p=-q^6=0;
II. q is non-negative. q can take ANY value: positive, negative, zero. We don't have any restrictions on its value;
III. If q is negative then p is negative. p is negative means that q is not zero.
Answer: A (I only).
Answer: A
Question: 5670/(28*13.5) = ?
Options:
A)11
B)15
C)16
D)19
E)18
Rationale: B
15
? = 5670/378 = 15
Answer: B
Question: What is next in series
J F M A M ? ?
Options:
A)MS
B)SS
C)FJ
D)JJ
E)DD
Rationale: D
JJ
Series is the name of months . January, February ...
Therefore June and July is the answer. Hence J J is correct option
Answer: D
Question: The HCF of two numbers is 62 and the other two factors of their LCM are 11 and 12. What is the largest number.
Options:
A)462
B)744
C)480
D)504
E)555
Rationale: Explanation:
HCF of the two numbers = 62
HCF will be always a factor of LCM
62 is factor of LCM
other two factors are 11 & 12
Then the numbers are (62 *11) and (62 x 12)
= 682 and 744
Answer: Option B
Answer: B
Question: A can finish a work in 18 days B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work?
Options:
A)5
B)5 1/2
C)6
D)8
E)9
Rationale: Explanation:
B's 10 day's work = 1/15 * 10 = 2/3
Remaining work = (1 - 2/3) = 1/3
Now, 1/18 work is done by A in 1 day.
1/3 work is done by A in (18 * 1/3) = 6 days.
ANSWER IS C
Answer: C
Question: A speaks truth in 75% case and B in 80% of the cases. In what percentage of cases are they likely to contradict each other, narrating the same incident?
Options:
A)40
B)23
C)35
D)60
E)21
Rationale: P( A)=75/100, P(B)=80/100
P( A’)=1/4
P(B’)=1/5
P( A and B contradict each other)=P(A).P(B’)+P(A’).P(B)
=35%
ANSWER C
Answer: C
Question: Arun went for a movie nine days ago. He goes to watch movies only on Thursdays. What day of the
week is today?
Options:
A)Wednesday
B)Saturday
C)Friday
D)Sunday
E)None of these
Rationale: Explanation :
Clearly it can be understood from the question that 9 days ago was a Thursday
Number of odd days in 9 days = 2 (As 9-7 = 2, reduced perfect multiple of 7 from total days)
Hence today = (Thursday + 2 odd days) = Saturday
Answer : Option B
Answer: B
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:
Options:
A)Rs. 2000
B)Rs. 10,000
C)Rs. 15,000
D)Rs. 20,000
E)Rs. 22,000
Rationale: Principal = Rs. 100 x 5400
--------------- = Rs. 15000.
12 x 3
Answer: Option C
Answer: C
Question: There are 11 teams in a soccer league and each team plays each of the other teams once. How many games will be played in total?
Options:
A)40
B)45
C)50
D)55
E)60
Rationale: 11C2=55
The answer is D.
Answer: D
Question: 200 is increased by 25%. Find the final number.
Options:
A)200
B)210
C)250
D)190
E)220
Rationale: ExplanationFinal number = Initial number + 25%(original number) = 200 + 25%(200) = 200 + 50 = 250.Answer C
Answer: C
Question: In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number T and the smallest possible number of students that could have taken both geometry and biology?
Options:
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 T of students that could have taken both geometry and biology, is 119.
Thus, the answer is 119 - 31 = 88.
Answer: D.
Answer: D
Question: Consider a quarter of a circle of radius 81. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.
Options:
A)86*(sqr2 -1)
B)88*(sqr3 -1)
C)4*(sqr7 - 1)
D)81* (sqr2 -1)
E)None of these
Rationale: I got 81/(sqr2 +1) and just forgot to multiply by (sqr2 -1).
Answer is D
Answer: D
Question: Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 6 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 6 minute mark.)
Options:
A)24
B)25
C)26
D)27
E)28
Rationale: 6 minutes is 360 seconds.
Lamp A and Lamp B will flash together every 24 seconds.
360/24=15.
In the time period, Lamp A and Lamp B will flash together 15 times.
Lamp A and Lamp C will flash together every 30 seconds.
360/30=12.
In the time period, Lamp A and Lamp C will flash together 12 times.
Lamp B and Lamp C will flash together every 40 seconds.
360/40=9.
In the time period, Lamp B and Lamp C will flash together 9 times.
All three lights will flash together every 2*2*2*3*5=120 seconds.
360/120=3.
We have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together.
The number of times that exactly two lights flash together is 15+12+9-9=27 times.
The answer is D.
Answer: D
Question: The price of a jacket is reduced by 20%. During a special sale the price of the jacket is reduced another 25%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
Options:
A)32.5
B)35
C)48.1
D)65
E)66.67
Rationale: 1) Let the price of jacket initially be $100.
2) Then it is decreased by 20% , therefore bringing down the price to $80.
3) Again it is further discounted by 25%, therefore bringing down the price to $60.
4) Now 60 has to be added byX %in order to equal the original price.
60 + ( X% ) 60 = 100.
Solving this eq for X, we get X = 66.67
Ans is E.
Answer: E
Question: If Rs.3250 be divided among Ram, Shyam and Mohan in the ratio of 1/2:1/3:1/4 then the share of each are?
Options:
A)Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.750
B)Ram = Rs.7500, Shyam = Rs.1000, Mohan = Rs.750
C)Ram = Rs.1500, Shyam = Rs.1000, Mohan = Rs.250
D)Ram = Rs.1500, Shyam = Rs.1080, Mohan = Rs.750
E)Ram = Rs.1500, Shyam = Rs.1002, Mohan = Rs.750
Rationale: 1/2:1/3:1/4 = 6:4:3
Ram = 6/13 * 3250 = 1500
Shyam = 4/13 * 3250 = 1000
Mohan = 3/13 * 3250 = 750
Answer:A
Answer: A
Question: If S = {50, 72, 108, 120, 205}, how much less is the mean of the numbers in S than the median of the numbers in S?
Options:
A)2
B)3
C)5
D)8
E)9
Rationale: Mean = (50 + 72 + 108 + 120 + 205)/5 = 111
Median = 108
Difference = 111-108 = 3
Option B
Answer: B
Question: A man can row 8 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man?
Options:
A)7.82 km
B)6 km
C)5.76 km
D)5.66 km
E)10 km
Rationale: M = 8
S = 1.2
DS = 9.2
US = 6.8
x/9.2 + x/6.8 = 1
x = 3.91
D = 3.91 * 2 = 7.82
ANSWER:A
Answer: A
Question: If X and Y are sets of integers, X # Y denotes the set of integers that belong to set X or set Y, but not both. If X consists of 16 integers, Y consists of 18 integers, and 6 of the integers are in both X and Y, then X # Y consists of how many integers?
Options:
A)6
B)16
C)22
D)30
E)174
Rationale: The number of integers that belong to set X ONLY is 16-6=10;
The number of integers that belong to set Y ONLY is 18-6=12;
The number of integers that belong to set X or set Y, but not both is 10+12=22.
Answer: C
Answer: C
Question: The area of a rectangle is x2 + 4x -12. What are the dimensions of the rectangle (length and width)?
Options:
A)x + 6 , x + -2
B)x + 7 , x + -2
C)x + 8 , x + -2
D)x + 9 , x + -2
E)none
Rationale: Solution
The main idea is to factor x2 + 4x -12
Since -12 = -2 × 6 and -2 + 6 = 4
x2 + 4x -12 = ( x + -2) × ( x + 6)
Since the length is usually longer, lenth = x + 6 and width = x + -2
Answer A
Answer: A
Question: Pipes A and B can fill a tank in 8 and 24 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
Options:
A)12 hr
B)28 hr
C)23 hr
D)24 hr
E)24 hr
Rationale: Explanation :
Part filled by pipe A in 1 minute = 1/8
Part filled by pipe B in 1 minute = 1/24
Part emptied by pipe C in 1 minute = 1/12
Net part filled by pipe A, pipe B and pipe C in 1 minute = 1/8+1/24−1/12=2/24=1/12
i.e, the tank will be filled in 12 minutes
Answer is A
Answer: A
Question: A straight pipe 3 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?
Options:
A) 1/6 and 1/4 only
B) 1/4 and 1/3 only
C) 1/6, 1/4, and 1/3
D) 1/12, 1/6 and 1/4
E) 1/12, 1/6, and 1/3
Rationale: Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4.
In this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red thirds of the length).
Distinct lengths would be: 3=3/12=1/4, 4-3=1=1/3and 6-4=2=2/12=1/6meters long pieces.
Answer: C.
Answer: C
Question: 4211.01 + 22.261 - ? = 2645.759
Options:
A)1587.512
B)1586.532
C)1588.021
D)1586.422
E)None of these
Rationale: Explanation :
Required Value = 4211.01 + 22.261 - 2645.759 = 1587.512. Answer : Option A
Answer: A
Question: A number when divided by 243 gives a remainder 26, what remainder will be obtained by dividing the same number 14?
Options:
A)7
B)6
C)9
D)2
E)3
Rationale: Explanation:
243 + 26 = 269/14 = 3 (Remainder)
Answer: E
Answer: E
Question: What percent of a day is 4 hours?
Options:
A)12%
B)12.5%
C)13%
D)11.3%
E)None of these
Rationale: Explanation :
Solution: required percentage = (4/100 * 24) = 12.5%
Answer : B
Answer: B
Question: A can do a piece of work n 7 days of 9 hours each and B alone can do it in 6 days of 7 hours each. How long will they take to do it working together 8 2/5 hours a day?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: A can complete the work in (7*9) = 63 days
B can complete the work in (6*7) = 42 days
--> A’s one hour’s work = 1/63 and B’s one hour work = 1/42.
(A+B)’s one hour work = 1/63+1/42 = 5/126
Therefore, Both can finish the work in 126/5 hours.
Number of days of 8 2/5 hours each = (126*5/(5*42)) = 3 day
Answer : A.
Answer: A