mathewhe/aqua_rat huggingface dataset:
Question: The weight of a hollow sphere is directly dependent on its surface area. The surface area of a sphere is 4π·R^2, where R is the radius of the sphere. If a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams, a hollow sphere of radius 0.3 cm made of the same metal would weigh how many Q grams?
(A) Q= 16
(B) Q=32
(C) 64
(D) 128
(E) 512
Rationale: Weight directly proportional to 4 pi r^2
Now, 4pi is constant, so, weight is directly proportional to r^2.
When radius = 0.15, weight = 8, so (0.15) ^ 2 proportional to 8;
(0.15)^2 * 4 proportional to 8*4, solving further
(0.15)^2 * 2 ^2 = (0.15*2)^2 = 0.3 ^ 2; so answer = 32 (B)
Answer: (B) Q=32
Question: Two trains running in the same direction with a speed of 60kph and 50kph having lengths of 200m each. How long it will take the trains to completely pass each other(in seconds)?
(A) 13.09
(B) 32.17
(C) 54.9
(D) 112.98
(E) 143.88
Rationale: Relative speed of trains with respect to each other=60-50=10kph=2.78m/s
Distance need to be covered=200+200=400
Time taken to pass each other=400/2.78=143.88s
Answer: E
Answer: (E) 143.88
Question: 6^9 - 6^2 is approximation of which of the following?
(A) 9^7
(B) 9^8
(C) 6^9
(D) 9^11
(E) 9^10
Rationale: => Since 9^2 is a small number compared to 9^9, it can be disregarded. Thus, 6^9-6^2=6^9 is derived and the answer is C.
Answer: (C) 6^9
Question: A sum is divided among B, C and D in such a way that for each rupee B gets, C gets 150 paisa and D gets 50 paisa. If the share of C is RS. 40, what is the total amount?
(A) 70
(B) 75
(C) 80
(D) 85
(E) 90
Rationale: b:c:d = 100:150:100
20:30:10
30 --- 40
60 --- ? => 80
Answer:C
Answer: (C) 80
Question: How many integers from 100 to 800, inclusive, remains the value unchanged when the digits were reversed?
(A)  50
(B)  60
(C)  80
(D) 70
(E)  90
Rationale: question is asking for palindrome
first digit possibilities - 1 through 7 = 7
8 is not possible here because it would result in a number greater than 8 (i.e 808 , 818..)
second digit possibilities - 0 though 9 = 10
third digit is same as first digit
=>total possible number meeting the given conditions = 7 *10 = 70
Answer is D.
Answer: (D) 70
Question: The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:
(A) 380
(B) 395
(C) 400
(D) 425
(E) Either (a) or (b)
Rationale: Let the numbers be x and y.
Then, xy = 9375 and	x	= 15.
y
xy	=	9375
(x/y)	15
y2 = 625.
y = 25.
x = 15y = (15 x 25) = 375.
Sum of the numbers = x + y = 375 + 25 = 400.
ANSWER : C
Answer: (C) 400
Question: Set A = {1, 2, 3, 4, 5, 6, y}
Which of the following possible values for y would cause Set A to have the smallest standard deviation?
(A) 1
(B) 2.5
(C) 3
(D) 3.5
(E) 7
Rationale: SD is minimum or least when the number is closest to the mean of the existing numbers
Calculating mean of the rest of the numbers gives mean = (approx)3.6
So the new number should be near to the mean and only number closest to the mean is 3.5
Answer: Option D
Answer: (D) 3.5
Question: 35% of the employees of a company are men. 60% of the men in the company speak French and 40% of the employees of the company speak French. What is % of the women in the company who do not speak French?
(A) 4%
(B) 10%
(C) 96%
(D) 90.12%
(E) 70.77%
Rationale: No of employees=100(say)
Men=35
Women=65
Men speaking french=0.6*35=21
Employees speaking french=0.4*100=40
Therefore women speaking French=40-21=19
And women not speaking French=65-19=46
% of women speaking French=46/65*100=70.77%
Answer E
Answer: (E) 70.77%
Question: A builder decided to build a farm house in 40days. He employed 100men in the beginning and 100 more after 35 days and completed the construction in stipulated time. If he had not employed the additional men , how many days behind schedule would it have been finished?
(A) 5
(B) 7
(C) 10
(D) 15
(E) 12
Rationale: 200 men do the rest of the work in 40-35 = 5days
100 men can do the rest of the work in 5*200/100 = 10days
Required number of days = 10-5 = 5 days
Answer is A
Answer: (A) 5
Question: In how many ways can 5 boys and2 girls be arranged at a table if 2 girls are never together?
(A) 257
(B) 287
(C) 290
(D) 400
(E) 480
Rationale: Total ways of arranging 7 person in a circle = 6! = 720 ways
If we consider two women as one, then we have 5+1=6 persons. Arranging these six persons in circle will take = 5! = 120 ways
And two women can arrange themselves in 2! ways
Total ways in which two women sit together in circle = 5!*2! = 240 ways
Total ways in which two women doesn’t sit together in circle = 6! - 5!*2! = 720 - 240 = 480 ways
E
Answer: (E) 480
Question: Walking 7/6 of his usual rate, a boy reaches his school 5 min early. Find his usual time to reach the school?
(A) 22
(B) 28
(C) 99
(D) 35
(E) 66
Rationale: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
5 --------- ?
= 35 m
Answer:D
Answer: (D) 35
Question: 40, 45, 50, 55, 60, 75, 75, 90, 100, 100.
The list above shows the scores of 10 schoolchildren on a certain test. If the standard deviation of the 10 scores is 21.2, rounded to the nearest tenth, how many of the scores are more than 1 standard deviation below the mean of the 10 scores?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The average of {40, 45, 50, 55, 60, 75, 75, 90, 100, 100} is 69.
1 standard deviation below the mean is 69 - 21.2 = 47.8. Hence there are two scores (40 and 45) more than 1 standard deviation below the mean.
Answer B.
Answer: (B) 2
Question: How many diagonals does a polygon with 15 sides have, if one of its vertices does not connect to any diagonal?
(A) 80
(B) 90
(C) 77
(D) 88
(E) 99
Rationale: If I calculate it using the formulae, #diagonals = n (n-3)/2Each vertex sends of n-3 diagonals
n= 15-1 then 14*(14-3)/2 = 77
Correct Option:C
Answer: (C) 77
Question: What is the least value of x. So that 1894x is divisible by 3?
(A) 2
(B) 5
(C) 1
(D) 6
(E) 7
Rationale: The sum of the digits of the number is divisible by 3, then the number is divisible by3.
1+ 8 + 9 + 4+ x= 22 +x
Least value of X may be 2
Therefore 22 +2 = 24 is divisible by 3.
A
Answer: (A) 2
Question: Which of the following number is divisible by 24 ?
(A) 31214
(B) 61212
(C) 512216
(D) 3125832
(E) None of these
Rationale: Explanation :
24 = 3 × 8 where 3 and 8 are co-prime numbers. 3 and 8 are also factors of 24. Hence
Hence if a number is divisible by 3, and 8, the number will be divisible by their product 24 also.
If a number is not divisible by 3 or 8, it is not divisible by 24
You must learn Divisibility Rules to say whether a given number is divisible by another number
without actually performing the division.
31214 is not divisible by 3 and 8 => 31214 is not divisible 24
61212 is not divisible by 8 though it is divisible by 3 => 61212 is not divisible 24
512216 is not divisible by 3 though it is divisible by 8 => 512216 is not divisible 24
3125832 is divisible by 3 and 8 => 3125832 is divisible 24. Answer : Option D
Answer: (D) 3125832
Question: Three positive integers a, b, and c are such that their average is 22 and a ≤ b ≤ c. If the median is (a + 13), what is the least possible value of c?
(A) 22
(B) 25
(C) 26
(D) 27
(E) 29
Rationale: Solution
Given Data
3 positive integers
Average of a, b, and c = 22
So, a+b+c3a+b+c3 = 66 or a + b + c = 66
a ≤ b ≤ c
Median = (a + 13)
Median of these 3 numbers a, b, and c is ‘b’ because a ≤ b ≤ c
Therefore, b = a + 13
Objective To find the least value of 'c'
Theoretically, the least value of c is when c = b.
Therefore, a + (a + 13) + (a + 13) = 66 (b and c are equal and b, the median, is a + 13)
Or 3a = 40 or a = 13.33
So, b = c = 10+ 13.33 = 23.33
However, we know that these numbers are all integers.
Therefore, a, b, and c cannot take these values.
So, the least value for c with this constraint is NOT likely to be when c = b
Let us increment c by 1. Let c = (b + 1)
In this scenario, a + (a + 13) + (a + 14) = 66
Or 3a = 39 or a=13 The value of the numbers is an integer
If a = 13, b = 26 and c = 27
The least value for c that satisfies all these conditions is 27.
Correct answer is choice D.
Answer: (D) 27
Question: If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. c-a=2
II. a-c is positive integer
III. (a+b+c)/3 is an integer
(A) I
(B) II
(C) I and III
(D) II and III
(E) I, II and III
Rationale: If a, b, c are consequitive positive integers and a<b<c, which of the following must be true?
1. c-a=2
2. abc is an even integer
3. (a+b+c) /3 is an integer
1.
a=a
b=a+1
c=a+2
c-a=a+2-a=2.
Correct
2. a-c is negative because a<c - false
3. (a+b+c) /3 is an integer
Again;
a=a
b=a+1
c=a+2
a+b+c=(a+a+1+a+2)=3a+3
3a is always divisible by 3
3 is divisible by 3.
Thus3a+3is also divisible by 3.
Rule:
if integer x is divisible by n
and
integer y is divisible by n
then; x+y must be divisible by n
Correct.
Ans :C
Answer: (C) I and III
Question: 9.4 , 9.9 , 9.9 , 9.9 , 10.0 , 10.2 , 10.2 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.3 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?
(A) 90%
(B) 85%
(C) 80%
(D) 75%
(E) 70%
Rationale: D. 75%
Answer: (D) 75%
Question: what is the least number by which 15,625 must be divided to get a number perfect square
(A) 21
(B) 25
(C) 24
(D) 40
(E) 45
Rationale: 15,625/25=625
625=(25)^2
Ans-25
ANSWER:B
Answer: (B) 25
Question: The ratio of the adjacent angles of a parallelogram is 5 : 13. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?
(A) 168°
(B) 134°
(C) 156°
(D) 224°
(E) None of these
Rationale: The measures of the adjacent angles of a parallelogram add up to be 180°
Given
So, 5x + 13x = 180°
Or, 18x = 180°
Or, x = 10°
Hence the angles of the parallelogram are 50° and 130°
Further it is given
We know sum of all the four angles of a quadrilateral is 360°
So, 5y + 6y + 7y + 12 y = 360°
Or, 5y + 6y + 7y + 12 y = 360°
Or, 30y = 360°
Or, y = 12°
Hence the angles of the quadrilateral are 60° , 72, 84° and 144°
Will be 50° + 84° = 134°
Answer : B
Answer: (B) 134°
Question: A candidate got 31% of the votes polled and he lost to his rival by 2451 votes. How many votes were cast?
(A) 6150
(B) 6250
(C) 6350
(D) 6450
(E) 6550
Rationale: Let x be the total number of votes.
0.31x + 2451 = 0.69x
0.38x = 2451
x = 2451/0.38 = 6450
The answer is D.
Answer: (D) 6450
Question: Calculate the area of a triangle, if the sides are 30 cm, 21 cm and 10 cm, what is its area?
(A) 145 cm2
(B) 105 cm2
(C) 125 cm2
(D) 115 cm2
(E) 135 cm2
Rationale: The triangle with sides 30 cm, 21 cm and 10 cm is right angled, where the hypotenuse is 30 cm.
Area of the triangle = 1/2 * 21 * 10 = 105 cm2
Answer: B
Answer: (B) 105 cm2
Question: total 48 matches are conducted in Knockout match type. How many players will be participated in that tournament?
(A) 48
(B) 47
(C) 40
(D) 42
(E) 47
Rationale: 47 players
ANSWER:E
Answer: (E) 47
Question: A will was written such that an estate would be divided among five beneficiaries with the remainder donated to charity. One stipulation in the will is that no one beneficiary can receive an amount within 10% of another's amount. If one of the beneficiaries received $10,000, what is the smallest possible range between the highest and lowest amounts (rounded to the nearest dollar) among the five beneficiaries?
(A) $3996
(B) $3395
(C) $2892
(D) $3736
(E) $23436
Rationale: 1st - 10,000.
2nd - 0.9*10,000 = 9000
3rd - 0.9*9,000 = 8,100
4th - 0.9*8,100 = ~7,290
5th - 0.9*7,290 = ~6,561
Range = 10,000 - 6,561 = 3,439.
Answer: B.
Answer: (B) $3395
Question: Find the average of all prime numbers between 30 and 50?
(A) 39.8
(B) 31.2
(C) 12.4
(D) 17.9
(E) 20.9
Rationale: there are five prime numbers between 30 and 50.
They are 31,37,41,43 and 47.
Therefore the required average=(31+37+41+43+47)/5 =199/5 =39.8.
Option A
Answer: (A) 39.8
Question: A train 60 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 7
(B) 6
(C) 8
(D) 2
(E) 3
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 60 * 3/55
= 3 sec.
Answer E
Answer: (E) 3
Question: a pizza which is thin is cut into 'x' pieces by 4 straight lines then the lowest possible value of x is?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 4 parallel lines will give minimum number of pieces.
5 pieces.
ANSWER:C
Answer: (C) 5
Question: A one-foot stick is marked in 1/3 and 1/5 portion. How many total markings will there be, including the end points?
(A) 10
(B) 7
(C) 6
(D) 5
(E) 8
Rationale: LCM of 15 = 15
1/3 marking are (Table of 5) 0...... 5 ......10..... 15
(Total = 4)
1/5 marking are (Table of 3) 0 ....... 3 ...... 6...... 9........ 12......15 (Total = 6)
Overlapping markings are 0 ........ 15 (Total = 2)
Total markings = 4+6-2 = 8
Answer = E
Answer: (E) 8
Question: A person takes 5hrs 45 min in walking to a place and riding back. He would have gained 3hrs by riding both ways. The time he would take to walk both ways is?
(A) 5 hours 45 min
(B) 5 hours 55 min
(C) 6 hours 45 min
(D) 8 hours 45 min
(E) 9 hours
Rationale: ----------------------------------------------------------------
Solution 1
----------------------------------------------------------------
Given that time taken for riding both ways will be 3 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding one way = time needed for waking one way - 3 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 3 hours = 8 hours 45 min
D
Answer: (D) 8 hours 45 min
Question: Find the compound interest and the amount on Rs.8000 at 5% per annum for 3 years when C.I is reckoned yearly?
(A) 1261
(B) 1228
(C) 2773
(D) 288
(E) 2774
Rationale: A = 8000(21/20)3
= 9261
= 8000
---------
1261.Answer: A
Answer: (A) 1261
Question: A survey was sent to 70 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey?
(A) 2%
(B) 6%
(C) 4%
(D) 28%
(E) 63%
Rationale: case 1: (7/70)=x/100
x=10%
case 2: (9/63)=y/100
y=14%
So percent increase is =(y-x)=(14-10)%=4%
Answer is C
Answer: (C) 4%
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.
(A) 125/167
(B) 125/186
(C) 125/126
(D) 125/186
(E) 125/128
Rationale: Required probability
= 1 - 1/126
= 125/126
Answer: C
Answer: (C) 125/126
Question: S is a set containing 8 different positive odd primes. T is a set containing 7 different numbers, all of which are members of S. Which of the following statements CANNOT be true?
(A)  The median of S is prime.
(B)  The median of T is prime
(C)  The median of S is equal to the median of T.
(D)  The sum of the terms in S is prime.
(E)  The sum of the terms in T is prime.
Rationale: Here is my explanation. The question states:S is a set containing 9 different positive odd primes. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?
(A) The median of S is prime.
Thismust be true. If there are an odd number of members of a set, then the median is a member of the set: it's the middle number, when all the numbers are ranked from smallest to biggest. Every number in S is a positive odd prime, so the median is one of them, and is prime.
(B) The median of T is prime.
Thismay or may not be true. If a set has an even number of members, the median is average of the two numbers in the middle, when ranked from smallest to biggest. The average of two odd numberscould beeven (average of 71 and 73 is 72), and hence not prime, or itcould beodd (the average of 71 and 79 is 75). For particularly well chosen odd numbers, the average can be not only odd but also prime -- for example, the average of 89 and 113 is 101, another prime number. If the two middle numbers of T were 89 and 113, the median would be 101, a prime number.
(C) The median of S is equal to the median of T.
Under most configurations for S and T, this wouldn't happen. If you weren't trying to make it happen, it would be unlikely to happen by chance. BUT, if the number dropped going from from S to T was the median of S (say, 101), and if the two middle numbers of T happen to have an average of that number that was dropped (for example, if the two numbers were 89 and 113), then the medians would be equal. In other words, the three middle numbers of S would have to be {. . ., 89, 101, 133, . . .}, and when 101 is dropped in going to T, the median of two would be the average of 89113, which happens to be 101. It's an exceptional case, but itcouldbe true.
(D) The sum of the terms in S is prime.
Thismay or may not be true. The sum of 9 odd numbermustbe an odd number. That odd numbercould beprime. For example, the sum of the first nine odd prime numbers {3, 5, 11, 13, 17, 19, 23, 29} is 127, which is prime. If you drop 3 and include the next prime, 31, the set {5, 11, 13, 17, 19, 23, 29, 31} has a sum of 155, which is clearly not prime.
(E) The sum of the terms in T is prime.
Thismust be false. The sum of eight odd numbers must be an even number. Only 2 is prime, and all other even numbers are not. Therefore, the sum of eight odd prime numbers will be an even number bigger than two, and absolutely cannot be prime.
D
Answer: (D)  The sum of the terms in S is prime.
Question: Total number of students in a class is 95. if the total number of girls in the class is 45, then the ratio of total number if boys to total number girls is
(A) 9:10
(B) 7:8
(C) 10:9
(D) 9:11
(E) 8:12
Rationale: Let the total number of boys in the class be x.
Then, according to the question,
x + 45 = 95
x = 95 - 45 = 50
Hence, the required ratio of total number of boys to total number of girls = B:G = 50:45 = 10:9
ANSWER :C
Answer: (C) 10:9
Question: If there are 210 workers in a factory, and on a certain day, 198 were present. Calculate the percentage that showed up for work? (round to the nearest tenth).
(A) 94.3%
(B) 95.3%
(C) 93.3%
(D) 92.3%
(E) 91.3%
Rationale: 198/210*100=94.28
94.3%
correct answer A
Answer: (A) 94.3%
Question: Health insurance Plan P requires the insured person to pay $500 but then the insurance pays 70% of the cost over $500. Plan Q requires the insured to pay the initial $400, but then pays 60% of the cost over $400. Which of the following is a cost level for which both insurance plans pay out the same amount?
(A) $700
(B) $800
(C) $900
(D) $1000
(E) $1100
Rationale: 0.7(x-500)=0.6(x-400)
0.1x=350-240
x=1100
The answer is E.
Answer: (E) $1100
Question: A Pentagon marked P,Q,R,S and T on its five sides. five colors, black, brown,blue,violet and white are used to paint the five sides of the pentagon. If the adjacent faces are painted with the different colors, in how many ways can the pentagon be painted?
(A) 5
(B) 9
(C) 12
(D) 6
(E) 3
Rationale: If the base of the pentagon is Black, then in order the adjacent faces to be painted with the different colors. 4 side faces can be painted in Brown-White-Violet-Blue Brown-White-Violet-Blue OR White-Blue-Violet-Brown White-Blue-Violet-Brown .
But we can have the base painted in either of the four colors, thus the total number of ways to paint the Pentagon is 5*1=5.
Answer: A.
Answer: (A) 5
Question: If goods be purchased for Rs.840 and one-fourth be sold at a loss of 20% at what gain percent should the remainder be sold so as to gain 20% on the whole transaction?
(A) 733 1/3%
(B) 163 1/3%
(C) 33 1/3%
(D) 213 1/3%
(E) 133 1/3%
Rationale: Explanation:
1/4 CP = 210 SP = 21*(80/100) = 168
SP = 840*(120/100) = 1008
1008 - 168 = 840
3/4 SP = 630
Gain = 210
630 --- 210
100 --- ? => 33 1/3%
Answer:C
Answer: (C) 33 1/3%
Question: Tom opened a shop investing Rs.30000. Jose joined him 2 months later, investing Rs.45000. They earned a profit of Rs.54000 after completion of one year. What will be Jose's share of profit?
(A) 20000
(B) 21000
(C) 22000
(D) 25000
(E) 30000
Rationale: SoL = ~s- So Anju’s share = [5/9] x 54000 = 30000
E
Answer: (E) 30000
Question: Convert the 13/36 m/s into kilometers per hour?
(A) 1.6kmph
(B) 2.3 kmph
(C) 1.3 kmph
(D) 1.7 kmph
(E) 3.3 kmph
Rationale: 13/36 m/s = 13/36 * 18/5 = 13/10 = 1.3 kmph.Answer: C
Answer: (C) 1.3 kmph
Question: There is a sequence such that each term is positive integer and each digit of the terms in the sequence has 3 to be ordered, what is the value K of 100th term?
(A) 126
(B) 192
(C) 232
(D) 252
(E) 342
Rationale: (1~99) 19, (100~199)  19, (200~299) 19. The 100th term should be 100-(19+19+19)=43th number. Hence, the correct answer K is 342. The correct answer is E.
Answer: (E) 342
Question: In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 12,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: this is equivalent to :-
2x * 4y * 5z = 12000
y = z (given)
2x * 4y * 5y = 12000
2x * y^2 = 12000/20
2x * y^2 = 600
now from options given we will figure out which number will divide 800 and gives us a perfect square :-
which gives us x = 3 as
2* 3 * y^2 =600
y^2 = 100
y =10
Number of red chips = 3 hence C
Answer: (C) 3
Question: A large petrol tank has two inlet tubes (a large one and a small one) and one outlet tube. It takes 3 hours to fill the tank with the large inlet tube. On the other hand, it takes 6 hours to fill the tank with the small inlet tube. The outlet tube allows the full tank to be emptied in 9 hours.
What fraction of the tank (initially empty) will be filled in 0.64 hours if all three tubes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).
(A) 1
(B) 3
(C) 2
(D) 5
(E) 6
Rationale: A
In one hour,
Soln 1:
the large inlet tube fills 1 / 3 of the tank;
the small inlet tube fills 1 / 6 of the tank;
the outlet tube empties 1 / 9 of the tank; and therefore
all three tubes together fill [ (1 / 3) + (1 / 6) − (1 / 9) ] of the tank.
Fraction of the tank that will be filled in 0.64 hours =
0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.
Soln 2:
Let V be the total volume of the tank. From equation (1),
Flow Rate (large inlet tube) = V / 3
Flow Rate (small inlet tube) = V / 6
Flow Rate (outlet tube) = V / 9.
Substituting in equation (2),
Rate of Accumulation in tank = (V / 3) + (V / 6) − (V / 9).
Using the above result in equation (1),
Time required to fill the complete tank = V / [ (V / 3) + (V / 6) − (V / 9) ].
Note that V cancels out on simplifying the above expression.
Fraction of the tank that will be filled in 0.64 hours =
0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.
Answer: (A) 1
Question: A train passes a station platform in 36 sec and a man standing on the platform in 24 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
(A) 288
(B) 180
(C) 881
(D) 1277
(E) 121
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 24 = 360 m.
Let the length of the platform be x m . Then,
(x + 360)/36 = 15 => x = 180 m.
Answer: B
Answer: (B) 180
Question: Find the value of (950+ 220/900) × 900
(A) 854542
(B) 856945
(C) 758965
(D) 855220
(E) 826450
Rationale: (855000+220)/900 * 900 = 855000+220 = 855220
Answer : D
Answer: (D) 855220
Question: Find the greatest number that will divided 43,91 and 183 so as to leave the same remainder in each case
(A) 4
(B) 7
(C) 9
(D) 13
(E) 15
Rationale: Solution
Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F. of 48, 92 and 140 = 4. Answer A
Answer: (A) 4