mathewhe/aqua_rat huggingface dataset:
Question: Find the unit's digit in 264^102 +264^103
(A) zero 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) zero 0
Question: If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is:
(A) 1:1
(B) 1:9
(C) 1:2
(D) 1:5
(E) 1:6
Rationale: Explanation:
A square and a rhombus on the same base are equal in area
Answer: A) 1:1
Answer: (A) 1:1
Question: You had a math quiz at class. The quiz had 5 questions; three of them have 3 marks each, and the other two have 4 marks each. You managed to correctly solve 2 questions with the 3 marks and one question with the 4 marks. What is the percentage of the marks that you got in this quiz?
(A) 48.8%
(B) 58.8%
(C) 38.8%
(D) 28.8%
(E) None
Rationale: Solution:
The total marks = 3x3 + 2x4 = 17 marks
Marks obtained = 2x3 + 4 = 10 marks
Percent of marks obtained = 10/17 x 100 = 58.8%
Answer B
Answer: (B) 58.8%
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 92.16, the number of the member is the group is:
(A) 57
(B) 67
(C) 77
(D) 87
(E) 96
Rationale: Explanation:
Money collected = (92.16 x 100) paise = 9216 paise.
∴ Number of members = √(9216) = 96.
Answer: E
Answer: (E) 96
Question: There are 660 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
(A) 75
(B) 110
(C) 125
(D) 175
(E) 225
Rationale: female = x
Male = 660-x
x/2 + 660-x/4 = 1/3* (660)= 220
x= 220
x/2 = 110 is supposed to be the answer
M is missing something
Correct Option B
Answer: (B) 110
Question: For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.367] = 1 and [1.988] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?
(A) 0
(B) 1
(C) 27
(D) 54
(E) Cannot be determined
Rationale: It cannot be determined.As we do not know the actual value of K.
however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer
K=[lCM of 80 and 45] * (any integer)
for value of k(60) * any integer unit value will be always zero .
A
Answer: (A) 0
Question: Isabelle decided to go on an 8 mile run in which she ran from home to the school four miles away and then back the same route. The first four miles took her 40 minutes to complete, and the returning four miles took her 24 mins to complete. What was the wind speed in mph?
(A) 1 mph
(B) 2 mph
(C) 3 mph
(D) 4 mph
(E) 5 mph
Rationale: Explanation:
Speed from home to school: (4/40) X 60 = 6 mph
Speed from school to home: (4/24) X 60 = 10 mph
Wind speed: 1/2 (10 - 6) = 4/2= 2 mph
Answer: Option B
Answer: (B) 2 mph
Question: Four of the following five numbered parts (a), (b), (c), (d) and (e) are equal. The number of the part which is not equal to the other four parts is the answer.
(A) 115 × 8 ÷ 10 + 8
(B) 425 ÷ 17 × 4
(C) 36 × 5 ÷ 6 + 17 × 4
(D) 2(6) + √256 + 20
(E) 35 × 12 ÷ 14 + 14 × 5
Rationale: All others are equal to 100. But option (c) gives a value equal to 98.
Answer C
Answer: (C) 36 × 5 ÷ 6 + 17 × 4
Question: If m and n are positive integers of W such that m is a factor of n, how many positive multiples of m are less than or equal to 2n ?
(A) 2m/n + 1
(B) 2n/m + 1
(C) 2n/(m+1)
(D) 2m/n
(E) 2n/m
Rationale: Lets say N=10, M=5
2N = 20. so the answer should be 4 (20/5)
lets try to plug in the answers:
A-not an integer
B-not an integer
C-not an integer
D-1 (not the answer)
E-4 - the answer. (the only one).
I would choose E.
Method 2
N=M*A (A is an integer)
So - A=N/M
therefore in 2N A will be 2N/M
Again - Answer is E.
Answer: (E) 2n/m
Question: A rectangular Box 60 m long and 40 m wide has two concrete crossroads running in the middle of the box and rest of the box has been used as a lawn. The area of the lawn is 2109 sq. m. what is the width of the road?
(A) 3 m
(B) 4 m
(C) 5 m
(D) 6 m
(E) 2 m
Rationale: Total area of cross roads=60x+40x−x2
But total area of the cross roads =291 m2
Hence,
60x+40x−x2=291
⇒100x−x2=291
⇒x2−100x+291=0
⇒(x−97)(x−3)=0
⇒x=3
ANSWER:A
Answer: (A) 3 m
Question: Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute).
(A) 3 hours 5 minutes
(B) 4 hours 5 minutes
(C) 5 hours 5 minutes
(D) 6 hours 5 minutes
(E) 7 hours 5 minutes
Rationale: In 1 hour pump A can fill 1/5 of a tank and pump B can fill 1/8 of the same tank. So in 1 hour the two pumps working together can fill
1/5 + 1/8 = 13 / 40 of a tank
Since the rate of the two pumps working together is 13/40, the time t needed to fill the tank by the two pumps is found by solving
(13/40) t = 1
t = 40 / 13 = 39/13 + 1/13 hours
= 3 hours and (1/13)*60 minutes
= 3 hours 5 minutes (rounded to the nearest minute)
correct answer A
Answer: (A) 3 hours 5 minutes
Question: A clock store sold a certain clock to a collector for 35 percent more than the store had originally paid for the clock. When the collector tried to resell the clock to the store, the store bought it back at 15 percent of what the collector had paid. The shop then sold the clock again at a profit of 65 percent on its buy-back price. If the difference between the clock's original cost to the shop and the clock's buy-back price was $105, for how much did the shop sell the clock the second time?
(A) $75.44
(B) $88.23
(C) $64.77
(D) $54.32
(E) $43.99
Rationale: Now, in the question above, lets say the original cost of the clock to store was C$ and then it sold the same to the collector at 35% profit.
This means the clocks' selling price was C (1.35) and this becomes cost price for the collector.
Now, when the collector tries to sell the same clock to the store, the store buys it for 15% the price at which the collector bought it.
Thus, you get = 1.35*0.15*C = 0.2025 C
Furthermore, the store sells the clock for the second time for 65% profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy-back * 1.65 = 1.65 * 0.2025 C
Finally given that C - 0.2025 C = 105 ----> C = 131.66$
Thus, the cost of the clock the second time around = 1.65*0.2025 C = 1.65 * 0.2025 * 131.66 = 43.99$. Hence E is the correct answer.
Answer: (E) $43.99
Question: The area of an isosceles trapezoid with sides of length 5 and bases of length 6 and 12 is?
(A) 44
(B) 42
(C) 40
(D) 38
(E) 36
Rationale: Isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side, the longer side with side 12 will be divided into 3 parts= 6, 3 and 3 (Making one square and two right triangles)
For the right triangle, height will be= (5^2-3^2)^1/2= 4
And the area of trapezoid = 1/2 (B1+B2)H= 1/2*18*4= 36
E
Answer: (E) 36
Question: Two tains of equal lengths take 10 seconds and 20 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
(A) 12
(B) 14
(C) 16
(D) 20
(E) 13.3
Rationale: Sol.
Speed of the first train = [120 / 10] m/sec = 12 m/sec.
Speed of the second train = [120 / 20] m/sec = 6 m/sec.
Relative speed = (12 + 6) = m/sec = 18 m/sec.
∴ Required time = (120 + 120) / 18 secc = 13.3 sec.
Answer E
Answer: (E) 13.3
Question: The probability that a computer company will get a computer hardware contract is 3/4 and the probability that it will not get a software contract is 5/9. If the probability of getting at least one contract is 4/5, what is the probability that it will get both the contracts?
(A) 11/30
(B) 31/60
(C) 41/80
(D) 51/120
(E) 71/180
Rationale: Let, A ≡ event of getting hardware contract
B ≡ event of getting software contract
AB ≡ event of getting both hardware and software contract.
P(A) = 3/4, P(~B) =5/9
=> P(B) = 1- (5/9) = 4/9.
A and B are not mutually exclusive events but independent events. So,
P(at least one of A and B ) = P(A) + P(B) - P(AB).
=> 4/5 = (3/4) + (4/9) - P(AB).
=> P(AB) = 71/180.
Hence, the required probability is 71/180.
The answer is E.
Answer: (E) 71/180
Question: Tough and Tricky questions: Word Problems.
AK Car Company wants to manufacture a new car known as Model X, and it is trying to determine how many cars it needs to sell in order to make an annual profit of $30,500,000. The annual fixed costs for Model X total $50,200,000. In addition, each Model X car has an average cost of $5,000 per vehicle to manufacture. If the Company forecasts it will sell 20,000 Model X cars this year, at what price must the Company sell the car to achieve the desired annual profit?
(A) $4,035
(B) $4,036
(C) $9,035
(D) $16,140
(E) $36,140
Rationale: The AK company plans to make a profit of $30,500,000 and it needs to earn the fixed costs of $50,200,000, so it needs to earn $80,700,000 on top of the costs for the production of the 20,000 cars.
Therefore, price of each car needs to be the unit costs plus $80,700,000/20,000. After removing the 0's, we end with the unit costs plus $8,070/2, which is $5,000 plus $4,035. Therefore, Answer C is correct.
Answer: (C) $9,035
Question: How many consonants are present between the first and third vowel in the sequence of English alphabet ?
(A) 12
(B) 13
(C) 6
(D) 10
(E) None of these
Rationale: Explanation:
Ref : A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
The first and third vowels are A and I respectively. There are 7 letters between A and I; out of which 'E' is a vowel. Thus, there are 6 consonants between A and I.
ANSWER C
Answer: (C) 6
Question: In how many ways the word "PACK" can be arranged?
(A) 14
(B) 24
(C) 28
(D) None
(E) Cannot be determined
Rationale: Explanation :
The required number of ways = 4!
= 24
Answer : B
Answer: (B) 24
Question: Andrew travelling to 7 cities. Gasoline prices varied from city to city. $1.75, $1.61, $1.79, $2.11, $1.96, $2.09, $1.82. What is the median gasoline price?
(A) $1
(B) $1.82
(C) $1.92
(D) $2.13
(E) $2.15
Rationale: Ordering the data from least to greatest, we get:
$1.61, $1.75, $1.79, $1.82, $1.96, $2.09, $2.11
The median gasoline price is $1.82. (There were 3 states with higher gasoline prices and 3 with lower prices.)
B
Answer: (B) $1.82
Question: A cat leaps 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?
(A) 11:15
(B) 15:11
(C) 16:15
(D) 15:16
(E) 11:16
Rationale: Solution: Given;
3dog = 4 cat;
Or, dog/cat = 4/3;
Let cat's 1 leap = 3 meter and dogs 1 leap = 4 meter.
Then, ratio of speed of cat and dog = 3*5/4*4 = 15:16.''Answer: Option D
Answer: (D) 15:16
Question: A train crosses a platform in 15 sec, same train crosses another platform of length 250 m in 20 sec. If the speed of the train is 15 m/sec then find the length of the platform?
(A) 277m
(B) 180m
(C) 165m
(D) 278m
(E) 175m
Rationale: Length of the train be ‘X’
(X + 250)/20 = 15
X = 50m
Let the length of the platform be y
(y + 50)/15 = (50 + 250)/20
4y + 200 = 900
X = 1750m
Answer: E
Answer: (E) 175m
Question: Define A = The sum of digits of the number 7^100 and B = The sum of the digits of A. What is the sum of the digits of B?
(A) 7
(B) 16
(C) 10
(D) 11
(E) Cannot be Determined
Rationale: Following approach will take you only couple of sec.
\(7^{100} = (7^{50})^2\)
The sum of digits (digital root) of a PERFECT SQUARE can only be 1, 4, 7 or 9.
For example \(7^2=49\) => DR=4+9=13 => 1+3=4 and etc.
Checking available options.
Answer A.
Answer: (A) 7
Question: A 260 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train ?
(A) 240 mts
(B) 270 mts
(C) 260 mts
(D) 250 mts
(E) 280 mts
Rationale: Explanation:
Relative speed = 120 + 80 = 200 km/hr.
= 200 x 5/18 = 500/9 m/sec.
Let the length of the other train be L mts.
Then, (L + 260)/9 = 500/9 => L = 240 mts.
ANSWER IS A
Answer: (A) 240 mts
Question: A small, experimental plane has three engines, one of which is redundant. That is, as long as two of the engines are working, the plane will stay in the air. Over the course of a typical flight, there is a 1/4 chance that engine one will fail. There is a 75% probability that engine two will work. The third engine works only half the time. What is the probability that the plane will crash in any given flight?
(A)  7/12
(B)  1/4
(C)  1/2
(D)  7/24
(E)  17/24
Rationale: In probability questions the trap answer is just the multiple of the numbers in the question.
i.e. if you multiply 1/3 * 1/4 * 1/2 = 1/24 is trap answer
The other trap answer could be 2/3 * 3/4 * 1/2 = 6/24 is trap answer
So lets say you have30 secsand you want to guess the answer then B, C are ruled out because they can be traps. You best guess is A, D, E. So you have 33% chances of being correct.
A
Answer: (A)  7/12
Question: A store raised the price of an item by exactly 20 percent. Which of the following could NOT be the resulting price of the item?
(A) 6
(B) 12
(C) 18
(D) 24
(E) 58
Rationale: If it raised the value by 20% then the resulting price is 1.2 times the original price. So the final answer has to be a multiple of 1.2. Check the answers.
6 - Yes
12 - Yes
18 - Yes
24 - Yes
58 - No
Answer : E
Answer: (E) 58
Question: A departmental store charges the commission of 25 percent on the first sale of items worth $50,000 and then an additional 10 percent on any sale price that exceeds the initial $50,000. If the department store earned $24,000 in commissions for the sale of a series of diamonds, what was the sale price of the diamond set?
(A)  $215,000
(B)  $165,000
(C)  $115,000
(D)  $240,000
(E)  $160,000
Rationale: 24,000 = 0.25 *(50000) + 0.10 (x - 50000)
24000 - 12500 = 0.10 (x-50000)
115000 = x - 50000
x = 1,65,000
Answer : B
Answer: (B)  $165,000
Question: The price of an item is discounted 10 percent on day 1 of a sale. On day 2, the item is discounted another 10 percent, and on day 3, it is discounted an additional 30 percent. The price of the item on day 3 is what percentage of the sale price on day 1?
(A) 63%
(B) 40%
(C) 64.8%
(D) 70%
(E) 72%
Rationale: original price = 100
day 1 discount = 10%,price = 100-10 =90
day 2 discount = 10%,price = 90-9=81
day 3 discount = 30%,price = 81-24.3= 56.7
which is 56.7/90 *100 of the sale price on day 1= ~63%
Answer A
Answer: (A) 63%
Question: A boat can travel with a speed of 24 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 112 km downstream
(A) 3 hours
(B) 4 hours
(C) 5 hours
(D) 6 hours
(E) 7 hours
Rationale: Explanation:
Speed of the boat in still water = 24 km/hr
speed of the stream = 4 km/hr
Speed downstream = (22+5) = 28 km/hr
Distance travelled downstream = 112 km
Time taken = distance/speed = 112/28 = 4 hours
Answer: Option B
Answer: (B) 4 hours
Question: Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.
Then,	((6x + 6) + 4)/ ((5x + 6) + 4)	=	11/10
10(6x + 10) = 11(5x + 10)
5x = 10
x = 2.
Sagar's present age = (5x + 6) = 16 years.
ANSWERS : C
Answer: (C) 16
Question: The sum of five consecutive even numbers is 500. Find the middle number of the five?
(A) 140
(B) 66
(C) 100
(D) 99
(E) 120
Rationale: Middle number =500/5
=100
Ans C
Answer: (C) 100
Question: One vessel contains a mixture of 4 parts pure wine and 3 parts soda, whereas the other vessel contains a mixture of 9 parts pure wine and 5 parts soda. Compare the strength of the wine.
(A) 35;36
(B) 10 : 9
(C) 7 : 4
(D) 14 : 5
(E) None of these
Rationale: 4/7 : 9/14
LCM of 7,14 = 14
(5/7)*14: (9/14)*14
10:9
Answer is B.
Answer: (B) 10 : 9
Question: A part-time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee's total income did not change. By what percent W should the number of hours worked be increased?
(A) 12.5%
(B) 20%
(C) 25%
(D) 50%
(E) 100%
Rationale: Correct Answer: C
Solution: C. We can set up equations for income before and after the wage reduction. Initially, the employee earns W wage and works H hours per week. After the reduction, the employee earns .8W wage and works X hours. By setting these equations equal to each other, we can determine the increase in hours worked: WH = .8WX (divide both sides by .8W) 1.25H = X We know that the new number of hours worked W will be 25% greater than the original number. The answer is C.
Answer: (C) 25%
Question: A and B can do a work in 4 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 78
Rationale: Work done by A and B in the first two hours, working alternately = First hour A + Second hour B = 1/4 + 1/12 = 1/3.
Total time required to complete the work = 2 * 3 = 6 days.Answer:D
Answer: (D) 6
Question: There are 21 Kids in a classroom. 12 Kids are wearing socks and 8 are wearing Shoes. 6 Kids are wearing both.
How many are Bare Feet ?
(A) 1
(B) 2
(C) 4
(D) 5
(E) 7
Rationale: 12 kids wear socks
8 kids wear shoes
6 wear both.
12 â€“ 6 = 6 (wear only socks)
8 â€“ 6 = 2 (wear only shoes)
6 (wear both)
hence, 21 -14 = 7
7 kids are with bare feet.
E
Answer: (E) 7
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) 250
(B) 277
(C) 299
(D) 266
(E) 292
Rationale: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250.Answer: A
Answer: (A) 250
Question: The perimeter of an equilateral triangle is 60. If one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 70, then how long is the base of isosceles triangle?
(A) 15
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: The base of the isosceles triangle is 70-20-20= 30 units
The answer is D.
Answer: (D) 30
Question: In a firm there are men and cows. In all, there are 21 heads and 64 feet. How many men and how many cows are in the firm?
(A) 8 men and 13 cows.
(B) 10 men and 11 cows.
(C) 6 men and 15 cows.
(D) 5 men and 16 cows.
(E) 11 men and 10 cows.
Rationale: 10 men and 11 cows.
Let M = men and C = cows. We can come up with 2 equations.
M + C = 21
2M + 4C= 64
Solving the 2 equations will give 10 men and 11 cows.
Answer B
Answer: (B) 10 men and 11 cows.
Question: In a certain math department, students are required to enroll in either Calculus or Trigonometry, each of which is offered in beginner and advanced courses. The number of students enrolled in Trigonometry is 50% greater than the number of students enrolled in Calculus, and 80% of Calculus students are enrolled in the beginner course. If 4/5 of students are in the beginner courses, and one student is selected at random, what is the probability that an advanced Trigonometry student is selected?
(A) 8%
(B) 12%
(C) 16%
(D) 20%
(E) 24%
Rationale: Let x be the number of students in calculus.
Then the number of students in trigonometry is 1.5x
The number of students on beginner calculus is 0.8x
The number of students in beginner trigonometry is 4/5*(2.5x) - 0.8x = 1.2x
The number of students in advanced trigonometry is 0.3x
The percentage in advanced trigonometry is 0.3x / 2.5x = 12%
The answer is B.
Answer: (B) 12%
Question: If a and b are different positive integers and a + b = a(a + b+1), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
Rationale: Number picking might not be the best way to solve MUST BE TRUE questions.
The question asks which of the followingMUSTbe true, or which of the following isALWAYStrue no matter what set of numbers you choose. For such kind of questionsif you can prove that a statement is NOT truefor one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So the set you chose just proves that II is not always true and hence it's not a part of a correct choice. As for I and III: they might be true for this particular set of numbers but not true for another set, so you can not say that I and III are always true just based on one set of numbers (it just happens to be that I and III are always true).
As forCOULD BE TRUEquestions:
The questions asking which of the followingCOULDbe true are different:if you can prove that a statement is truefor one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.
C
Answer: (C) III only
Question: Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $450, what were her original savings?
(A) $1500
(B) $1600
(C) $1700
(D) $1800
(E) $1900
Rationale: If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $450. So 1 / 4 of her savings is $450. So her original savings are 4 times $450 = $1800
correct answer D
Answer: (D) $1800
Question: A is thrice as good a work man as B and together they finish a piece of work in 16 days.The number of days taken by B alone to finish the work is :
(A) 64 days.
(B) 24 days.
(C) 52 days.
(D) 35 days.
(E) 28 days.
Rationale: Solution
(A’s 1 day’s work): (B’s 1 day’s work)= 3 : 1.
(A + B)'s 1 day’s work = 1/16
Divide 1/14 in the ratio 3 : 1.
∴ B’s 1 day’s work = (1/16 x1/4)= 1/64
Hence,B alone can finish the work in 64 days.
Answer A
Answer: (A) 64 days.
Question: Sunil invested $ 2300 fir 3 years and $ 800 for 4 years at the same rate of Simple Interest. If the total interest from these investments is $ 1350, what is the rate of interest?
(A) 12 3/4%
(B) 15 1/3%
(C) 15 1/2%
(D) 16%
(E) 13 1/4%
Rationale: (2300x3xR)/100+(800x4xR)/100=1350
101R=1350
R= 13 1/4%
Answer is E
Answer: (E) 13 1/4%
Question: A cylindrical water tower with radius 15 m and height 4 m is 3/4 full at noon. Every minute, .08π m3 is drawn from tank, while .03π m3 is added. Additionally, starting at 1pm and continuing each hour on the hour, there is a periodic drain of 4π m3. From noon, how many hours will it take to drain the entire tank?
(A) 20 2/7
(B) 90 6/7
(C) 91
(D) 91 3/7
(E) 97
Rationale: initial volume = (3/4)×∏×15²×4= 675∏
Relative Drain/ min = .08∏ - .03∏ = .05∏ m³/min drain
Relative drain / hour = .05∏×60 = 3∏ m³/ hr
Every one hour starting from 1pm, 4∏ m³ of water is drained. It means that only at the hour the water is drained and NOT “in that 1 hour“
So after 1 hr the relative drain would be 3∏ + 4∏ = 7∏m³ of water drain
What i did initially was formed an equation 675∏ = 7∏×n (n is the number of hrs) so ended up with 96.42. This wrong
Look at this way
after 96 hrs the amount of water drain will be 96×7∏ = 672∏ m³
Left over water in the tank after 96 hrs = 3∏ m³
From above we know that it take 1 more hour to drain that 3∏ m³.
So ans is 97hrs
Answer: (E) 97
Question: The edges of three iron cubes are 6cm; 8cm; 10cm respectively. A new cube was made by melting them. Find the edge of the new cube?
(A) 16
(B) 12
(C) 17
(D) 15
(E) 71
Rationale: 63 + 83 + 103 = a3
=> a = 12
Answer: B
Answer: (B) 12