RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A rectangular plot measuring 90 metres by 40 metres is to be enclosed by wire fencing. If the poles of the fence are kept 5 metres apart, how many poles will be needed ?
A.55
B.56
C.57
D.52
Answer: D.52
Explanation: Solution
Perimeter of the plot = 2(90 + 40) = 260 m.
∴ Number of poles = [260/5] =52m
Answer D
Question: Ashok borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years and at the rate of 14% p.a. for the period beyond five years. If he pays a total interest of 11,400/ - at the end of nine years, how much money did he borrow?
A.16,060
B.14,000
C.18,000
D.12,000
Answer: D.12,000
Explanation: We have, SI = p×r×t/100
∴ 11400 = p×6×2/100+p×9×3/100+p×14×4/100
or,12p + 27p + 56p = 11400 × 100
or, 95p = 11400 × 100
∴ p = 12000
Answer D
Question: Ten Students take a test. The scores of the test are as follows:
Student A:60
Student B:40
Student C:50
Student D:75
Student E:95
Student F:50
Student G:45
Student H:100
Student I:45
Student J:70
How many scores were greater than the median score but less than the mean score?
A.None
B.One
C.Two
D.Three
Answer: B.One
Explanation: List in order: 40,45,45,50,50,60,70,75,95,100
The median = (the average of two middle terms) = (50 + 60)/2 = 55.
The mean = (the sum)/(# of terms) = 630/10 = 63.
Only 60 is between 55 and 63.
Answer: B.
Question: An urn contains 6 red, 5 blue and 2 green marbles. If 2 marbles are picked at random, what is the probability that both are red?
A.6/13
B.5/26
C.6/26
D.9/26
Answer: B.5/26
Explanation: Option(B) is correct
P(Both are red), 6C2/13C2 = 5/26
ANSWER B
Question: A wooden box of dimensions 4 m x 2 m x 4 m is to carry rectangularboxes of dimensions 4 cm x 2 cm x 2 cm. The maximum number ofboxes that can be carried in the wooden box, is
A.9800000
B.2000000
C.7500000
D.1200000
Answer: B.2000000
Explanation: Explanation: Number = (400*200*400)/4*2*2 = 2000000 Answer: B
Question: Machine A can finish a job in 4 hours, Machine В can finish the job in 3 hours, and Machine С can finish the job in 6 hours. How many hours will it take for A, B, and С together to finish the job?
A.3/2
B.4/3
C.5/4
D.6/5
Answer: B.4/3
Explanation: The combined rate is 1/4+1/3+1/6 = 9/12 of the job per hour.
The time to complete the job is 12/9 = 4/3 hours.
The answer is B.
Question: P and Q started a business investing Rs. 96,000 and Rs. 28,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
A.17:6
B.24:7
C.25:6
D.21:3
Answer: B.24:7
Explanation: P:Q = 96000 : 28000
= 24:7
Answer:B
Question: Harkamal purchased 8kg of grapes at the rate of 80 per kg and 9 kg of mangoes at the rate of 55 per kg. How much amount did he pay to the shopkeeper?
A.A)1000
B.B)1055
C.C)1065
D.D)1135
Answer: D.D)1135
Explanation: Cost of 8 kg grapes = 80 × 8 = 640.
Cost of 9 kg of mangoes = 55 × 9 = 495.
Total cost he has to pay = 640 + 495 = 1135.
D)
Question: The average weight of 16 girls in a class is 50.25 kg and that of the remaining 8 girls is 45.15 kg. Find the average weights of all the girls in the class.
A.A)48.55
B.B)49
C.C)51
D.D)61
Answer: A.A)48.55
Explanation: Required average
= (50.25 x 16 + 45.15 x 8)/(16 + 8)
= (804 + 361.20)/24
= 1165.20/24
= 48.55kg
Answer is A
Question: A number of 41 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes?
A.13
B.12
C.15
D.16
Answer: A.13
Explanation: To maximize # of boxes we should minimize marbles per box: 12*3+1*5=41 --> 12+1=13.
Answer: A.
Question: On a test, students receive 2 points for each correct answer and are penalized by losing one point for each incorrect answer. There are 6 questions on the test and each question has 4 answer options, A, B, C, and D. It is known that 5 of the questions have option B as the correct answer and one question has option C as the correct answer. If a student marks B for the first 3 questions and C for the last 3 questions, what is the minimum possible score that student can receive?
A.-2
B.-1
C.0
D.1
Answer: C.0
Explanation: For the minimum possible score, let us take the worst case scenario
Suppose, he gets all of the last 3 qs wrong whose correct answer options are B and one of the first 3 qs wrong whose correct option is C
In that case, he will get only 2 out of the first 3 qs right.
Therefore, minimum possible score=(2*2)-(4*1)=0
Answer C
Question: When the integer n is divided by 8, the remainder is 3. What is the remainder if 6n is divided by 8?
A.0
B.1
C.2
D.3
Answer: C.2
Explanation: When n is divided by 8, the remainder is 3 may be written as
n = 8 k + 3
multiply all terms by 6
6 n = 6(8 k + 3) = 8(6k) + 18
Write 18 as 16 + 2 since 16 = 8 * 2.
= 8(6k) + 16 + 2
Factor 8 out.
= 8(6k + 2) + 2
The above indicates that if 6n is divided by 8, the remainder is 2. The answer is C.
Question: The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is:
A.29
B.28
C.600
D.277
Answer: C.600
Explanation: T.D. = B.G. x 100 = Rs. 24 x 100 = Rs. 120.
Rate x Time	10 x 2
P.W. =	100 x T.D.	= Rs. 100 x 120 = Rs. 600.
Rate x Time	10 x 2
Answer: C
Question: If there are 200 questions in a 3 hr examination. Among these questions are 15 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems?
A.72 min
B.25.11628 min
C.70 min
D.74.11682 min
Answer: B.25.11628 min
Explanation: x=time for type B prolems
2x=time for type A problem
total time=3hrs=180min
185x+15*2x=180
x=180/215
x=0.837209
time taken for type A problem=15*2*0.837209=25.11628min
ANSWER:B
Question: How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336
A.1
B.4
C.5
D.7
Answer: B.4
Explanation: B
By using your calculator you can calculate that the following numbers are divisible by 132 : 264, 396, 792 and 6336.
Required number of number = 4.
Question: Simplify: 18800+470+20
A.4
B.1
C.5
D.2
Answer: D.2
Explanation: 18800+470+20=(18800/470)+20=40/20=2.
Answer is D.
Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?
A.6000
B.7000
C.8000
D.9000
Answer: C.8000
Explanation: State A and State B had an equal number of candidates appeared.
In state A, 6% candidates got selected from the total appeared candidates
In state B, 7% candidates got selected from the total appeared candidates
But in State B, 80 more candidates got selected than State A
From these, it is clear that 1% of the total appeared candidates in State B = 80
=> total appeared candidates in State B = 80 x 100 = 8000
=> total appeared candidates in State A = total appeared candidates in State B = 8000
C)
Question: A fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans. A customer bought the pair of jeans for 30 percent more than the retailer paid for them. The price the customer paid was what percent greater than the cost of manufacturing the jeans?
A.65%
B.70%
C.75%
D.82%
Answer: D.82%
Explanation: find the product of the two increases: (14/10) * (13/10) which is 1.82 and a 82% increase.
D
Question: The length of a train and that of a platform are equal. If with a speed of 54 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
A.752
B.450
C.719
D.750
Answer: B.450
Explanation: Speed = [54 * 5/18] m/sec = 15 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 15 Ã¨ x = 15 * 60 / 2 = 450
Answer: B
Question: Sum of the squares of three numbers is 222 and the sum of their products taken two at a time is 131. Find the sum?
A.22
B.25
C.26
D.28
Answer: A.22
Explanation: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 222 + 2* 131
a + b + c = √484 = 22
A
Question: The number of new words that can be formed by rearranging the letters of the word 'MACHINE' is ?
A.5030
B.5039
C.5010
D.5033
Answer: B.5039
Explanation: Number of words which can be formed = 7! - 1
= 5040 - 1
= 5039.
Answer:B
Question: The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#36?
A.16
B.17
C.18
D.19
Answer: C.18
Explanation: First, let's translate the expression 21#36, using the definition given:
21#36 = 21×24×27×30×33×36
We need the prime factorization of this product.
Let's factor out 3 from each multiple.
21#36 = 3^6(7×8×9×10×11×12)
Now let's replace each consecutive integer with its prime factorization:
21#36 = 3^6(7×2^3×3^2×(2×5)×11×(2^2×3))
Let's group the prime bases:
21#36 = 2^6×3^9×5×7×11
The sum of the exponents is 6 + 9 + 1 + 1 + 1 = 18
The answer is C.
Question: The distance between two planets is 3.04 × 10^8 light years. What is the distance between the two planets, in parsecs? (1 parsec = 3.26 light years)
A. 9.3 × 10^5
B. 9.9 × 10^6
C. 9.3 × 10^7
D. 9.9 × 10^7
Answer: C. 9.3 × 10^7
Explanation: 3.04*10^8 light years = 3.04*10^8/3.26 parsecs.
3.04/3.26 is a little bit less than 1, something like 0.9, thus 3.04*10^8/3.26 = ~0.93*10^8 = 9.3*10^7.
Answer: C.
Question: The distance between a food bank and a church is approximately 8.0 x 10^5 inches. Which of the following is closest to the distance between the food bank and the church, in kilometers? (1 kilometer is approximately 3.9 x 10^4 inches.)
A.22.8
B.23.4
C.19.86
D.20.5
Answer: D.20.5
Explanation: We know that 1 kilometer = 3.9x10^4 inches. Therefore, we now have a ratio of (1 kilometer/3.9x10^4 inches).
We also know that the distance between the food bank and the church is approximately 8.0x10^5 inches. To convert inches to kilometers, we need to multiply 8.0x10^5 inches by the ratio we just found out.
kilometers = 8.0x10^5 inches x (1 kilometer/3.9x10^4 inches) [note: "inches" cancel out, leaving us with just km]
km = 8.0x10^5/3.9x10^4 km
km = 20.51 = 20.5 km
Therefore, we can see that the closest answer is D.
Question: The equation x = 2y^2 + 5y - 18, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is
A.3x + y + 15 = 0
B.y - 3x - 11 = 0
C.-2x - y - 7 = 0
D.-3x + y - 18 = 0
Answer: D.-3x + y - 18 = 0
Explanation: The question is made to look difficult though it is pretty simple if you focus on just the line and use process of elimination. (Remember that GMAT does not focus on parabolas so basically, the question should be quite do-able even if someone doesn't know how to handle parabolas.)
We need equation of l. Its slope must be 3.
Slope in option A and C is not 3 so we are left with B, D and E
The line has a point (-5, y) on it where y is positive (since the point lies in upper left quadrant).
In options B and E, if you put x = -5, you get -ve value for y co-ordinate. So ignore them.
Answer must be (D)
Question: The average ageof A, B and their C 3 years ago was 25 years and that of B and the C 5 years ago was 10 years. The present age of the A is:
A.46 years
B.56 years
C.51 years
D.58 years
Answer: C.51 years
Explanation: Sum of the present ages of husband, wife and child = (25 x 3 + 3 x 3) years = 81 years.
Sum of the present ages of wife and child = (10 x 2 + 5 x 2) years = 30 years.
Husband's present age = (81 - 30) years = 51 years.
C
Question: The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations Q could be chosen from this menu?
A.10
B.20
C.40
D.80
Answer: C.40
Explanation: Q=4C1 * 5C2
= 4 * (5*4*3!)/(3!2!)
= 4 * 10
= 40
Answer - C
Question: The present ages of Tim and Lee are in the ratio of 5:6 respectively. Seven years hence, the ratio of their ages will be 6:7 respectively. What is Tim's present age?
A.40 years
B.32 years
C.35 years
D.34 years
Answer: C.35 years
Explanation: Let x be the Tim's age.
And y be the Lee's age.
Then, x/y = 5/6 ===> y = 6x/5
And, x+7/y+7 = 6/7
==> 7x+49 = 6y+42
==> 7x = 67-7
By substituting 7x=(36x/5)-7
==>35x-36x=-35
Therefore, x=35
ANSWER:C
Question: On decreasing the price of a colour TV by 15%, its sale is increased by 30%. The effect on the revenue is?
A.20 % decrease
B.25.5 % increase
C.16% decrease
D.30 % increase
Answer: B.25.5 % increase
Explanation: Net% change in revenue
= ( x + y + xy/100) %
= [-15 + 30 + ( -15 x 30)/100]% or 25.5%
ANSWER:B
Question: The perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle
A.A)72
B.B)45
C.C)729
D.D)34
Answer: B.B)45
Explanation: Explanation:
Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 36/2 = 45 cm2
Answer: Option B
Question: Find the arithmetic mean W of all roots of the following equation- see an attachment.
A.2
B.1
C.0.5
D.-1/3
Answer: C.0.5
Explanation: arithmetic mean W your answer C and E are same, can you correct one of them please. thanks.C
Question: judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 9th position from either end of the row.
Can you find out how many girls are practicing together?
A.4
B.9
C.17
D.18
Answer: C.17
Explanation: As judith is 9th from either end of the row, it means that 8 girls are on one of her sides and 8 are present on the other.
8 + 8 + 1(judith herself) = 17.
Hence, 17 girls are practicing the dance together.
correct answer is C)17
Question: A certain number X when divided by 243 leaves a remainder of 98. Which of the following can be subtracted from X to make X divisible by 81?
A.17
B.27
C.37
D.47
Answer: A.17
Explanation: X=243y+98
so X/81 = 243y/81 + 98/81
since 243 is divisible by 81 the remainder of X/81 is remainder of 98/81 that is 17
Therefore subtracting 17 from X will make it divisible by 81
hence A is the answer
Question: If selling price is doubled, the profit triples. Find the profit percent?
A.108%
B.100%
C.120%
D.900%
Answer: B.100%
Explanation: Let C.P. be Rs. x and S.P. be Rx. y.
Then, 3(y - x) = (2y - x) => y = 2x
Profit = (y - x) = Rs. (2x - x) = Rs. x
Profit % = x/x * 100 = 100%.
Answer: B
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 4 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
A.3:1
B.19:4
C.19:8
D.19:5
Answer: A.3:1
Explanation: Quantity of alcohol in vessel P = 62.5/100 * 4 = 5/2 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/2 + 7/2 = 6 litres
As 8 litres of mixture is formed, ratio of alcohol and water in the mixture formed
= 600 : 200 = 3:1.
Answer: A
Question: Which term of the AP: 121, 117, 113, ...... is its first negative term?
A.-1
B.-2
C.-3
D.-5
Answer: C.-3
Explanation: 121,117,113,......5,1,-3
ANSWER:C
Question: Of a certain group of 100 people, 40 graduated from High School O, 65 graduated from College Y, and 30 live in City Z. What is the greatest possible number of people in this group who did not graduate from High School O, did not graduate from College Y, and do not live in City Z ?
A. 5
B. 15
C. 35
D. 65
Answer: C. 35
Explanation: 1. o+y+z+oy+yz+oz+oyz+ none=100. Fornoneto be maximum others have to be minimum
2. We know the underlined portions sum to 65 and that is the minimum value of others
3. Maximumnone= 100-65=35=C
Question: Kim is taking a math class, and the teacher gives a multiple choice test consisting of 7 questions. If each question has 4 answer choices, and Kim answers every question, in how many different ways can she complete the test?
A.a 40
B.b 400
C.c 4^7
D.d 8^5
Answer: C.c 4^7
Explanation: different ways to solve each question is 4.
So, 4*4*4*4.. 7 times ----> 5^8
Answer will be C.
Question: If there are n rays and all of them are reversed after 2006 reversals, then a possible value of n is
A.2237
B.3777
C.2002
D.3772
Answer: C.2002
Explanation: has to be same number less than (or equal to) k and of the same type as k.
k = 2006 then n = 2002.
Answer:C
Question: If you keep rolling a pair of dice together till a sum of 5 or 7 is obtained, then what is the probability that a sum of 5 comes before a sum of 7?
A.5/5
B.4/5
C.3/5
D.2/5
Answer: D.2/5
Explanation: This can be solved in a generic and complex way but let us not go into all that.
There can be four ways through which the pair of dice results in a sum of 5. There can be six ways through which the pair of dice can result in a sum of 7.
Now, we want the probability of the pair of dice resulting in a sum of 5 before a sum of 7. Thus probability = 4/(4+6) = 4/10 or 2/5.
correct answer is D)2/5
Question: An inspector rejects 0.08% of the meters as defective. How many will he examine to reject 2?
A.1500
B.2000
C.2500
D.3000
Answer: C.2500
Explanation: Let the number of meters to be examined be x
Then, 0.08% of x = 2
(8/100)*((1/100)*x = 2
x = 2500
Answer is C
Question: A car during its journey travels 30 minutes at a speed of 40 kmph, another 45 minutes at a speed of 60 kmph, and 2 hours at a speed of 70 kmph.The average speed of the car is
A.63.07 kmph
B.64 kmph
C.62.02 kmph
D.64.02 kmph
Answer: A.63.07 kmph
Explanation: First car travels 30 min at speed of 40 kmph
distance = 40 x 1/2 = 20 m
Then car travels 45 min at a speed of 60 kmph
distance = 45 min at speed of 60 kmph
distance = 60 x 3/4 = 45 m
at last it travels 2 hours at speed of 70 kmph
distance = 70 x 2 = 140 m
Total distance = 20 + 45 + 140 = 205
Total time= 1/2 + 3/4 + 2 = 3.25
Average speed of the car = 205/3.25 = 63.07
ANSWER:A
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
A.34
B.35
C.36
D.37
Answer: C.36
Explanation: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec.
Answer: Option C
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
A.2.87
B.2.88
C.2.67
D.2.21
Answer: B.2.88
Explanation: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer:B
Question: In how many V ways can the wordGMATbe arranged so that no such arrangement has A as the first letter?
A.6
B.12
C.18
D.24
Answer: C.18
Explanation: Number of ways of arranging the word GMAT = 4! = 24
Number of ways of arranging the word GMAT so that A is always in the first = 3! = 6
Number of ways of arranging GMAT so that A is not in the beginning V= 24 - 6 = 18
Answer: C
Question: A miniature gumball machine contains 5 blue, 4 green, and 1 red gumball, which are identical except for their colors. If the machine dispenses three gumballs at random, what is the probability that it dispenses one gumball of each color?
A.1/3
B.1/4
C.1/5
D.1/6
Answer: D.1/6
Explanation: The total number of ways to dispense 3 gumballs is 10C3=120.
The number of ways to choose one of each color is 5*4*1=20.
P(dispensing one of each color)=20/120=1/6.
The answer is D.
Question: What is the maximum number E of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
A.36
B.32
C.24
D.21
Answer: C.24
Explanation: 27 cubic centimetre cubes gives side = 3cm
so if:
L*W*H is 9*12*8, then max. cube we can have are 3*4*2 = 24
L*W*H is 9*8*12, then max. cube we can have are 3*2*4 = 24
L*W*H is 12*8*9, then max. cube we can have are 4*2*3 = 24
L*W*H is 12*9*8, then max. cube we can have are 4*3*2 = 24
L*W*H is 8*12*9, then max. cube we can have are 2*4*3 = 24
L*W*H is 8*9*12, then max. cube we can have are 2*3*4 = 24
In all cases we get E=24 cubes.
Ans. C
Question: A person can swim in still water at 20 km/h. If the speed of water 12 km/h, how many hours will the man take to swim back against the current for 40km?
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: M = 20
S = 12
US = 20 - 12 = 8
D = 40
T = 40/8 = 5 Answer:C
Question: If n = 2p, where p is a prime number greater than 2, how many different positiveevendivisors does n have, including n ?
A. Two
B. Three
C. Four
D. Six
Answer: A. Two
Explanation: This is an interesting question because we are immediately given the option to insert any prime number we wish for p. Since this is a problem-solving question, and there can only be one correct answer, we can select any value for p, as long as it is a prime number greater than 2. We always want to work with small numbers, so we should select 3 for p. Thus, we have:
n = 4 x 3
n = 12
Next we have to determine all the factors, or divisors, of P. Remember the term factor is synonymous with the term divisor.
1, 12, 6, 2, 4, 3
From this we see that we have 4 even divisors: 12, 6, 2, and 4.
If you are concerned that trying just one value of p might not substantiate the answer, try another value for p. Let’s say p = 5, so
n = 4 x 5
n = 20
The divisors of 20 are: 1, 20, 2, 10, 4, 5. Of these, 4 are even: 20, 2, 10 and 4. As we can see, again we have 4 even divisors.
No matter what the value of p, as long as it is a prime number greater than 2, n will always have 4 even divisors.
The answer is A.
Question: The product of all the prime numbers less than 25 is closest to which of the following powers of 10?
A.a) 10^9
B.b) 10^8
C.c) 10^8*2.23
D.d) 10^6
Answer: C.c) 10^8*2.23
Explanation: Group these numbers so as to get product close to a multiple of 10, so they can be rewritten as (2*5)(3*7)(11*19)(13*17)*23 or 10*21*209*221* 23
Now take out power of 10 from each number and rewrite
10*10*100*100*10 (1*2.1*2.09*2.21*2.3) or 10^7*(1*2.1*2.09*2.21*2.3)=10^7*10*2.23
=2.23*10^8
C
Question: Somehow or other I got talked into buying something on the installment plan. I'm notsure I got a good deal. The payments to date,according to my checkbook, have reached Rs.96.The second year cost Rs.2.00 more than the first year; the third year cost Rs.3.00 more thanthe second; and the fourth year cost me Rs.4.00 more than the third. What were mypayments the first year?
A.18
B.20
C.22
D.24
Answer: B.20
Explanation: let payments for the first year=x
given,x+x+2+x+5+x+9=96
4x+16=96
x=20
ANSWER:B
Question: A cubical block of metal weighs 7 pounds. How much will another cube of the same metal weigh if its sides are twice as long?
A.48
B.32
C.24
D.56
Answer: D.56
Explanation: For example our cube have a side 1 meter, so we have 1 cubical meter in this cube
and this cubical meter weigth 7 pounds
If we take cube with side 2 meters we will have 8 cubical meters in this cube
8 meters * 7 pounds = 56 pounds
So answer is D
And similar but more theoretical approach:
if we have sides a and b than they have equal ration with their areas:
a/b = a^2/b^2
and they have equal ration with their volumes:
a/b = a^3/b^3
we have two sides 1/2 so their volume will be in ratio 1/8
weight of one cube * volume of another cube
7 * 8 = 56
So answer is D
Question: A, B and C shared profits in ratio of 5 : 7 : 8. Theypartnered for 10months, 8months and 7months respectively. What was he ratio of their investments ?
A.10 : 49 : 45
B.20 : 49 : 64
C.10 : 19 : 64
D.20 : 35 : 64
Answer: D.20 : 35 : 64
Explanation: Simply multiply profit sharing ratio with investment ratio to get investment amount ratio.
Let X is the total investment
â‡’10 x = 5
â‡’ 8 x = 7
â‡’ 7x = 8
â‡’ Final investment ratio = 20 : 35 : 64
D
Question: In a business, A and C invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by A and B was 3 : 2 . If B receive 18000,how much amount was their profit?
A.58000
B.48200
C.60400
D.58500
Answer: D.58500
Explanation: Explanation :
Assume that investment of C = x
Then, investment of A =2x
Investment of B = 4x/3
A:B:C = 2x : 4x/3 : x = 2 : 4/3 : 1 =6 : 4 : 3
Let their profit was y
18000 = y*4/(6+4+3)
y = 18000*13/4 = 58500
Answer : Option D