In the rectangular solid above, if each dimension of the rectangular solid is an integer greater than 1 and the area of two sides of the solid is 14 and 18 respectively, what is the volume of the solid?a)42b)126c)252d)882e)Cannot be DeterminedCorrect answer is option 'B'. Can you explain this answer?

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GMAT Exam > GMAT Questions > In the rectangular solid above, if each dimen...

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a)
42
b)
126
c)
252
d)
882
e)
Cannot be Determined

Correct answer is option 'B'. Can you explain this answer?

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Test: Rectangular Solids- 2

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In the rectangular solid above, if each dimension of the rectangular s...

Given:

Let the dimensions of the rectangular solid be L, B, H.
L, B and H are integers
L > 1, B>1 and H>1
Let L*B = 14
And, let B*H = 18

To find: Volume of the rectangular solid

Approach:

Volume of the rectangular solid = L*B*H
- Since we’re given the values of L*B and B*H, we can write L∗B∗H=
- So, to find the volume, we need to find the value of B

Integer B is the common divisor of L*B and B*H and is greater than 1. Since we’re given the values of L*B and B*H, we can find the common divisors of these 2 values.

If we get only one common divisor (of L*B and B*H) greater than 1, then we’ll be able to find a unique value of B, and hence of the volume
If we get multiple common divisors greater than 1, then we’ll get multiple values of B, and hence of the volume. In this case, the answer will become ‘(A unique value) cannot be determined’

Working Out:

Finding the common divisor(s) of L*B and B*H
- L*B = 14 = 2*7
- B*H = 18 = 2*3²
- So, the common divisors of L*B and B*H = {1, 2}
- The only common divisor greater than 1 is 2
- So, B = 2
Finding the volume

Looking at the answer choices, we see that the correct answer is Option B

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In the rectangular solid above, if each dimension of the rectangular solid is an integer greater than 1 and the area of two sides of the solid is 14 and 18 respectively, what is the volume of the solid?a)42b)126c)252d)882e)Cannot be DeterminedCorrect answer is option 'B'. Can you explain this answer?

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