In the rectangular solid above, if each dimension of the solid is an

Official Solution

Steps 1 & 2: Understand Question and Draw Inferences

Let the length, breadth, and height of the rectangular solid be L, B and H respectively.

We are given that L, B, H are integers.

We need to find the volume of the solid, that is, the value of the product LBH.

Step 3: Analyze Statement 1 independently

Statement 1 states that "The area of two sides of the rectangular solid is 4 and 20 respectively

Let the two sides whose area is 4 be B and L, and the two sides whose area is 20 be B and H.
So, we can write: B*L = 4
In how many ways can 4 be expressed as a product of 2 numbers?
We can write 4 = 1*4 or 2*2
This means (B,L) are either (1,4) or (2,2)

Let’s now analyze the second piece of information given in St. 1

B*H = 20 = 1*20 = 2*10 = 4*5
This means (B,H) are either (1,20) or (2,10) or (4,5)

Note that the pairs of sides (B,L) and (B,H) share one dimension – B.
Applying this constraint on the possible values of (B,L) and (B,H) deduced above, we get:

(B,L,H) = (1,4,20) and Volume = 1 * 4 * 20 = 80
OR
(B,L,H) = (2,2,10) and Volume = 2 * 2* 10 = 40
OR
(B,L,H) = (4,1,5) and Volume - 4 * 1 * 5 =20

Since we’ve not been able to determine a unique value of the volume, Statement 1 alone is not sufficient.

Step 4: Analyze Statement 2 independently

Statement 2 states that: The area of two sides of the rectangular solid is 4 and 5 respectively.

Let the two sides whose area is 4 be B and L, and the two sides whose area is 5 be L and H.
So, we can write: L*B = 4 = 1*4 = 2*2

This means (L,B) is either (1,4) or (2,2)
Also, L*H = 5 = 1*5
Since 5 is a prime number, it can only be expressed as a product of 1 and 5 itself.

This means (L, H) = (1,5)
Now, the pairs of sides (L,B) and (L,H) share one dimension – L
Applying this constraint on the possible values of (L,B) and (H,L) deduced above, we get:

L = 1, H = 5 and B = 4
Therefore, LBH = 1*4*5 = 20

Since Statement 2 leads us to a unique value of the volume of the solid, it is sufficient.

Hence the correct answer is Option B .

Thanks,
Saquib
Quant Expert
e-GMAT

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