In the rectangular solid above, if each dimension of the solid is an integer, what is the volume of the solid?(1) The area of two sides of the rectangular solid is 4 and 20 respectively(2) The area of two sides of the rectangular solid is 4 and 5 respectively.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'B'. Can you explain this answer?

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In the rectangular solid above, if each dimension of the solid is an integer, what is the volume of the solid?

(1) The area of two sides of the rectangular solid is 4 and 20 respectively

(2) The area of two sides of the rectangular solid is 4 and 5 respectively.

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
d)
EACH statement ALONE is sufficient to answer the question asked.
e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

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 solid is an i...

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:

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.

Step 5: Analyze Both Statements Together (if needed)

Since we have a unique answer from step 4, this step is not required.

Hence the correct answer is Option B

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In the rectangular solid above, if each dimension of the solid is an integer, what is the volume of the solid?(1) The area of two sides of the rectangular solid is 4 and 20 respectively(2) The area of two sides of the rectangular solid is 4 and 5 respectively.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'B'. Can you explain this answer?

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