What is the greatest possible (straight-line) distance between any two points on a certain rectangular solid of length L, width W, and height H, where H W L ?(1) The length, width, and height of the rectangular solid are the squares of prime integers.(2) The roots of the equation x2 13x = -36 are the width and the height of the rectangular solid.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'E'. Can you explain this answer?

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What is the greatest possible (straight-line) distance between any two points on a certain rectangular solid of length L, width W, and height H, where H < W < L ?

(1) The length, width, and height of the rectangular solid are the squares of prime integers.

(2) The roots of the equation x² – 13x = -36 are the width and the height of the rectangular solid.

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c)
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
EACH statement ALONE is sufficient.
e)
Statements (1) and (2) TOGETHER are NOT sufficient.

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

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What is the greatest possible (straight-line) distance between any two...

Steps 1 & 2: Understand Question and Draw Inferences

For the longest straight-line distance between any two points, you need the length, width, and height of the rectangular solid. You know that the height, the width, and the length are in ascending order of magnitude.

Step 3: Analyze Statement 1

(1) The length, width, and height of the rectangular solid are the squares of prime integers.

This narrows the possibilities: L, W, and H could be 4, 9, 25, 49, and so forth, but there are still too many possibilities.

Statement (1) is not sufficient.

Step 4: Analyze Statement 2

(2) The roots of the equation x² – 13x = -36 are the width and the height of the rectangular solid.

Factor the expression to (x – 9)(x – 4) for the roots. Thus the height and the width are 4 and 9, respectively (Since H < W).

However, knowing H < W < L, the length could be any number greater than 9.

Statement (2) is not sufficient.

Step 5: Analyze Both Statements Together (if needed)

You know from the question that H < W < L.

You know from Statement 1 that L, W, and H could be 4, 9, 25, 49, and so forth.

You know from Statement 2 that H and W are 4 and 9, respectively.

Taken together, L could be 25, 49, 121, or the square of any prime number greater than 3.

Hence both the statements together are not sufficient.

Answer: Option (E)

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What is the greatest possible (straight-line) distance between any two points on a certain rectangular solid of length L, width W, and height H, where H < W < L ?(1) The length, width, and height of the rectangular solid are the squares of prime integers.(2) The roots of the equation x2 – 13x = -36 are the width and the height of the rectangular solid.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'E'. Can you explain this answer?

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What is the greatest possible (straight-line) distance between any two points on a certain rectangular solid of length L, width W, and height H, where H < W < L ?(1) The length, width, and height of the rectangular solid are the squares of prime integers.(2) The roots of the equation x2 – 13x = -36 are the width and the height of the rectangular solid.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'E'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about What is the greatest possible (straight-line) distance between any two points on a certain rectangular solid of length L, width W, and height H, where H < W < L ?(1) The length, width, and height of the rectangular solid are the squares of prime integers.(2) The roots of the equation x2 – 13x = -36 are the width and the height of the rectangular solid.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the greatest possible (straight-line) distance between any two points on a certain rectangular solid of length L, width W, and height H, where H < W < L ?(1) The length, width, and height of the rectangular solid are the squares of prime integers.(2) The roots of the equation x2 – 13x = -36 are the width and the height of the rectangular solid.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'E'. Can you explain this answer?.

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