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24 Oct 2025, 00:06
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Difficulty:
35%
(medium)
Question Stats:
90% (01:20) correct
9% (04:57) wrong based on 11 sessions
History
Date
Time
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Not Attempted Yet
In the rectangular solid above, all edges have integer lengths. If the areas of three of the faces of the solid are 15, 33, and 55, what is its volume?
A. 103
B. 165
C. 495
D. 9,075
E. 27,225
Attachment:
GMAT-Club-Forum-dpnzb9cb.png [ 3.2 KiB | Viewed 250 times ]
27 Oct 2025, 09:28
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Official Explanation
Try to find the three edge lengths of the solid. The areas of the rectangular faces are 15, 33, and 55, so the pairwise products of the edges (the edge lengths multiplied two at a time) must equal these values. Trial and error reveals that 3 × 5 = 15, 3 × 11 = 33, and 5 × 11 = 55. This implies that the side lengths of the solid are 3, 5, and 11.
Notice that the top and bottom faces of the solid have area 33, while the front and back have area 55, and the right and left faces have area 15. Then Volume = l × w × h = 11 × 3 × 5 = 165, (B).
Answer: B
GMAT-Club-Forum-lzn7j3eg.png [ 6.63 KiB | Viewed 241 times ]
Try to find the three edge lengths of the solid. The areas of the rectangular faces are 15, 33, and 55, so the pairwise products of the edges (the edge lengths multiplied two at a time) must equal these values. Trial and error reveals that 3 × 5 = 15, 3 × 11 = 33, and 5 × 11 = 55. This implies that the side lengths of the solid are 3, 5, and 11.
Notice that the top and bottom faces of the solid have area 33, while the front and back have area 55, and the right and left faces have area 15. Then Volume = l × w × h = 11 × 3 × 5 = 165, (B).
Answer: B
Attachment:
GMAT-Club-Forum-lzn7j3eg.png [ 6.63 KiB | Viewed 241 times ]
