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16 Oct 2025, 12:28
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
66% (02:18) correct
33% (00:57) wrong based on 3 sessions
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The cube above has volume equal to 64 cubic feet. If Points M and N are the midpoints of two edges of the cube, what is length MN, in feet?
A. \(4\sqrt{3}\)
B. \(3\sqrt{6}\)
C. \(4\sqrt{6}\)
D. \(6\sqrt{2}\)
E. \(2\sqrt{6}\)
Attachment:
GMAT-Club-Forum-g3rr7ebb.png [ 12.41 KiB | Viewed 142 times ]
18 Oct 2025, 04:55
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Official Explanation
If s is the side length of a cube, then the cube’s volume = \(s^3\). Here, \(64 = s^3,\) so \(s = 4,\). Then AB = 4, and MA = NB = 2 in the figure below, because M and N are midpoints of two of the edges.
Now draw MB and form the two right triangles, MAB and MBN.
MB is the hypotenuse of a right triangle with legs equal to 2 and 4, so
by the Pythagorean Theorem. This length becomes a leg in the second right triangle MBN.
Therefore,
Answer: E
GMAT-Club-Forum-pcayy9do.png [ 9.54 KiB | Viewed 104 times ]
GMAT-Club-Forum-qlkecpct.png [ 11.33 KiB | Viewed 104 times ]
GMAT-Club-Forum-ajb0953u.png [ 6.8 KiB | Viewed 106 times ]
GMAT-Club-Forum-vrvpczp1.png [ 4.52 KiB | Viewed 106 times ]
GMAT-Club-Forum-rk501dgi.png [ 5.98 KiB | Viewed 104 times ]
If s is the side length of a cube, then the cube’s volume = \(s^3\). Here, \(64 = s^3,\) so \(s = 4,\). Then AB = 4, and MA = NB = 2 in the figure below, because M and N are midpoints of two of the edges.
Now draw MB and form the two right triangles, MAB and MBN.
MB is the hypotenuse of a right triangle with legs equal to 2 and 4, so
by the Pythagorean Theorem. This length becomes a leg in the second right triangle MBN.
Therefore,
Answer: E
Attachment:
GMAT-Club-Forum-pcayy9do.png [ 9.54 KiB | Viewed 104 times ]
Attachment:
GMAT-Club-Forum-qlkecpct.png [ 11.33 KiB | Viewed 104 times ]
Attachment:
GMAT-Club-Forum-ajb0953u.png [ 6.8 KiB | Viewed 106 times ]
Attachment:
GMAT-Club-Forum-vrvpczp1.png [ 4.52 KiB | Viewed 106 times ]
Attachment:
GMAT-Club-Forum-rk501dgi.png [ 5.98 KiB | Viewed 104 times ]
