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15 Feb 2022, 03:45
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
93% (00:45) correct
7%
(02:02)
wrong
based on 27
sessions
History
Date
Time
Result
Not Attempted Yet
Which of the following statements about the cube above must be true?
I. FD is parallel to GA.
II. ΔGCF and ΔAHD have the same area.
III. AF = GD
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
Attachment:
2019-01-08_1602.png [ 9.52 KiB | Viewed 1177 times ]
kungfury42
Joined: 07 Jan 2022
Last visit: 31 May 2023
Posts: 580
Own Kudos:
Given Kudos: 724
Schools: NUS '25 (A)
GMAT 1: 740 Q51 V38
GPA: 4
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15 Feb 2022, 05:47
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Bunuel
Quote:
Faces GHAB and FEDC are parallel to each other. We further also know that ∠GHA = ∠FED = 90° and GH=HA=FE=DE (sides of the same cube) which means that triangles GHA and FED are right angled isosceles triangles. Therefore, ∠HAG = ∠EDF = 45°
Therefore, we have two diagonals GA and FD which lie on parallel faces and have the same inclination of 45° with their base. Clearly, FD || GA
Quote:
∠GFC = ∠HAD = 90° also GF=FC=HA=AD (sides of the same cube) therefore, both ΔGCF and ΔAHD are congruent to each other and will have the same areas.
Quote:
Both AF and GD are the body diagonals of the same cube and will be equal in length.
Hence, our answer is option E, all I, II and III are correct.
