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PyjamaScientist
Admitted - Which School Forum Moderator
Joined: 25 Oct 2020
Last visit: 04 Apr 2026
Posts: 1,125
Given Kudos: 633
Schools: Ross '25 (M$)
GMAT 1: 740 Q49 V42 (Online)
Products:
04 Dec 2021, 11:46
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
43% (02:48) correct
57%
(02:48)
wrong
based on 121
sessions
History
Date
Time
Result
Not Attempted Yet
In \(\triangle \)ABC point D is on the side AB between vertices A and B. If CD = AB, is AD > BC?
(1) \(\angle\)ADC = 110\(^{\circ}\)
(2) \(\angle\)ACD = 30\(^{\circ}\)
(1) \(\angle\)ADC = 110\(^{\circ}\)
(2) \(\angle\)ACD = 30\(^{\circ}\)
05 Dec 2021, 14:59
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PyjamaScientist
Statement 1 Alone:
First, draw AB. Pick any point D on AB and draw CD = AB with a 110-degree angle in any direction. Complete the rest of the triangle by connecting AC and BC.
Then we just proved we can pick any point D on AB, therefore statement 1 alone is insufficient.
Statement 2 Alone:
Draw AB, then pick any point D on AB and draw CD = AB. Connect AC, then rotate CD with respect to point D so that \(\angle\)ACD = 30\(^{\circ}\). Finally, connect BC.
Then we just proved we can pick any point D on AB, therefore statement 2 alone is insufficient.
Both Statements Combined:
Draw triangle ACD first with the 30 and 110-degree angles. Extend AD to AB so that AB = DC and connect BC.
Then we just proved the shape has all fixed angles and we cannot change the ratios of lengths. Thus combined it is sufficient.
Answer: C
15 Dec 2021, 00:37
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PyjamaScientist pls provide OE
