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Updated on: 20 Apr 2020, 01:55
Originally posted by KhegayVladislav on 20 Apr 2020, 01:31.
Last edited by Bunuel on 20 Apr 2020, 01:55, edited 1 time in total.
Last edited by Bunuel on 20 Apr 2020, 01:55, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
73% (01:46) correct
27%
(01:20)
wrong
based on 52
sessions
History
Date
Time
Result
Not Attempted Yet
If angles P and Q are supplementary, angles P and R are complementary, and x is the sum of the measure of the three angles, then which of the following must be true?
(A) x = 90
(B) 90 < x < 180
(C) x = 180
(D) 180 < x < 270
(E) x = 270
(A) x = 90
(B) 90 < x < 180
(C) x = 180
(D) 180 < x < 270
(E) x = 270
20 Apr 2020, 01:54
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KhegayVladislav
Supplementary angles are two angles that add up to 180. So, P + Q = 180°.
Complementary angles are two angles that add up to 90°. So, P + R = 90°. Here notice that each of P and Q cannot be less than 0 and greater than 90°.
Since the sum of the measure of the three angles is x, then P + Q + R = x°.
Sum 1 and 2: P + P + Q + R = 270°. Since P + Q + R = x°, then P + x = 270°. This gives x = 270° - P. Since \(P_{min} = 0°\), then \(x_{max} =270°\) and since \(P_{max}=90°\), then \(x_{min}=180°\).
Therefore, 180 < x < 270.
Answer: D.
P.S. Please read carefully and follow our posting rules: https://gmatclub.com/forum/rules-for-po ... 33935.html. Please pay attention to rule 3 and 7. Thank you.
General Discussion
20 Apr 2020, 01:39
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KhegayVladislav
P+Q = 180
P+R = 90
SInce P is part of Complementary and Supplementary angles both therefore
P can not exceed 90
i.e. 0 < P < 90
Let. P = 0
then Q = 180
and
R = 90
then x = P + Q + R = 0+180+90 = 270
Let. P = 90
then Q = 90
and
R = 0
then x = P + Q + R = 90+90+0 = 180
i.e. 180 < x < 270
ANswer: Option D
