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04 Oct 2022, 01:30
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E
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Difficulty:
75%
(hard)
Question Stats:
36% (01:53) correct
64%
(01:38)
wrong
based on 53
sessions
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If quadrilateral ABCD is inscribed into a circumference. What is the value of angle A?
(1) AC = CD
(2) Measure of angle D is 70 degrees
(1) AC = CD
(2) Measure of angle D is 70 degrees
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
05 Oct 2022, 00:23
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Given quadrilateral ABCD is a cyclic quadrilateral. We need to find value of angle A.
(1) AC = CD
=> This does not give information about ∠BAC. If we move side AB of the cyclic quadrilateral keeping AC = CD we will get different values for angle A.
Statement 1 alone is not sufficient.
(2) Measure of angle D is 70 degrees
=> Cyclic quadrilateral property: Opposite angles of cyclic quadrilateral are supplementary. (Hence, exterior angle at a vertex is equal to the opposite interior angle.)
i.e., ∠A + ∠D = 180 => ∠A + 70 = 180 => ∠A = 110 degrees.
Statemen 2 alone is sufficient.
Answer: B
(1) AC = CD
=> This does not give information about ∠BAC. If we move side AB of the cyclic quadrilateral keeping AC = CD we will get different values for angle A.
Statement 1 alone is not sufficient.
(2) Measure of angle D is 70 degrees
=> Cyclic quadrilateral property: Opposite angles of cyclic quadrilateral are supplementary. (Hence, exterior angle at a vertex is equal to the opposite interior angle.)
i.e., ∠A + ∠D = 180 => ∠A + 70 = 180 => ∠A = 110 degrees.
Statemen 2 alone is sufficient.
Answer: B
