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05 Jan 2018, 09:41
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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:
85%
(hard)
Question Stats:
44% (02:09) correct
56%
(01:58)
wrong
based on 93
sessions
History
Date
Time
Result
Not Attempted Yet
Point A lies on a circle whose center is at point C. Does point B lie inside the circle?
1) \(BC^2 = AC^2 + AB^2\)
2) ∠CAB is greater than ∠ABC
1) \(BC^2 = AC^2 + AB^2\)
2) ∠CAB is greater than ∠ABC
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 Jan 2018, 10:19
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Point A lies on a circle whose center is at point C. Does point B lie inside the circle?
(1) \(BC^2 = AC^2 + AB^2\).
This statement implies that triangle ABC is right angled at A (BC being hypotenuse) So, AB is perpendicular to AC, which is radius (AB is tangent to the circle). Thus, B is outside the circle. Sufficient.
Little technicality here: this statement to be sufficient it should be mentioned that A and B are different points. I'm assuming it's given
(2) ∠CAB is greater than ∠ABC.
Larger side of a triangle is opposite larger angle. Hence, this statement implies that BC is larger than AC (radius). Thus, B is outside the circle. Sufficient.
We could use the same logic also for (1): BC (hypotenuse) is larger than AC (radius). Thus, B is outside the circle. Sufficient.
Answer: D.
Hope it's clear.
Untitled.png [ 4.49 KiB | Viewed 2959 times ]
Untitled1.png [ 4.85 KiB | Viewed 2886 times ]
(1) \(BC^2 = AC^2 + AB^2\).
This statement implies that triangle ABC is right angled at A (BC being hypotenuse) So, AB is perpendicular to AC, which is radius (AB is tangent to the circle). Thus, B is outside the circle. Sufficient.
Little technicality here: this statement to be sufficient it should be mentioned that A and B are different points. I'm assuming it's given
(2) ∠CAB is greater than ∠ABC.
Larger side of a triangle is opposite larger angle. Hence, this statement implies that BC is larger than AC (radius). Thus, B is outside the circle. Sufficient.
We could use the same logic also for (1): BC (hypotenuse) is larger than AC (radius). Thus, B is outside the circle. Sufficient.
Answer: D.
Hope it's clear.
Attachment:
Untitled.png [ 4.49 KiB | Viewed 2959 times ]
Attachment:
Untitled1.png [ 4.85 KiB | Viewed 2886 times ]
31 Aug 2023, 10:25
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