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15 Aug 2018, 11:21
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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:
65%
(hard)
Question Stats:
51% (02:12) correct
49%
(02:04)
wrong
based on 70
sessions
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Not Attempted Yet
A rhombus PQRS has A, B, C, D as mid points of its sides PQ, QR, RS and SP respectively. A, B, C, D are joined to form quadrilateral ABCD. What is the perimeter of quadrilateral ABCD?
(1) PQ = 10 units.
(2) PR = 16 units.
(1) PQ = 10 units.
(2) PR = 16 units.
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
15 Aug 2018, 12:36
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amanvermagmat
ABCD is a rectangle. (When we joint the midpoints of a rhombus , a rectangle emerges)
Rephrased question stem:- What is the perimeter of the rectangle ABCD?
a) Length & breadth , both required
St1:- PQ = 10 units
We can only determine the diagonals of the rectangle. PQ=BD=10=PS=AC.
Not sufficient to determine length & breadth of the rectangle.
St2:- PR = 16 units
In the triangle QRP, AB || PR and A & B are the midpoints of two of it's sides , so \(AB=\frac{PR}{2}=\frac{16}{2}\)=8 units=breadth of rectangle.
There is no sufficient info to determine the length of rectangle, BC.
Combining, we have, in the right angled triangle ABC, AC=diagonal=10 units(from st1) and AB=8 units (from st2)
So, \(BC=\sqrt{10^2-8^2}\)=6 units
Now perimeter can be determined using the formula: P=2(AB+BC)
Sufficient.
Ans. (C)
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09 Oct 2019, 13:00
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