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19 Nov 2017, 09:20
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D
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Difficulty:
15%
(low)
Question Stats:
80% (01:26) correct
20%
(01:47)
wrong
based on 205
sessions
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If the length of a certain rectangle is 2 greater than the width of the rectangle, what is the perimeter of the rectangle?
(1) The length of each diagonal of the rectangle is 10.
(2) The area of the rectangular region is 48.
(1) The length of each diagonal of the rectangle is 10.
(2) The area of the rectangular region is 48.
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
19 Nov 2017, 09:33
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Bunuel
let the width be \(x\), so length will be \(x+2\)
hence perimeter \(= 2[x+x+2] = 2(2x+2)\). we need the value of \(x\) to determine the perimeter
Statement 1: implies \(\sqrt{length^2+width^2}=diagonal\)
\(\sqrt{x^2+(x+2)^2}=10\)
or \(x^2+x^2+4x+4=100 => x^2+2x-48=0\)
so \((x-6)(x+8)=0\), hence \(x=6\) or \(-8\)
As width cannot be negative so \(x=6\). Sufficient
Statement 2: \(x(x+2)=48 => x^2+2x-48=0\)
Same as statement 1 above. we get \(x=6\). Sufficient
Option D
KanishkM
Joined: 09 Mar 2018
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Schools: DeGroote'21 Desautels '21 NUS '21
12 Feb 2019, 00:03
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Bunuel
l = b + 2
What is the perimeter.
Do be vary that in such questions, particularly while solving a quadratic equation,
if we get 2 positive values, the answer can be E
Nevertheless here that situation didn't arise
from 1, length of diagonal is given
\(d^2 = l^2 + b^2\), substitute for l, we can get an unique value
from 2, area is given
again we can get an unique value for perimeter
D
