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Hussain15
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Joined: 18 Jun 2009
Last visit: 07 Jul 2021
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Concentration: Strategy, General Management
Schools: Stanford '14 (D) Booth '14 (D) Johnson '14 (D)
GMAT 1: 680 Q48 V34
C
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What is the perimeter of rectangle R?
(1) The area of rectangle R is 60.
(2) The length of a diagonal of rectangle R is 13.
(1) The area of rectangle R is 60.
(2) The length of a diagonal of rectangle R is 13.
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
whiplash2411
Joined: 09 Jun 2010
Last visit: 02 Mar 2015
Posts: 1,760
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Status:Three Down.
Concentration: General Management, Nonprofit
Schools: HBS '17 (M) Stanford '17 (A)
Updated on: 26 Jun 2010, 20:54
Originally posted by whiplash2411 on 26 Jun 2010, 08:24.
Last edited by whiplash2411 on 26 Jun 2010, 20:54, edited 1 time in total.
Last edited by whiplash2411 on 26 Jun 2010, 20:54, edited 1 time in total.
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I think the answer is C.
Statement 1: Area = 60
This implies that \(l*b = 60\) where l and b are length and breadth respectively. This could mean a million possibilities. So insufficient and we are down to BCE.
Statement 2: Length of diagonal = 13.
This implies that \(\sqrt{l^2 + b^2} = 13\)
So at this point, I am a little confused about one tiny detail.
Scenario 1: We can assume that all sides of the rectangle are integers, in which case Statement alone is sufficient since the only two integers whose sum of squares is 13 are 12 and 5. So we are done.
Scenario 2: We cannot assume that all sides are integers, in which case statement two is insufficient and we use statement 1 with statement 2 to figure out the answer.
b = \(\frac{60}{l}\)
Substituting that into statement 2, we get:
\(\sqrt{l^2 + (60/l)^2} = 13\)
This can be solved for a value of l and hence we get C as our answer. What's the OA?
Statement 1: Area = 60
This implies that \(l*b = 60\) where l and b are length and breadth respectively. This could mean a million possibilities. So insufficient and we are down to BCE.
Statement 2: Length of diagonal = 13.
This implies that \(\sqrt{l^2 + b^2} = 13\)
So at this point, I am a little confused about one tiny detail.
Scenario 1: We can assume that all sides of the rectangle are integers, in which case Statement alone is sufficient since the only two integers whose sum of squares is 13 are 12 and 5. So we are done.
Scenario 2: We cannot assume that all sides are integers, in which case statement two is insufficient and we use statement 1 with statement 2 to figure out the answer.
b = \(\frac{60}{l}\)
Substituting that into statement 2, we get:
\(\sqrt{l^2 + (60/l)^2} = 13\)
This can be solved for a value of l and hence we get C as our answer. What's the OA?
26 Jun 2010, 09:23
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Hussain15
Let the sides be \(x\) and \(y\). Question: \(P=2(x+y)=?\)
(1) \(area=xy=60\). Clearly insufficient.
(2) \(x^2+y^2=13^2=169\). Also insufficient.
(1)+(2) Square P --> \(P^2=4(x+y)^2=4(x^2+2xy+y^2)\) as from (1) \(xy=60\) and from (2) \(x^2+y^2=169\), then \(P^2=4(x^2+2xy+y^2)=4(169+120)=4*289\) --> \(P=\sqrt{4*289}=2*17=34\). Sufficient.
Answer: C.
