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20 Sep 2018, 01:59
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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:
15%
(low)
Question Stats:
77% (01:04) correct
23%
(01:08)
wrong
based on 102
sessions
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Not Attempted Yet
[Math Revolution GMAT math practice question]
What is the perimeter of a rectangle?
1) The square of the diagonal is \(52\).
2) The area of the rectangle is \(24\).
What is the perimeter of a rectangle?
1) The square of the diagonal is \(52\).
2) The area of the rectangle is \(24\).
20 Sep 2018, 06:43
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MathRevolution
Target question: What is the perimeter of a rectangle?
This is a good candidate for rephrasing the target question.
Let x = the length of the rectangle's base
Let y = the length of the rectangle's height
So, the perimeter of the rectangle = 2x + 2y
REPHRASED target question: What is the value of 2x + 2y?
The video below has tips on rephrasing the target question
Statement 1: The square of the diagonal is 52
In other words, (length of diagonal)² = 52
We can create a RIGHT triangle with the base, height and diagonal.
As such, we can apply the Pythagorean Theorem to write: x² + y² = 52
Is this information (x² + y² = 52) enough to determine the value of 2x + 2y?
NO.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 4 and y = 6. Notice that x² + y² = 4² + 6² = 52. In this case, the answer to the REPHRASED target question is 2x + 2y = 8 + 12 = 20
Case b: x = √51 and y = 1. Notice that x² + y² = (√51)² + 1² = 52. In this case, the answer to the REPHRASED target question is 2x + 2y = 2√51 + 2
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The area of the rectangle is 24
In other words, xy = 24
Is this information enough to determine the value of 2x + 2y?
NO.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 4 and y = 6. Notice that xy = (4)(6) = 24. In this case, the answer to the REPHRASED target question is 2x + 2y = 8 + 12 = 20
Case b: x = 2 and y = 12. Notice that xy = (2)(12) = 24. In this case, the answer to the REPHRASED target question is 2x + 2y = 4 + 24 = 28
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that x² + y² = 52
Statement 2 tells us that xy = 24, which also means 2xy = 48
Add the two red equations to get: x² + 2xy + y² = 100
Factor the left side to get: (x + y)² = 100
This means that: x + y = 10
Multiply both sides by 2 to get: 2x + 2y = 20
Perfect!!
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT
Answer: C
RELATED VIDEO
20 Sep 2018, 07:02
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What is the perimeter of a rectangle?
we require to know 2(L+B), so we have to know dimensions or SUM of dimensions
1) The square of the diagonal is \(52\).
the square of diagonal is SUM of the square of the dimensions, so \(L^2+B^2=D^2........L^2+B^2=52\) But remember that the dimensions need not be integers
there can be various combinations of L and B satisfying this..
a) L=7 and B=\(\sqrt{3}\).....\(7^2+\sqrt{3}^2=49+3=52\) but \(2(L+B)=2(7+\sqrt{3})\)
b) L=6 and B=4........\(6^2+4^2=36+16=52\) but \(2(L+B)=2(6+4)=20\)
Insuff
2) The area of the rectangle is \(24\).
area = LB = 24
L=6 and B=4 OR L=12 and B = 2
different cases
Insuff
combined..
\(L^2+B^2=52...........(L+B)^2-2LB=52\) but statement II tells us that LB is 24
so \((L+B)^2-48=52........(L+B)^2=100........\)
but perimeter can only be positive, so L+B=10 and perimeter = 2*10=20
sufficient
C
we require to know 2(L+B), so we have to know dimensions or SUM of dimensions
1) The square of the diagonal is \(52\).
the square of diagonal is SUM of the square of the dimensions, so \(L^2+B^2=D^2........L^2+B^2=52\) But remember that the dimensions need not be integers
there can be various combinations of L and B satisfying this..
a) L=7 and B=\(\sqrt{3}\).....\(7^2+\sqrt{3}^2=49+3=52\) but \(2(L+B)=2(7+\sqrt{3})\)
b) L=6 and B=4........\(6^2+4^2=36+16=52\) but \(2(L+B)=2(6+4)=20\)
Insuff
2) The area of the rectangle is \(24\).
area = LB = 24
L=6 and B=4 OR L=12 and B = 2
different cases
Insuff
combined..
\(L^2+B^2=52...........(L+B)^2-2LB=52\) but statement II tells us that LB is 24
so \((L+B)^2-48=52........(L+B)^2=100........\)
but perimeter can only be positive, so L+B=10 and perimeter = 2*10=20
sufficient
C
