What is the perimeter of rectangle R ?
(1) R is a square.
(2) The area of R is 36.
OA is C
Please explain
What is the perimeter of rectangle R ?
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- sachin_yadav
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Target question: What is the perimeter of rectangle R?sachin_yadav wrote:What is the perimeter of rectangle R?
(1) R is a square.
(2) The area of R is 36.
Statement 1: R is a square
Since R can be a square of ANY SIZE, then it can have ANY perimeter.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Aside: A square is a TYPE of rectangle
Statement 2: The area of R is 36
There are MANY rectangles that satisfy this condition. Here are two:
Case a: rectangle R could have height 6 and width 6 (so the area is 36), in which case the perimeter is 24
Case b: rectangle R could have height 3 and width 12 (so the area is 36), in which case the perimeter is 30
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that R is a square
Statement 2 tells us that this SQUARE has area 36
There's ONLY ONE square in the universe that has area 36, and that's a square in which all sides have length 6. If all sides have length 6, then the perimeter of R is 24
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
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Hi sachin_yadav,
You'll notice that Brent's approach focused heavily on considering the multiple possibilities that could fit each piece of information (the 2 Facts underneath the prompt). This approach is a rather important part of getting DS questions correct, so you should be thinking about whether a given Fact leads to just one possible answer or if it leads to more than one possible answer. Get in the habit of taking notes, drawing pictures and proving what's possible. You'll see your score improves significantly as a result.
GMAT assassins aren't born, they're made,
Rich
You'll notice that Brent's approach focused heavily on considering the multiple possibilities that could fit each piece of information (the 2 Facts underneath the prompt). This approach is a rather important part of getting DS questions correct, so you should be thinking about whether a given Fact leads to just one possible answer or if it leads to more than one possible answer. Get in the habit of taking notes, drawing pictures and proving what's possible. You'll see your score improves significantly as a result.
GMAT assassins aren't born, they're made,
Rich
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Question : What is the perimeter of rectangle R?sachin_yadav wrote:What is the perimeter of rectangle R ?
(1) R is a square.
(2) The area of R is 36.
Please explain
Let, L be the Length and W be the Width of the rectangle then
Question Rephrased : 2(L+W) = ?
Statement 1) R is a square
i.e L = w therefore perimeter = 2(L+W) = 2(L+L) = 4L
But L is unknown therefore INSUFFICIENT
Statement 2) The area of R is 36
i.e. LxW = 36
Case 1: L = 6 and W = 6 then Perimeter = 2(L+W) = 24
Case 2: L = 9 and W = 4 then Perimeter = 2(L+W) = 26
INCONSISTENT Answer Therefore INSUFFICIENT
Combining the Two statements
L = W and LxW = 36
i.e. L^2 = 36 i.e. L = W = 6
Therefore, Perimeter = 2(L+W) = 2(6+6) = 24
SUFFICIENT
Answer: Option C
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