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24 Oct 2019, 01:10
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D
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Difficulty:
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76% (01:11) correct
24%
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wrong
based on 54
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If the length of a rectangle is 1 greater than the width of the rectangle, what is the perimeter of the rectangle?
(1) The length of the diagonal of the rectangle is 5.
(2) The area of the rectangular region is 12.
(1) The length of the diagonal of the rectangle is 5.
(2) The area of the rectangular region is 12.
24 Oct 2019, 13:16
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If L and W are the length and width, we know L = W + 1. Using Statement 1, we know that W, W+1 and 5 are, in increasing order, the three sides of a right triangle. That must be the 3-4-5 triangle, since only one value of W is possible (if the two short sides of a right triangle are W and W+1, then the larger W is, the larger the hypotenuse will be, so for only one value of W can the hypotenuse be 5). So Statement 1 lets us find the lengths of the sides of the rectangle, and thus the perimeter.
For Statement 2, we know (W)(W+1) = 12, and again since W > 0, only one value of W can make this equation work, since as W gets bigger, the left side gets bigger overall, and for only one positive value of W will the left side equal 12. We can see W = 3 works, so again we know the dimensions of the rectangle, and the answer is D.
For Statement 2, we know (W)(W+1) = 12, and again since W > 0, only one value of W can make this equation work, since as W gets bigger, the left side gets bigger overall, and for only one positive value of W will the left side equal 12. We can see W = 3 works, so again we know the dimensions of the rectangle, and the answer is D.
24 Oct 2019, 15:28
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I thought both statements are forming quadratic equations .Hence answer should be C.Can GMAT give such questions which will be based on actually solving equations??
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