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In the trapezoid above with height \(x,\) the sides with measures \(y\) and \(z\) are parallel. What is the area of the

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In the trapezoid above with height \(x,\) the sides with measures \(y\) and \(z\) are parallel. What is the area of the

by Gmat_mission » Sun Jun 06, 2021 10:31 am

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In the trapezoid above with height \(x,\) the sides with measures \(y\) and \(z\) are parallel. What is the area of the trapezoid?

(1) \(z+y = \dfrac{20}{x}\)

(2) \(x=2\)

Answer: A

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Source: — Data Sufficiency |

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Re: In the trapezoid above with height \(x,\) the sides with measures \(y\) and \(z\) are parallel. What is the area of

by Ian Stewart » Tue Jun 08, 2021 4:27 am

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One way to find the area of a trapezoid is to average the lengths of the parallel sides, then multiply that average by the height. Applying that here, the area we want to find is

[ (z +y)/2 ] * x

and now in Statement 1, if we multiply both sides by x, and divide both sides by 2, the left side will look exactly like the expression above:

z + y = 20/x
(z + y)(x) = 20
[(z + y)/2] * x = 10

so Statement 1 is sufficient. Statement 2 is clearly insufficient, so the answer is A.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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