GMAT考题：OG2017Q-DS-247

GMAT考题

What is the area of rectangular region R ?

(1) Each diagonal of R has length 5.

(2) The perimeter of R is 14.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

毕出

题目分析：

设长方形长为x宽为y，题目求xy的值。

（1）对角线长为5，根据勾股定理有，~$x^2+y^2=25$~，无法确定xy的值。

（2）长方形的周长为14，即2(x+y)=14，x+y=7，也无法确定xy的值。

结合条件1和条件2，将x+y=7两边平方得~$x^2+2xy+y^2=49$~，又因为~$x^2+y^2=25$~，所以有2xy=49-25=24，即xy=12。长方形面积为12。

因此，本题答案为（C），两个条件结合起来才能解题，任何单独一个均不行。

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