GMAT考题：OG2017Q-DS-262

GMAT考题

题库 / OG2017Q-DS-262

In the figure above, line segment OP has slope ~$1 \over 2$~ and line segment PQ has slope 2. What is the slope of line segment OQ ?

(1)Line segment OP has length~$2\sqrt{5}$~ .

(2)The coordinates of point Q are (5,4).

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.

考题讲解

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题目分析：

（1）设P的坐标为(x,y)，因为OP的斜率为1/2，所以有y/x=1/2即x=2y，因为OP的长为~$2\sqrt{5}$~，所以有~$x^2+y^2=20$~，~$4y^2+y^2=20$~，解得y=2，x=4，得到P的坐标为(4,2)。设Q的坐标为(a,b)，因为PQ的斜率为2，所以有~$\frac{a-4}{b-2}=2$~，只有该式无法求得a和b的值，也无法求得OQ的斜率~$\frac{b}{a}$~的值，不能求解题目。

（2）已知Q的坐标，则OQ的斜率为~$\frac{5-0}{4-0}=\frac{5}{4}$~，题目得解。

因此，本题答案为（B），仅条件2可以解题，条件1不行。

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