GMAT OG2019 数学DS新题第238题(附解析)

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238. Each of the 256 solid-colored marbles in a box is either blue, green, or purple What is the ratio of the number of blue marbles to the number of purple marbles in the box ?

(1) The number of green marbles in the box is 4 times the number of blue marbles in the box.

(2) There are 192 green marbles in the box.

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

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

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

D. Each statement ALONE is sufficient.

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

题目大意

一个盒子里256个纯色的玻璃球,要么是蓝的,要么是绿的,要么是紫的。蓝色玻璃球的数量与盒子里紫色玻璃球的数量之比是多少?

(1) 盒子里的绿色玻璃球数是盒子里蓝色玻璃球数的4倍。

(2) 盒子里有192个绿色的玻璃球。

解题思路

(1) 绿球是蓝球的4倍,无法求出篮球和紫球的数量之比,条件不充分;

(2) 盒子里有192个绿球,无法求出篮球和紫球的数量之比,条件不充分;

(1) +(2),设蓝球是x个,则绿球为4x = 192,求得x = 48,所以蓝球有48个。

紫球的数量=总量-蓝球-绿球 = 256 - 192 - 48 = 16

蓝球数量:紫球数量 = 48:16 = 3:1。条件充分。

正确答案: C

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