2. 外语
  3. If x and y are integers, is xy + 1 divisible by 3 ? (1) When x is divided by 3, the remainder is 1. (2) When y is divided by 9,

If x and y are integers, is xy + 1 divisible by 3 ? (1) When x is divided by 3, the remainder is 1. (2) When y is divided by 9,

admin2022-10-18  74
问题 If x and y are integers, is xy + 1 divisible by 3 ?
(1) When x is divided by 3, the remainder is 1.
(2) When y is divided by 9, the remainder is 8.
选项 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.
答案C
解析 Determine whether xy+ 1 is divisible by 3, where x and y are integers.
(1)     It is given that the remainder is 1 when x is divided by 3. It follows that x = 3q + 1 for some integer q. So, xy + 1 = (3q + l)y + 1. If y = 2, then xy + 1 = 6q + 3, which is divisible by 3. However, if y = 1, then xy + 1 = 3q + 2, which is not divisible by 3; NOT sufficient.
(2)     It is given that the remainder is 8 when y is divided by 9. It follows that y = 9r + 8 for some integer r. So, xy + 1 = (9r + 8)x + 1. If x = 1, then xy+1 = 9r+9, which is divisible by 3. However, if x = 2, then xy + 1 = 18r + 17, which is not divisible by 3; NOT sufficient.
Taking (1) and (2) together gives x = 3q + 1 and y = 9r + 8, from which it follows that xy + 1 = (3q+l)(9r+8) + l = 27qr+9r+24q + 9 = 3(9qr + 3r +8q + 3), which is divisible by 3.
The correct answer is C;
both statements together are sufficient.
转载请注明原文地址:https://www.kaotiyun.com/show/dttO777K
本试题收录于： GMAT QUANTITATIVE题库GMAT分类
0

GMAT QUANTITATIVE

GMAT

相关试题推荐
随机试题
最新回复(0)