题目信息
If m and n are positive integers, what is the value of 
+ 
?
+ ?
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.
参考答案及共享解析
共享解析来源为网络权威资源、GMAT高分考生等； 如有疑问，欢迎在评论区提问与讨论
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已选答案：
正确答案：
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Arithmetic Fractions
If m = 1 and n = 12, then m and n are positive integers, mn = 12, and
= 6. However, if m = 3 and n = 4, then m and n are positive integers, mn = 12, and 
= 2; NOT sufficient.
If m = 2 and n = 1, then m and n are positive integers, 
and 
are in lowest terms, and 
. However, if m = 2 and n = 3, then m and n are positive integers, 
and 
are in lowest terms, and 
; NOT sufficient.
Given (1) and (2), the table below shows that only one possibility exists for the values of m and n, and hence there is only one possible value of
.
The correct answer is C;both statements together are sufficient.
If m = 1 and n = 12, then m and n are positive integers, mn = 12, and
= 6. However, if m = 3 and n = 4, then m and n are positive integers, mn = 12, and = 2; NOT sufficient.
If m = 2 and n = 1, then m and n are positive integers, and are in lowest terms, and . However, if m = 2 and n = 3, then m and n are positive integers, and are in lowest terms, and ; NOT sufficient.Given (1) and (2), the table below shows that only one possibility exists for the values of m and n, and hence there is only one possible value of
.| (m,n) |  lowest terms? |
 lowest terms? |
| (1,12) |  , YES |
 , NO |
| (2,6) |  , YES |
 , NO |
| (3,4) |  , NO |
 , NO |
| (4,3) |  , YES |
 , YES |
| (6,2) |  , NO |
 , NO |
| (12,1) |  , NO |
 , YES |
The correct answer is C;both statements together are sufficient.
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