2. 外语
  3. If m and n are positive integers, what is the value of 3/m+n/4? (1) mn = 12 (2) 3/m is in lowest terms and n/4 is in lowest term

If m and n are positive integers, what is the value of 3/m+n/4? (1) mn = 12 (2) 3/m is in lowest terms and n/4 is in lowest term

admin2022-10-18  23
问题 If m and n are positive integers, what is the value of 3/m+n/4?
(1) mn = 12
(2) 3/m is in lowest terms and n/4 is in lowest terms.
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 (1)    If m = 1 and n = 12, then m and n are positive integers, mn = 12, and 3/m + n/4=6.
However, if m = 3 and n = 4, then m and n are positive integers, mn = 12 and 3/m + n/4=2;
NOT sufficient.
(2)    If m = 2 and n = 1, then m and n are positive integers,
3/m and n/4 are in lowest terms, and 3/m + n/4=3/2+1/4. However, if m = 2 and n = 3, then w and n are positive integers, 3/m + n/4 are in lowest terms, and 3/m + n/4=3/2+3/4;
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 3/m + n/4.

The correct answer is C;
both statements together are sufficient.
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