题目信息
If S is the sum of the first n positive integers, what is the value of n ?
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
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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 Sequences and series
Given that S < 20, n could be 5 since
= 
= 15 < 20. However, n could also be 4 since 
= 
= 10 < 20; NOT sufficient.
Given that S2 > 220, n could be 5 since 
= 
= 15 and 152 = 225 > 220. However, n could also be 6 since 
= 21 and 212 = 441 > 220; NOT sufficient.
Given (1) and (2) together, it is clear from the following table that n = 5.
The correct answer is C;both statements together are sufficient.
Given that S < 20, n could be 5 since
= = 15 < 20. However, n could also be 4 since = = 10 < 20; NOT sufficient.
Given that S2 > 220, n could be 5 since = = 15 and 152 = 225 > 220. However, n could also be 6 since = 21 and 212 = 441 > 220; NOT sufficient.Given (1) and (2) together, it is clear from the following table that n = 5.
| n | S | S2 | allowed/not allowed |
| ≤ 4 | ≤ 10 | ≤ 100 | not allowed by (2) |
| 5 | 15 | 225 | allowed by (1) and (2) |
| ≥ 6 | ≥ 21 | ≥ 441 | not allowed by (1) |
The correct answer is C;both statements together are sufficient.
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