题目信息
A country's per capita national debt is its national debt divided by its population. Is the per capita national debt of Country G within $5 of $500 ?
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：
E:Statements (1) and (2) TOGETHER are NOT sufficient.
Arithmetic Estimation
Briefly, the question is whether
495 ≤
≤ 505 is true.
We are given that 42.5 billion ≤ debt < 43.5 billion. However, no information is given about the population; NOT sufficient. We are given that 85.5 million ≤ population < 86.5 million. However, no information is given about the debt; NOT sufficient.
Given (1) and (2), then to determine whether
lies between 495 and 505, we will investigate the minimum possible value of 
and the maximum possible value of 
. To simplify the discussion that follows, we will assume that the upper bounds given in (1) and (2) can be achieved. This will not affect our conclusions because with this assumption, the estimates we obtain will still justify our conclusions. The minimum possible value of 
is 
× 1,000. Since 
, which is less than 
, it follows that the minimum possible value of 
is less than 
× 1,000 = 500 − 5 = 495. The maximum possible value of 
is 
. Since 
, which is greater than 
, it follows that the maximum possible value of 
is greater than 
× 1,000 = 500 + 5 = 505.
Since the minimum possible value of
is less than 495 and the maximum possible value of 
is greater than 505, it is not possible to determine whether or not 
lies between 495 and 505.
The correct answer is E;both statements together are still not sufficient.
Briefly, the question is whether
495 ≤
≤ 505 is true.We are given that 42.5 billion ≤ debt < 43.5 billion. However, no information is given about the population; NOT sufficient. We are given that 85.5 million ≤ population < 86.5 million. However, no information is given about the debt; NOT sufficient.
Given (1) and (2), then to determine whether
lies between 495 and 505, we will investigate the minimum possible value of and the maximum possible value of . To simplify the discussion that follows, we will assume that the upper bounds given in (1) and (2) can be achieved. This will not affect our conclusions because with this assumption, the estimates we obtain will still justify our conclusions. The minimum possible value of is × 1,000. Since , which is less than , it follows that the minimum possible value of is less than × 1,000 = 500 − 5 = 495. The maximum possible value of is . Since , which is greater than , it follows that the maximum possible value of is greater than × 1,000 = 500 + 5 = 505.Since the minimum possible value of
is less than 495 and the maximum possible value of is greater than 505, it is not possible to determine whether or not lies between 495 and 505.The correct answer is E;both statements together are still not sufficient.
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