gmatt1476 wrote:
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 ?
(1) Country G's national debt to the nearest $1,000,000,000 is $43,000,000,000.
(2) Country G's population to the nearest 1,000,000 is 86,000,000.
DS19350.01
Let D be the debt and let P be the population. The original question: Is \(495\leq \frac{D}{P}\leq 505\) ?
1) We know that \(42{,}500{,}000{,}000\leq D<43{,}500{,}000{,}000\), but no information is given about the population. Thus, we can't get a definite answer to the original question. \(\implies\)
Insufficient2) We know that \(85{,}500{,}000\leq P<86{,}500{,}000\), but no information is given about the debt. Thus, we can't get a definite answer to the original question. \(\implies\)
Insufficient1&2) First, we check whether the maximum possible value for D/P meets the upper bound condition in the original question.
Is \(\frac{435{,}000}{855}\leq 505\) ? To answer the question, we should use multiplication rather than division.
Since (855)(505)=431,775 is not greater than 435,000 , the maximum possible value for D/P is greater than the upper bound in the original question.
Then, we check whether the minimum possible value for D/P meets the upper bound condition in the original question. It's important that we check the upper bound condition, not the lower bound condition. Imagine that it could meet the lower bound condition with or without meeting the upper bound condition.
Is \(\frac{425{,}000}{865}\leq 505\) ?
Since (865)(505)=436,825 is greater than 425,000 , the minimum possible value for D/P is not greater than the upper bound in the original question.
Thus, we can't get a definite answer to the original question. \(\implies\)
InsufficientAnswer: E