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21 Sep 2019, 15:12
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
57% (02:12) correct
43%
(02:00)
wrong
based on 1992
sessions
History
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Time
Result
Not Attempted Yet
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
(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
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22 Sep 2019, 15:41
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gmatt1476
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. \(\implies\) Insufficient
2) 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. \(\implies\) Insufficient
1&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. \(\implies\) Insufficient
Answer: E
23 Oct 2020, 13:03
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gmatt1476
To make the math easier, let's ignore the last six 0's in each statement, as follows:
1. Country G's national debt to the nearest $1,000 is $43,000
2. Country G's population to the nearest integer is 86
Each statement on its own is clearly insufficient.
Statements combined:
Case 1: National debt = 43,000 and population = 86
Per capita debt \(= \frac{43,000}{86} = 500\)
In this case, the answer to the question stem is YES.
The question stem will be NO if the per capita debt exceeds 505.
Since \(\frac{43,000}{86} = 500\), \(\frac{43,000}{86} + \frac{5.1*86}{86} = 500 + 5.1 = 505.1\)
Case 2: National debt = 43,000 + 5.1*86 = 43,438.6 and population = 86
As shown in the blue statement above, per capita debt = 505.1
In this case, the answer to the question stem is NO.
Since the answer is YES In Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.
