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09 Oct 2023, 09:38
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For how many integer values of \(n\) does the expression \(\frac{100}{n - 7}\) yield an integer?
A. 4
B. 9
C. 12
D. 16
E. 18
A. 4
B. 9
C. 12
D. 16
E. 18
09 Oct 2023, 09:38
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Official Solution:
For how many integer values of \(n\) does the expression \(\frac{100}{n - 7}\) yield an integer?
A. 4
B. 9
C. 12
D. 16
E. 18
Given that \(n\) is an integer, \(\frac{100}{n - 7}\) will be an integer if \(n-7\) is a divisor of 100. Upon factorizing 100, we find \(100 = 2^2*5^2\). Thus, 100 has \((2+1)(2+1) = 9\) positive divisor. However, there are an equal number of negative divisors. Therefore, \(\frac{100}{n - 7}\) will be an integer for 18 values of \(n-7\), and consequently for 18 values of \(n\).
Answer: E
For how many integer values of \(n\) does the expression \(\frac{100}{n - 7}\) yield an integer?
A. 4
B. 9
C. 12
D. 16
E. 18
Given that \(n\) is an integer, \(\frac{100}{n - 7}\) will be an integer if \(n-7\) is a divisor of 100. Upon factorizing 100, we find \(100 = 2^2*5^2\). Thus, 100 has \((2+1)(2+1) = 9\) positive divisor. However, there are an equal number of negative divisors. Therefore, \(\frac{100}{n - 7}\) will be an integer for 18 values of \(n-7\), and consequently for 18 values of \(n\).
Answer: E
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miag
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Schools: Anderson '26 (A) Haas '26 (A) Kellogg '26 (A)
GMAT Focus 1: 675 Q87 V83 DI80
Posts: 403
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15 Apr 2025, 08:56
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this was a great question!
