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24 Sep 2023, 13:44
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E
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For how many integer values of n does the expression 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
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24 Sep 2023, 14:01
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Bunuel
100/(n - 7) = integer → (n-7) is a factor of 100
\(100 = 2^2*5^2\)
Total number of factors = 3 * 3 = 9 ⇒ The 9 values represent positive values of the denominator. We can also have a negative denominator. Hence 9 * 2 = 18
n - 7 = 1 → n = 8
n - 7 = 2 → n = 9
n - 7 = 4 → n = 11
n - 7 = 5 → n = 12
n - 7 = 10 → n = 17
n - 7 = 20 → n = 27
n - 7 = 25 → n = 32
n - 7 = 50 → n = 57
n - 7 = 100 → n = 107
n - 7 = -1 → n = 6
n - 7 = -2 → n = 5
n - 7 = -4 → n = 3
n - 7 = -5 → n = 2
n - 7 = -10 → n = -3
n - 7 = -20 → n = -13
n - 7 = -25 → n = -18
n - 7 = -50 → n = -43
n - 7 = -100 → n = -93
Option E
09 Oct 2023, 09:40
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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
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 more fresh GMAT Club Tests questions check this post: Boost Your GMAT Quant Score with Our Practice Questions.
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 more fresh GMAT Club Tests questions check this post: Boost Your GMAT Quant Score with Our Practice Questions.
