fulanoian wrote:
Hi Bunuel! Why is it D (16) and not E (18) if 18 values satisfy the condition that 100/ (n-7) is an integer? What am I missing?Thanks!
Bunuel wrote:
OfficialSolution:
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:D
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:D
Yes, 18 corresponds to E, not D. Edited. Thank you!
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Statistics : Posted by Bunuel • on 09 Oct 2023, 09:38 • Replies 3 • Views 394
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