Difference between revisions of "1994 AJHSME Problems/Problem 10"
Mrdavid445 (talk | contribs) (Created page with "==Problem== For how many positive integer values of <math>N</math> is the expression <math>\dfrac{36}{N+2}</math> an integer? <math>\text{(A)}\ 7 \qquad \text{(B)}\ 8 \qquad \t...") |
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<math>\text{(A)}\ 7 \qquad \text{(B)}\ 8 \qquad \text{(C)}\ 9 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 12</math> | <math>\text{(A)}\ 7 \qquad \text{(B)}\ 8 \qquad \text{(C)}\ 9 \qquad \text{(D)}\ 10 \qquad \text{(E)}\ 12</math> | ||
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| + | ==Solution== | ||
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| + | We should list all the positive divisors of 36 and count them. By trial and error, the divisors of 36 are found to be 1,2,3,4,6,9,12,18,36, for a total of 9. However, 1 and 2 can't be expressed as N+2 for POSITIVE integer N, so there are 7 possibilities. <math>\text{(A)}</math> | ||
Revision as of 13:23, 5 July 2012
Problem
For how many positive integer values of 
is the expression 
an integer?
Solution
We should list all the positive divisors of 36 and count them. By trial and error, the divisors of 36 are found to be 1,2,3,4,6,9,12,18,36, for a total of 9. However, 1 and 2 can't be expressed as N+2 for POSITIVE integer N, so there are 7 possibilities. 
