If \(k = (n + 2)(n - 2),\) where \(n\) is an integer value greater than \(2,\) what is the value of \(k?\)

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If \(k = (n + 2)(n - 2),\) where \(n\) is an integer value greater than \(2,\) what is the value of \(k?\)

(1) \(k\) is the product of two primes
(2) \(k < 100\)

Answer: E

Source: Official Guide

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VJesus12 wrote:
Thu Sep 16, 2021 11:52 am
If \(k = (n + 2)(n - 2),\) where \(n\) is an integer value greater than \(2,\) what is the value of \(k?\)

(1) \(k\) is the product of two primes
(2) \(k < 100\)

Answer: E

Source: Official Guide
Let us begin with (2)
\((n-2) \ast (n+2) = n^2 - 4\)
since \(k<100\) we have \(96, 77, 60, 45, 32, 21, 12, 5\) Not sufficient \(\Large{\color{red}\chi}\)

For (1); from the above list we have \(7\times 11, 7\times 3\) in addition to possible numbers \(>100\); hence, not sufficient \(\Large{\color{red}\chi}\)

(1) & (2) together we have \(77, 21\) Not sufficient \(\Large{\color{red}\chi}\)

Therefore, E