msbandi4321 wrote:

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

My approach:

Given that K=(N+2)(N-2) and according to statement 1 K is the product of two prime numbers then (N+2) = prime and (N-2)= prime. I interpret that to mean that N is two intervals away from 2 prime numbers, the only example I could think of to fit this description would be (5+2)(5-2) (7)(3) = 21. What other prime numbers would fit this description? Where am I going wrong on this statement? Should I just assume that there will be more prime numbers to fit this premise? Am I supposed to remember prime numbers past 100? I see the second statement says that K<100 and I realize that the statement is clearly insufficient on its own so I selected "A."

OA is "E"

Can someone explain where I am going wrong with this one?

Thanks in advance.

OA: E

Given: \(k = (n + 2)(n - 2)\) and \(n>2\)

(1) \(k\) is the product of two primes

Difference between Two primes would be \((n+2)-(n-2)= n+2-n+2=4\), Primes number can \({3,7};{7,11};\).....

as there is no unique value of \(k\) , \(k\) can be \(21,77\) or ......

So Statement \(1\) alone is not sufficient.

(2) \(k < 100\)

\(k\) can be \(1,2,3,4\)...............

There is no unique value of \(k\) , so Statement \(2\) alone is not sufficient.

Combining (1) and (2), we get

\(k\) can be 21 or 77, so combining (1) and (2) also is insufficient to give unique value of \(k\)

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