nafishasan60 wrote:

P is a prime number. If 6p is between 15 and 95, which of the following can be a value of 7p + 2?

A. 15

B. 79

C. 121

D. 65

E. 21

If p is 3, then 6p is 18.

If p is 13, then 6p is 78.

So p must be between 3 and 13, inclusive, and thus 7p + 2 must be between 23 and 93, inclusive. We see that both answer choices B 79 and D 65 are between 23 and 93.

If 7p + 2 = 79, then 7p = 77 and p = 11.

If 7p + 2 = 65, then 7p = 63 and p = 9.

Since p = 11 is a prime (and p = 9 is not a prime), then 7p + 2 = 79.

Alternate Solution:

Let’s test each answer choice:

A) 7p + 2 = 15

If 7p + 2 = 15, then 7p = 13 and p is not an integer.

B) 7p + 2 = 79

If 7p + 2 = 79, then 7p = 77 and p = 11. We see that 6p = 66 is between 15 and 95; therefore B is the correct choice.

Answer: B

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