If p is a prime number, what is the value of p? (1) 10

Question

If p is a prime number, what is the value of p?

(1) 10 < p - 3 < 16
(2) p^2 = 289

KSBGC · Answer

p is a prime no.

statement 1: 10<p-3<16
 =10+3<p-3+3<16+3 ( by adding 3)
 =13<p<19
we get the perfect range here. the only prime between 13 and 19 is 17. sufficient.

statement 2: P^2=289. we know that (+-)17^2=289.
since 289 is the result of a perfect square p could be negative or positive. but it is mentioned that p is a prime. thus p is +17.

The correct answer is D.

benejo · Answer

(1) Only prime in the range is 17.
(2) 17^2 = 289

Answer (D)

US09 · Answer

IMO D.

1) Straightaway p=17. Sufficient.
2) P=+/-17, but it is given that p is a prime number and prime numbers are not negative. Therefore, p=17. Sufficient.

Mo2men · Answer

As stated in question stem that p is prime, so statement 2 is sufficient as 17 is the only prime.

KSBGC · Answer

as far as i know prime can't be negative. Thus statement 2 is not sufficient. in statement 2 we have both positive and negative value for p.

Mo2men · Answer

You are totally right but the question stated, 'If p is a prime number,...' so it is for certain p is prime. The statement 2 gives you 2 solution one is prime and other is not. So pick the prime one. It is the same problem when you see 'if x is positive....., what is value of x? Here , Statement 2 gives you 17 & -17 but it is sufficient because it is stated that x is positive.

If the question does not state that prime, then statement 2 is insufficient.

According the question p is prime, but statement 2 gives you, for example, 2 solutions 13 & 17, then statement 2 is insufficient.

I hope it helps

If p is a prime number, what is the value of p? (1) 10 < p - 3 < 16

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