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What is the value of the integer p?

Expert replies
Source: — Data Sufficiency |

by [email protected] » Sat Mar 31, 2018 11:51 am
Hi M7MBA,

We're told that P is an INTEGER. We're asked for the value of P. This question can be solved by TESTing VALUES, a bit of math knowledge and a little arithmetic.

1) P is a PRIME number.

There are LOTS of different prime numbers, so P could be 2, 3, 5, 7, etc.
Fact 1 is INSUFFICIENT

2) 88 ≤ P ≤ 95

With Fact 2, P could be any of 8 integers in the given range.
Fact 2 is INSUFFICIENT

Combined, we know...
P is PRIME
88 ≤ P ≤ 95

At this point, we have to do a little work to determine how many prime numbers are in that given range. None of the EVEN numbers are prime (since they're all divisible by 2), so we know that 88, 90, 92 and 94 are NOT prime. 95 is divisible by 5, so it's NOT prime. 93 is divisible by 3, so it's NOT prime either. That leaves us with 89 and 91. IF they're BOTH prime, then the answer is E/Neither, but IF ONLY ONE of them is prime, then the answer is C/Together. You have to do just a little more work to prove the correct answer. You don't have to try dividing any even numbers into 89 and 91 (since EVENs don't divide into ODDs). If you've already tried 3 and 5, the next logical choice would be 7. The number 91 IS divisible by 7 (7x13 = 91), so 91 is NOT prime. That leaves us with just one answer.
Combined, SUFFICIENT.

Final Answer: C

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