VJesus12 wrote: ↑Fri Jul 09, 2021 11:31 am
Can the positive integer \(p\) be expressed as the product of two integers, each of which is greater than \(1?\)
(1) \(31 < p < 37\)
(2) \(p\) is odd.
Answer:
A
Source: Official Guide
Target question: Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?
This question is a great candidate for
rephrasing the target question.
If an integer p can be expressed as the product of two integers, each of which is greater than 1, then that integer is a composite number (as opposed to a prime number). So . . . .
REPHRASED target question:
Is integer p a composite number?
Aside: We have a video with tips on rephrasing the target question (below)
Statement 1: 31 < p < 37
There are 5 several values of p that meet this condition. Let's check them all.
p=32, which means
p is a composite number
p=33, which means
p is a composite number
p=34, which means
p is a composite number
p=35, which means
p is a composite number
p=36, which means
p is a composite number
Since the answer to the
REPHRASED target question is the SAME ("yes, p IS a composite number") for every possible value of p, statement 1 is SUFFICIENT
Statement 2: p is odd
There are several possible values of p that meet this condition. Here are two:
Case a: p = 3 in which case
p is not a composite number
Case b: p = 9 in which case
p is a composite number
Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer : A
