Number properties - how do I even start?

Question

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

Patrick_GMATFix · Answer

The only integers who cannot be expressed as the product of two integers greater than 1 are prime numbers. So this question is asking "is p non-prime?". Statement (1) is SUFFICIENT since all integers between 31 and 37 are non-primes. According to statement (2), p may be prime (3) or non-prime (21), so that statement is NOT SUFFICIENT. The answer is A. I go through the question in detail in the full solution below (taken from the GMATFix App).

-Patrick

Brent@GMATPrepNow · Answer

LulaBrazilia wrote: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

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 free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

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 target question is the same 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 target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Pazoki · Answer

Brent@GMATPrepNow wrote:LulaBrazilia wrote: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 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 target question with certainty, statement 2 is NOT SUFFICIENT Hi Brent, In stem question we see, is P can be products of 2 integer greater than 1? 1) is Sufficient, ok. 2) P is odd. then P can not be 3 because P is a multiple of two integer greater than 1 which at least is 3*3=9, am I right? Thanks

MartyMurray · Answer

Pazoki wrote:In stem question we see, is P can be products of 2 integer greater than 1?

1) is Sufficient, ok.
2) P is odd. then P can not be 3 because P is a multiple of two integer greater than 1
which at least is 3*3=9, am I right?

Pazoki,

When reading questions you have to be careful to determine whether what said is information or a question.

You have incorrectly taken what is actually a question and used it as information.

The question asks whether p is a multiple of two integers greater than 1. It does not include information indicating that p must be a multiple of two integers greater than 1.

Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.

OptimusPrep · Answer

LulaBrazilia wrote: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

Required: Can p be expressed as the product of two integers, each of which is greater than 1
Or is p = x*y, where x and y are greater than 1.
This means p can have the numbers that are not prime, since a prime number has only 2 factors: 1 and the number itself.

Statement 1: 31 < p < 37
Values of p can be = 32, 33, 34, 35, 36
None of these is prime, hence p can be written as a product of x and y
SUFFICIENT

Statement 2: p is odd.
Odd numbers can both be prime and non prime
INSUFFICIENT

Correct Option: A

OptimusPrep · Answer

Pazoki wrote: 1) is Sufficient, ok.
2) P is odd. then P can not be 3 because P is a multiple of two integer greater than 1
which at least is 3*3=9, am I right?

Thanks

You are talking about just the opposite thing.
The question asks if P can be written as a multiple of two integers > 1
3 = 1*3. This cannot be written as a product of two integers > 1
Where as 9 = 3*3, this can be written as a product of two integers > 1
Hence we cannot say anything about p.
INSUFFICIENT

Matt@VeritasPrep · Answer

Pazoki wrote: In stem question we see, is P can be products of 2 integer greater than 1? Yup! Rephrased, this asks whether p is composite, since it would have TWO factors other than itself and one (at least one of which is unique, since it could be a square, as you mention).

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