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
I know that the correct answer is A ( i.e. statement 1 is sufficient.) But somehow I am not being able to get this. Can someone please explain the solution?
Regards,
Ani
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All the numbers from 32 to 36 can be expresses as the product of 2 integers
es: 32=8x4
33=11x3
34=2x17
35=5x 7
36=12x3
and all integers are greater that 1. So, Stat 1 is sufficient
Stat 2:
p is odd:
p=3 can be written by 1x3 but one of the 2 integers is not greater than 1 (indeed is 1)
if p=35 can be expressed by 5x7
Stat 2: is not sufficient
this is my reasoning to answer this question.. I don t know if this can help!
es: 32=8x4
33=11x3
34=2x17
35=5x 7
36=12x3
and all integers are greater that 1. So, Stat 1 is sufficient
Stat 2:
p is odd:
p=3 can be written by 1x3 but one of the 2 integers is not greater than 1 (indeed is 1)
if p=35 can be expressed by 5x7
Stat 2: is not sufficient
this is my reasoning to answer this question.. I don t know if this can help!
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When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.ani781 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
