Can the positive integer p be expressed as the product of two integers

Question

Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?

(1) p is odd.
(2) 41 < p < 49

chetan2u · Answer

The wordings can be rewritten as 
Is p a composite number?
So look for whether p is prime.

1) p is odd
3, 5, 7......NO
9,15, 21....yes

2) 41<p<49
47....no
42, 45....yes

Combined
45....yes
43, 47...no

E

adamfunk · Answer

For DS questions, I ALWAYS try to prove the statement insufficient by getting two opposing answers to the question stem.

Back to the question, "Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?"
For each statement I'm looking for a positive integer that provides the answer "Yes" and a positive integer that provides the answer "No" to this question.

(1) p is odd.

3 = 1 * 3, NO
15 = 3 * 5, YES
Not Sufficient

(2) 41 < p < 49
43 = 1 * 43, NO
45 = 5 * 9, YES
Not sufficient

Both statements combined still leave me with 43 and 45 as possible integers for p making the correct answer E.

exc4libur · Answer

(1) insufic
p=3: 3x1 no
p=6: 2x3 yes

(2) insufic
p=42: 2x21 yes
p=43: 43x1 no

(1/2) insufic
p=45: 5x9 yes
p=43: 43x1 no

(E)

SairamRamo · Answer

A number can be represented as either product of 1 and the number itself, or by factorizing it

S1 p is odd.

We can definitively say that the positive integer p be expressed as the product of two integers, each of which is greater than 1

S1 not sufficient

(2) 41 < p < 49

Primes number (43, 47) can be expressed as a product of 2 integers, one of them being 1
whereas composite number (42, 45, 46, 48) can be represented as either product of 1 and the number itself, or by factorizing it

S2 not sufficient

S1 + S2 -> we boil down N = 43, 45, 47

in case of 43,47 -> They cannot be represented as a product of 2 numbers without using 1

whereas 45 -> Can be represented as a product of 2 numbers without using 1

S1 + S2 : Not sufficient

IMO E

carouselambra · Answer

IMO E

Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?
<Question stem basically asks if p is a composite number>

(1) p is odd.
Not sufficient - p can be 3,9,13,15..

(2) 41 < p < 49
Not sufficient - p can be 42,43,44,45...48

Combining - p=43,45,47
While we know that 43 and 47 are prime, we also know that 45 can be expressed in the form of its factors.
Hence, not sufficient.

GCMEMBER · Answer

Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?

(1) p is odd.

For p = 3, 3 = 1*3
p can not be expressed as the product of two integers, each of which is greater than 1

For p = 15, 15 = 3*5
p can be expressed as the product of two integers, each of which is greater than 1
Not sufficient

(2) 41 < p < 49

For p = 42, 42 = 2*21
p can be expressed as the product of two integers, each of which is greater than 1

For p = 43, 43 = 1*43
p can not be expressed as the product of two integers, each of which is greater than 1
Not sufficient

(1) + (2)

For p = 43, 43 = 1*43
p can not be expressed as the product of two integers, each of which is greater than 1
Not sufficient

For p = 45, 45 = 5*9
p can be expressed as the product of two integers, each of which is greater than 1
Not sufficient

Option E

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Can the positive integer p be expressed as the product of two integers

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GMAT Data Sufficiency (DS) Questions

Can the positive integer p be expressed as the product of two integers

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