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Intern  B
Joined: 15 Jan 2018
Posts: 17
Location: India
If p and q are positive integers, is pq a prime number?  [#permalink]

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1
1 00:00

Difficulty:   25% (medium)

Question Stats: 69% (00:51) correct 31% (00:42) wrong based on 34 sessions

### HideShow timer Statistics If p and q are positive integers, is pq prime number?

(1) p > 2
(2) q is a prime number.

Retired Moderator D
Joined: 30 Jan 2015
Posts: 805
Location: India
Concentration: Operations, Marketing
GPA: 3.5
Re: If p and q are positive integers, is pq a prime number?  [#permalink]

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Gaara2018 wrote:
If p and q are positive integers, is pq prime number?

1. p>2
No information about q, p could be 3, 4, 5, 6, ....
Insufficient

2. q is a prime number.
No information about p, q could be 2, 3, 5, 7, ...
Insufficient

Combining both:
p * q = not a prime integer (in either of the above cases)
Sufficient

Hence, C.
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The few, the fearless !

Thanks Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: If p and q are positive integers, is pq a prime number?  [#permalink]

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Gaara2018 wrote:
If p and q are positive integers, is pq prime number?
1. p>2
2. q is a prime number.

Not a 700 level question..
pq will be prime if one of them is 1 and other a prime..
1) p>2
If p is 3 and q is 1.... yes
If p is 4 and q anything else....No
Insufficient

2) q is prime
Depend on p..
If p is 1... Yes otherwise No
Insufficient

Combined
Both p and q are >1
Ans is always No
Sufficient

C
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Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3359
Location: India
GPA: 3.12
Re: If p and q are positive integers, is pq a prime number?  [#permalink]

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Gaara2018 wrote:
If p and q are positive integers, is pq prime number?
1. p>2
2. q is a prime number.

1. p>2
Case 1: p = 3, q = 1 | pq is prime
Case 2: p = 4, q = 1 | pq is not prime (Insufficient)

2. q is a prime number.
Case 1: p = 1, q = 2 | pq is prime
Case 2: p = 2, q = 3 | pq is not prime (Insufficient)

By combining the information present in both the sentences, the minimum
value that p can take is 3 and if q is a prime number, the minimum value q
takes is 2. In such a case, the number pq is never prime (Sufficient - Option C)

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You've got what it takes, but it will take everything you've got Re: If p and q are positive integers, is pq a prime number?   [#permalink] 10 Aug 2018, 00:33
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# If p and q are positive integers, is pq a prime number?  