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Math Expert V
Joined: 02 Sep 2009
Posts: 64138
If p and q are positive integers, is pq prime number?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 68% (01:03) correct 32% (01:05) wrong based on 50 sessions

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

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

Project DS Butler Data Sufficiency (DS3)

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GMAT Club Legend  V
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Re: If p and q are positive integers, is pq prime number?  [#permalink]

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

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

Project DS Butler Data Sufficiency (DS3)

Question: Is pq = Prime?

Statement 1: p > 2

p may be 3 (prime) or 4 (non-prime) and no information about q hence

NOT SUFFICIENT

Statement 2: q is a prime number.

NOT SUFFICIENT

COmbinig

P > 2 and q = Prime

i.e. p*q can NOT be prime cause Prime numbers can be written only in 1*Prime form where one of the numbers must be 1 hence

SUFFICIENT

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Re: If p and q are positive integers, is pq prime number?  [#permalink]

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Bunuel 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: Let p = 3, q = 1 --> pq = 3*1 = 3 --> Prime Number
Case 2: Let p = 3, q = 2 --> pq = 3*2 = 6 --> Not a Prime Number
--> Insufficient

(2) q is a prime number
Case 1: Let q = 3, p = 1 --> pq = 1*3 = 3 --> Prime Number
Case 2: Let q = 3, p = 2 --> pq = 2*3 = 6 --> Not a Prime Number
--> Insufficient

Combining (1) & (2),
p > 2 & q is prime number
Since, both p & q are both >1, Factors of pq will be more than 1 DEFINITELY
--> pq is DEFINITELY not prime --> Sufficient

Option C
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Re: If p and q are positive integers, is pq prime number?  [#permalink]

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ST (1) : p > 2
no info about q . insufficient

ST (2) : q is a prime number.
no info about p . insufficient

combining both,
q= prime no, but p ≠ 1 , so pq not prime . unique answer . sufficient
[ a number will be prime no if its one factor is 1 and another one is the number itself which is prime ]

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Posts: 489
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GMAT 1: 780 Q51 V45
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Re: If p and q are positive integers, is pq prime number?  [#permalink]

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

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

Project DS Butler Data Sufficiency (DS3)

Analyzing the question:
We are asking if a product can be a prime number, this can only happen if we have:
One integer is prime, and the other integer is equal to 1.

There are no other cases to consider since both p and q must be integers.

Statement 1:
Given this, we need q to be equal to 1 in order to have pq be prime. We don't know if that is true yet so insufficient.

Statement 2:
This is also saying q >= 1. There are a lot more conditions to be met to say pq is prime, so this is insufficient.

Combined:
We know the product cannot be prime now, so combined sufficient.

Ans: C
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# If p and q are positive integers, is pq prime number?  