If p and q are prime numbers, is pq+1 an odd number?

Question

If  p  and  q  are prime numbers, is  pq+1  an odd number?

(1)  p – q = 5 
(2)  p = 7

stne · Answer

(1) p – q=5

p= 5 +q

So  p   is a prime number greater than  5 , so  p  has to be odd , that implies  q  has to be even.

So  q  is even and a prime hence it has to be  2 .

So  pq   is even and  pq+1  = odd

SUFF.

(2)p = 7

We know nothing about  q.

Status of  pq+1  will change depending on whether  q  is  2  or another prime.

INSUFF.

Ans A

Hope it helps.

eosqui · Answer

I think there is an issue with this one.
2) if p=7 in order for p*q+1 to be odd p*q needs to be even therefore the only number that q can be is 2. There is no other prime even number.

Bunuel · Answer

Where is the problem? You are right that the question is basically asking whether p or q, or both, are 2.

From (1): The difference between two primes being 5 (odd) means one of them must be even. Since the only even prime is 2, we get q = 2 and p = 7.

From (2): We only know that p = 7, but q could be 2 or some other prime, so (2) is not sufficient.

P.S. Pure algebraic questions are no longer a part of the  DS syllabus  of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems 
 Work Problems 
 Distance Problems 
 Mixture Problems 
 Percent and Interest Problems 
 Overlapping Sets Problems 
 Statistics Problems 
 Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check  GMAT Syllabus for Focus Edition

You can also visit the  Data Sufficiency forum  and filter questions by  OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources  to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.

If p and q are prime numbers, is pq+1 an odd number?

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GMAT Data Sufficiency (DS) Questions

If p and q are prime numbers, is pq+1 an odd number?

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