If Integer p is a Factor of 42, is p a Prime Number? GMAT Problem Solving

Question: If integer p is a factor of 42, is p a prime number?

(1) p > 6
(2) p < 21

1. Statement (1) ALONE is sufficient but statement (2) ALONE is not sufficient.
2. Statement (2) ALONE is sufficient but statement (1) ALONE is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“If integer p is a factor of 42, is p a prime number?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

This question has only one approach.
It is given in the question that integer p is a factor of 42. It is asked in the question that if p is a prime number or not.
We are given two statements, we have to verify whether these two statements are sufficient to solve the problem or not.
Given:
P is an integer and p is a factor of 42.
The positive factors of 42 are - 1,2,3,6,7,14,21,42
Coming to statement 1 we have,
P > 6
As the value of p > 6 then p can take values - 7,14,21,42
If the value of n = 7
The answer to the question is yes, p is a prime number.
If the value of n = 14
The answer to the question is no, p is not a prime number.
If the value of n = 21
The answer to the question is no, p is not a prime number.
If the value of n = 42
The answer to the question is no, p is not a prime number.
Therefore we cannot say whether p is a prime number or not.
This statement is not sufficient to get the answer.
Coming to statement 2 we get,
Given p < 21
As the value of p <21 then p can take values - 1,2,3,6,7,14
If the value of n = 1
The answer to the question is yes, p is a prime number.
If the value of n = 2
The answer to the question is yes, p is a prime number.
If the value of n = 3
The answer to the question is yes, p is a prime number.
If the value of n = 6
The answer to the question is no, p is not a prime number.
If the value of n = 7
The answer to the question is yes, p is a prime number.
If the value of n = 14
The answer to the question is no, p is not a prime number.
Therefore we cannot say whether p is prime or not.
This statement is not sufficient to get the answer.

Correct Answer: E

Some suggested GMAT Data Sufficiency Questions

• The Average Price of Three Stocks is $25 per Share GMAT Data Sufficiency 
• Given k is a Nonzero Integer, is k>0? GMAT Data Sufficiency 
• If J≠0, What Is The Value Of J? GMAT Data Sufficiency 
• Paint X Costs $15 per Gallon, and Paint Y Costs $20 per Gallon GMAT Data Sufficiency 
• What is the total value of Company H's stock? GMAT Data Sufficiency 
• Is PQ > 1? GMAT Data Sufficiency 
• How Many of the Students in a Certain Class are Taking Both a History and a Science Course? GMAT Data Sufficiency 
• The Set S of Numbers has the following Properties GMAT Data Sufficiency 
• A Contractor Combined x Tons of a Gravel Mixture that Contained 10 percent Gravel G GMAT Data Sufficiency 
• If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies GMAT Data Sufficiency 
• From a Group of M Employees, N Will be Selected, at Random GMAT Data Sufficiency 
• Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)? GMAT Data Sufficiency 
• Juan Bought Some Paperback Books That Cost $8 GMAT Data Sufficiency GMAT Data Sufficiency 
• The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT Data Sufficiency 
• X is Older Than Y, Z Is Younger Than W And V is Older Than Y. Is Z Younger Than X? GMAT Data Sufficiency 
• 2x+3y GMAT Data Sufficiency 
• The Selling Price of an Article is Equal to the Cost of the Article  GMAT Data Sufficiency 
• Buster leaves the trailer at noon and walks towards the studio GMAT Data Sufficiency 
• If x and y are positive integers and xy is divisible by prime number. Is p an even number? GMAT Data Sufficiency 
• What is the Product of 6 Consecutive Numbers? GMAT Data Sufficiency