If F is a factor of 105, is F is a prime number? (1) F is not divisib GMAT data sufficiency

Question: If F is a factor of 105, is F is a prime number?

Statement (1). F is not divisible by 3
Statement (2). F < 10

A. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are not sufficient.

Answer: B

Solution and Explanation:

Approach Solution 1:
Factorizing 105 we get,
105=3*5*7
Statement (1) It need not be a prime or not a prime because it could be divisible by both 5 and 7 even if it is not divisible by 3. Hence, insufficient
​Statement (2) F is unquestionably a prime if it is smaller than 10. For example, 3*7, 3*5, and 5*7 are all greater than 10. Hence, if it is smaller than 10, it must be a prime. Thus, this choice is adequate.

Correct option: B

Approach Solution 2:
We can approach this problem using the fundamental theorem of arithmetic, which states that any positive integer greater than 1 can be uniquely factored into a product of prime numbers.
From the problem statement, we know that 105 can be factored into 3 prime factors: 3, 5, and 7. Therefore, any factor of 105 must be a product of these primes.
Statement (1) tells us that F is not divisible by 3. This means that F cannot be a multiple of 3, so it must be either a product of 5 and/or 7, or 1. However, 1 is not considered a prime number, so we can conclude that F is not necessarily a prime number. For example, F could be 5, 7, or 35.
Statement (2) tells us that F is less than 10. We can list out all the possible factors of 105 that are less than 10: 1, 3, 5, 7. None of these factors are divisible by any of the other factors, so they are all prime numbers. Therefore, we can conclude that F is necessarily a prime number.
Correct option: B

Approach Solution 3:
The factors of 105 are 3,7 and 5
Statement 1. Given that it is not divisible by 3. Then the factor must be made from 7 and 5
The factors could be 5,7 and 35
5 and 7 are prime, but 35 is not.
Hence, this statement is not sufficient.
Statement 2. F is said to be a prime number smaller than 10.
So the factors 3*7, 3*5, and 5*7 are all eliminated. Hence, if it is smaller than 10, it must be a prime. Thus, this choice is sufficient.
Correct option: B

“If F is a factor of 105, is F is a prime number? (1) F is not divisib" - is a topic of the GMAT data sufficiency section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT data sufficiency questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and two statements. By using mathematics to answer the question, the candidate must select the appropriate response among five choices which states which statement is sufficient to answer the problem. The data sufficiency section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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