If P is an odd positive integer such that P

Question

If P is an odd positive integer such that P<75, then is the number of distinct factors of P greater than 2?

1) P+2 ends with 9
2) P isn't a multiple of 3

a) Statement 1) ALONE is sufficient but statement 2) ALONE isn't sufficient 
b) Statement 2) ALONE is sufficient but statement 1) ALONE isn't sufficient 
c) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE isn't sufficient 
d) EACH statement ALONE is sufficient 
e) Statement 1) and 2) TOGETHER aren't sufficient

T4Star · Answer

Stat1: P has a units digit of 7
P can be 17, 27
17 has 2 distinct factors (1, 17)
27 has more than 2 distinct factors (1,27,9,3)

Insufficient

Stat2: P isnt a multiple of 3. This is clearly insufficient as P may or may not be prime no.

Stat1+ Stat2 gives: P = 7, 17, 37, 47, 67
All these are prime nos. and have only 2 distinct factors

Option C!

PriyanshuR · Answer

then is the number of distinct factors of P greater than 2?
So basically we have to check if P is prime or not.

Statement1: Only tells us that the unit digit of P is 7.
Statement2: Removes any multiples of 3 from set  .

1+2: Gives us 17, 37, 47, 67 All of which are prime numbers with only 2 factors that are distinct. That is  NO , they do not have number of distinct factors greated than 2. And in a Yes/No question a Clear No is sufficient. Thus,  Option C

Danielmm · Answer

Can someone post the OA for this?

Bunuel · Answer

The OA (official answer) for this is C. You can always check the official answer in the original post by clicking the  Show Answer  button.

Here, when combining the statements, P can only be 17, 37, 47, or 67, all of which are prime numbers. A prime has exactly two factors, so the answer is C.

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 is an odd positive integer such that P<75, then is the number

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions