Mechmeera wrote:source Kaplan

How many positive factors does the positive integer x have?

(1) x is the product of 3 distinct prime numbers.

(2) x and 37 have the same number of positive factors.

Statement 2 indicates that x is PRIME, while statement 1 indicates that x is NOT prime.
Since it is guaranteed on the GMAT that the two statements will not contradict each other, this DS seems invalid.
I would ignore this problem.

I explain how to count positive factors here:
https://www.beatthegmat.com/all-factors- ... 15019.html

GMATGuruNY wrote:

Mechmeera wrote:source Kaplan

How many positive factors does the positive integer x have?

(1) x is the product of 3 distinct prime numbers.

(2) x and 37 have the same number of positive factors.

Statement 2 indicates that x is PRIME, while statement 1 indicates that x is NOT prime.
Since it is guaranteed on the GMAT that the two statements will not contradict each other, this DS seems invalid.
I would ignore this problem.

I explain how to count positive factors here:
https://www.beatthegmat.com/all-factors- ... 15019.html

3^7 is mistyped as 37. Sorry for the typo.
Please look into this once again.

To count the number of positive factors of an integer:

1) Prime-factorize the integer
2) Add 1 to each exponent
3) Multiply

For example:
72 = 2³ * 3².
Adding 1 to each exponent and multiplying, we get (3+1)*(2+1) = 12 positive factors.

Here's why:
To determine how many factors can be created from 72 = 2³ * 3², we need to determine the number of choices we have of each prime factor and to count the number of ways these choices can be combined:

For 2, we can use 2�, 2¹, 2², or 2³, giving us 4 choices.
For 3, we can use 3�, 3¹, or 3², giving us 3 choices.

Multiplying the number of choices we have of each factor, we get 4*3 = 12 positive factors.

Mechmeera wrote:source Kaplan

How many positive factors does the positive integer x have?

(1) x is the product of 3 distinct prime numbers.

(2) x and 3� have the same number of positive factors.

Statement 1:
x = a¹b¹c¹, where a, b and c are distinct prime numbers.
Adding 1 to each exponent and multiplying, we get:
(1+1)(1+1)(1+1) = 8 positive factors.
SUFFICIENT.

Statement 2:
Since we can count the number of positive factors for 3�, the number of positive factors for x can be determined.
SUFFICIENT.

The correct answer is D.

To determine the number of positive factors for 3�, we simply add 1 to the exponent:
7+1 = 8 positive factors.

S1::

x = p * q * r, where p, r, and q are distinct primes.

A number has three types of factors, broadly speaking:

Type I: 1 and itself
Type II: Its primes
Type III: The products of its primes

So our number has

1, itself, p, q, r, p*q, q*r, and p*r, for a total of 8 factors; SUFFICIENT.

S2::

This is definitely sufficient: we don't even need to know how to count the number of factors of 3�, so this is a freebie