If x is an Integer. Does x have greater than or equal to 3 f

[GMATinsight]

If x is an Integer. Does x have greater than or equal to 3 factors? (Source:GMAT INSIGHT)

(1) Difference between sum of the factors and Number of factors of x is even
(2) x > 3!

Source: www.GMATinsight.com

Answer: option E

[fiza gupta]

1) Difference between sum of the factors and Number of factors of x is even
perfect square always have odd numbers of factors and sum of factors is also Odd
example) 9 factors = 1,9,3 = 1+9+3 = 13
13-3 = 10
3 numbers of factors
example) 12 not perfect square:1,12,2,6,3,4=16+12 = 28
28-6 = 22
more than 3 number of factors
INSUFFICIENT

(2) x > 3!
x>6
can be 9(3 factors) or 12(6 factors) and many more
INSUFFICIENT

combining : still INSUFFICIENT

SO E

[Brent@GMATPrepNow]

If x is a positive integer. Does x have greater than or equal to 3 positive factors?

(1) Difference between sum of the factors and number of factors of x is even
(2) x > 3!

Target question: Does x have greater than or equal to positive 3 factors?

This is a great candidate for rephrasing the target question.

Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

What positive integers have exactly 2 positive factors? Prime numbers
What positive integers have exactly 1 positive factor? The number 1
The target question asks whether x has more than or equal to 3 factors? So, it's asking whether x is a COMPOSITE number. Now let's REPHRASE the target question:

REPHRASED target question: Is x a composite integer?

Statement 1: Difference between sum of the factors and number of factors of x is even
Let's TEST some values.
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 7. The factors of 7 are: {1,7}. The sum = 8 and there are 2 factors. 8 - 2 = 6, and 6 is even. In this case, x is NOT composite
Case b: x = 10. The factors of 10 are: {1,2,5,10}. The sum = 18 and there are 4 factors. 18 - 4 = 14, and 14 is even. In this case, x IS composite
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x > 3!
3! = (3)(2)(1) = 6. So, x is GREATER THAN 6
There are several values of x that satisfy statement 2. Here are two:
Case a: x = 7. In this case, x is NOT composite
Case b: x = 10. In this case, x IS composite
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several values of x that satisfy BOTH statements. Here are two:
Case a: x = 7. In this case, x is NOT composite
Case b: x = 10. In this case, x IS composite
Since we cannot answer the REPHRASED target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

RELATED VIDEOS
- Rephrasing the Target Question: https://www.gmatprepnow.com/module/gmat ... video/1100
- Prime Numbers: https://www.gmatprepnow.com/module/gmat ... /video/824