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

Question

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

Source:  https://www.GMATinsight.com

BrentGMATPrepNow · Answer

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-data-sufficiency?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 VIDEO
 https://www.youtube.com/watch?v=MyG1K3ee69w

Abhishek009 · Answer

PLUG IN SOME NUMBERS AND CHECK FOR STATEMENT - I

Let x = 3
No of factors is 2 ( ie , 1 & 3 )
Sum of the factors is 4 ( ie , 1 + 3 )

So, Difference between sum of the factors and Number of factors of 3 is 2 ( which is even )

Let x = 4
No of factors is 3 ( ie , 1 ,2 & 4 )
Sum of the factors is 7 ( ie , 1 + 2 + 4 )

So, Difference between sum of the factors and Number of factors of 7 is 4 ( which is even )
 
So, it's insufficient to state x have greater than or equal to 3 factors

USE STATEMENT - II

Same as my intelligent friend Brent Hanneson..

COMBINE BOTH THE STATEMENTS  
 
Still impossible 
  
Hence answer will be (E)

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

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GMAT Data Sufficiency (DS) Questions

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

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