An integer x divided by nine gives a number f, where 0

Question

An integer x divided by nine gives a number f, where 0<f<1. What is the value of x?

(1) x is not a prime number.

(2) 2x has less than 3 factors.

Project DS Butler Data Sufficiency (DS3) 
 For DS butler Questions  Click Here

Are You Up For the Challenge: 700 Level Questions

gvij2017 · Answer

Given 
X is integer 
X/9 = f and 0<f<1
So 0<X<9

Now st. 1 
x is not prime. x = 4, 6, 8 Not sufficient

St. 2 
2x has less than 3 factors. Means 2x has either one factor or two factors. 
For that x can be only 1 because or any other integer value of x, 2x will have 3 or more than 3 factors.

So Ans is B as x= 1.

Enchanting · Answer

Solution:
 •  \frac{x}{9} = f 
 o x is an integer
o  0 < f < 1 
  It means x is positive and less than 9   
 Statement 1:  x is not a prime number
 • Case 1: If  x = 4 , then  0 < \frac{4}{9} < 1 
• Case 2: If  x = 6 , then  0< \frac{6}{9} < 1 
 o Different values of x.
o Not sufficient.  
 Statement 2:  2x has less than 3 factors.
 • x is an integer.
• 2x is a prime number
 o Only prime which is multiple of 2 is 2
o  2x = 2 
o  x = 1 
 o Sufficient.   
Answer :  Option B

CrackverbalGMAT · Answer

Question data tells us that x can be any positive integer from 1 to 8  i.e. 1 ≤ x ≤ 8. That should come as a slight relief, after all, we are to pick one out of 8 values (if possible, that is).

From statement I alone, x is not a prime number. Leaving out 2, 3, 5 and 7, possible values of x are 1 or 4 or 6 or 8. Statement I alone is insufficient to find a unique value for x because all the above values give a quotient between 0 and 1, when divided by 9.
Answer options A and D can be eliminated. The possible answer options are B, C or E.

From statement II alone,  2x has less than 3 factors . This means that  2x is a number that can have 2 factors OR 1 factor .

If 2x has 1 factor , it can only be when  2x = 1  because  1 is the only number with ONE factor . If 2x = 1, x = ½ which violates the question data that x is an integer. 2x ≠ 1.

If 2x has 2 factors , it means that  2x represents a prime number . The possible values are 2 or 3 or 5 or 7. But  2x cannot be 3 or 5 or 7 since that would make x a fraction .

Therefore,  2x HAS to be 2 which means x HAS to be 1 . Statement II alone is sufficient to find a unique value for x. Answer options C and E can be eliminated.

The correct answer option is B .

Hope that helps!

sauravleo123 · Answer

x=int
x/9=f
Where 0<f<1
x=?
So x<9
Statement 1:
x#prime
So x=1,4,6,8
Insufficient
Statement 2:
2x< 3 factors
x can only be 1
Any other value will give atleast 3 factors
Sufficient
B

Posted from my mobile device

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

An integer x divided by nine gives a number f, where 0<f<1. What is th

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