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.

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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

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

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