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

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!

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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