If x is a non-zero integer (40 + 24)/x is an integer?

The question stem asks for whether 64/x is an integer ? i.e. whether x is a factor of 64.

Statement 1 says, x is a multiple of 4. However, NOT all multiples of 4 are factor of 64. eg. 12,40 etc. NOT Sufficient.

Statement 2 says, 8 <= x <= 64. i.e. value of x is any number within this range. Some will be factor of 64 & some will not. NOT Sufficient.

Combining 1 & 2 gives the same dual result as statement 1 & 2.

So Option (E) wins.

x could be 12 or 16 for either statement. NS for either. Ans E

Hi Bunuel,

Is this prompt formatted correctly? It seems odd to ask if (40+24)/X is an integer (as opposed to just writing it as "is 64/X an integer?"); is it meant to be 40 + (24/X)?

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

Yes, in the source it's (40+24)/x. Why didn't they write 64/x, is a mystery for me too...

If x is a non-zero integer (40 + 24)/x is an integer?

(1) x is a multiple of 4
(2) 8 <= x <= 64
____________________________

Is 64/x = Integer ?
This is possible only when x divides 64 leaving no remainder.

1) x = multiple of 4
4, x = integer
68, x != integer
Not Sufficient

2) x = 8,9,10,11,12.........,64
Not sufficient. Take x=8 or x=11

On combining, x = 11 (Not Suff), 8(Suff)

E it is

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If x is a non-zero integer (40 + 24)/x is an integer?

(1) x is a multiple of 4

(2) 8 <= x <= 64

If we modify the question, we ultimately want to know whether x is a factor of 64. There is one variable (x) and we need one equation to solve for the question; there are 2 equations given from the 2 conditions, making (D) our likely answer.
In condition 1, the answer is 'yes' when x=4, but 'no' when it is 12. This condition is insufficient.
In condition 2, the answer is 'yes' when x=4, but 'no' when it is 12. This condition is insufficient.
When looking at the conditions together, the answer is 'yes' when x=4, but 'no' when it is 12. This conditions as a whole are insufficient.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

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