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Re: If x is a non-zero integer (40 + 24)/x is an integer? [#permalink]

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29 Oct 2015, 08:24

Bunuel wrote:

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

(1) x is a multiple of 4

(2) 8 <= x <= 64

Kudos for a correct solution.

1 st Statement :- If x is a multiple of 4 then x = 4m; now if m = 1,2 then the expression is an integer but if m = 3 i.e. x = 12 then the expression is a non integer. Therefore insufficient. 2nd Statement :- x can be any integer value between 8 and 64. If x = 8 then the expression is an integer if x = 9 then it is not. Therefore insufficient Combining 1 and 2 :- x can be any integer value between 8 and 64 and is a multiple of 4 i.e. x = 8,12,16 ... Therefore if x = 8 then yes if x = 12 then no.. Hence insufficient.

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

(1) x is a multiple of 4

(2) 8 <= x <= 64

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)?

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

(1) x is a multiple of 4

(2) 8 <= x <= 64

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...
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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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Re: If x is a non-zero integer (40 + 24)/x is an integer? [#permalink]

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28 Sep 2017, 05:19

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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