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

Question

(1) x is a multiple of 4

(2) 8 <= x <= 64

goldfinchmonster · Answer

Ans Should be E.

The question asks whether X is a factor of 64, i.e whether X is either of these No. 1,2, 4, 8, 16, 32, 64.( all of both parity ).

Statement 1   - X is a multiple of 4. If it is 4 or 8 answer will be  yes , however if X is 12 or 24 the answer will be  No . Therefore   Not Sufficient .

Statement 2   - X is bitween 8 and 64 ( Inclusive ), Same as Statement 1, if X is 8 or 16 answer will be  yes  and if X is 12 or 24 the answer will be  No .

Therefore Not sufficient.

Combining both statements, X is a multiple of 4 which lies between 8 & 64 ( Inclusive ). As detailed above the answer will be   ambiguous  .

Hence E.

shameekv · Answer

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.

Therefore answer should be E

musunna · Answer

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.

BASSLJ · Answer

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

EMPOWERgmatRichC · Answer

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

Bunuel · Answer

Hi Rich,

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

keats · Answer

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

MathRevolution · Answer

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

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

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