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If x is a nonzero integer less than 36, is 36/x even?

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Bunuel
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If x is a nonzero integer less than 36, is 36/x even? [#permalink] New post   11 Apr 2016, 04:10
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If x is a nonzero integer less than 36, is 36/x even?

(1) 3 + x is an odd integer.
(2) x is a multiple of 4 and a factor of 36.
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Re: If x is a nonzero integer less than 36, is 36/x even? [#permalink] New post   11 Apr 2016, 06:47
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Bunuel wrote:
If x is a nonzero integer less than 36, is 36/x even?

(1) 3 + x is an odd integer.
(2) x is a multiple of 4 and a factor of 36.



(1) 3 + x is an odd integer
This tells us that x is an even integer < 36..
If x is 18, ans is YES
if x is 22 ans is NO
Insuff

(2) x is a multiple of 4 and a factor of 36.
Now we are told that x is a factor of 36 so 36/x will be an integer..
Also x is a multiple of 4 and 36 is 4*9, 36/x can never be EVEN so ans is NO
Suff

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Re: If x is a nonzero integer less than 36, is 36/x even? [#permalink] New post   11 Apr 2016, 10:21
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Bunuel wrote:
If x is a nonzero integer less than 36, is 36/x even?

(1) 3 + x is an odd integer.
(2) x is a multiple of 4 and a factor of 36.


x < 36 and not = 0
Is 36/x even?

Statement 1:
3 + x = odd
Since 3 is odd, therefore x has to be even for the sum to be even.
Case 1: x = 2, 36/2 = 18. Even
Case 2: x = 4, 36/4 = 9. Odd
Insufficient

Statement 2:
x is a multiple of 4 and a factor of 36
36 = 2^2*3^2
Factors of 36 that are multiples of 4 = 2^2, 2^2*3, 2^2*3^2 = 4, 12, 36
36/4 = 9 Odd
36/12 = 3 Odd
36/36 = 1 Odd
Hence 36/x is always odd.
Sufficient

Option B
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Re: If x is a nonzero integer less than 36, is 36/x even? [#permalink] New post   13 Apr 2016, 23:50
If x is a nonzero integer less than 36, is 36/x even?

(1) 3 + x is an odd integer.
(2) x is a multiple of 4 and a factor of 36.


Statement 1:

3 + x is an odd integer. Implies x is even integer

We can test values to see that this statement is not sufficient.

If x = 2 then 36/2 = 18 (Even)
If x = 4 then 36/4 = 9 (Odd)

Hence insufficient.

Statement 2:

Multiples of 4 that are factors of 36 are - 4, 12, 36.

So x is = 4, 12, 36. for the 3 values of x; 36/x is odd. Hence sufficient.

Answer B
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Re: If x is a nonzero integer less than 36, is 36/x even? [#permalink]
13 Apr 2016, 23:50
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Bunuel
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