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If x is an integer, is x an odd integer?

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Bunuel
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If x is an integer, is x an odd integer? [#permalink] New post   25 Dec 2016, 02:42
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If x is an integer, is x an odd integer?

(1) x(x + 1) is a multiple of 12.
(2) x^2 + x is divisible by 3 and 4.
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E
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prashantrchawla
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Re: If x is an integer, is x an odd integer? [#permalink] New post   25 Dec 2016, 03:05
If x is an integer, is x an odd integer?
Option 1: x(x + 1) is a multiple of 12......
When x = 3 then x(x+1) is multiple of 12 and when x=12 then x(x+1) is multiple of 12 but first time x is odd and second case x is even
... Not sufficient.

Option 2: x^2 + x is divisible by 3 and 4.
When x = 3 then divisible by 3 and 4....
when x=8 then not divisible......................................Not sufficient.. Taking both the options together,

Take x = 8, in this case it is divisible by 3 and 4 and also multiple of 12..
Take x=3, in this case x(x+1) is divisible by 3 and 4 and also multiple of 12... .. Not sufficient..... Answer is E.
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Re: If x is an integer, is x an odd integer? [#permalink] New post   25 Dec 2016, 05:25
Actually 1 and 2 say the same thing.
1) X(X+1) = x^2+X
2) a no divisible by both 3&4 has to be a multiple of 12. Divisibility test of 12.

All scenarios are irrespective of sign of the integer.

Hence ans is E

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Re: If x is an integer, is x an odd integer? [#permalink] New post   25 Dec 2016, 07:04
1 & 2 say the same and not one is self sufficient.

Hence E

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Re: If x is an integer, is x an odd integer? [#permalink] New post   25 Dec 2016, 08:35
Bunuel wrote:
If x is an integer, is x an odd integer?

(1) x(x + 1) is a multiple of 12.
(2) x^2 + x is divisible by 3 and 4.


x^2 + x = x(x + 1), so (1), (2) are the same.
Multiple of 12 can be 0, 12, 24,...
x = 0 --> 0*(0+1) is a multiple of 12 --> 0 is not an odd integer.
But x = 3 --> 3*(3+1) is a multiple of 12 --> 3 is an odd integer.
Answer: E
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Re: If x is an integer, is x an odd integer? [#permalink]
25 Dec 2016, 08:35
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Bunuel
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