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Is the positive number 'x' an integer?

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Is the positive number 'x' an integer?  [#permalink]

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Updated on: 15 Aug 2014, 09:00
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Difficulty:

55% (hard)

Question Stats:

57% (01:28) correct 43% (01:49) wrong based on 79 sessions

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Is the positive number x an integer?

(1) 3x is a perfect square.
(2) 2x is divisible by 4.

Source: 4gmat

Originally posted by alphonsa on 15 Aug 2014, 08:20.
Last edited by Bunuel on 15 Aug 2014, 09:00, edited 1 time in total.
Edited the question
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Re: Is the positive number 'x' an integer?  [#permalink]

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15 Aug 2014, 09:04
Is the positive number x an integer?

(1) 3x is a perfect square. If $$x=\frac{1}{3}$$, then 3x = 1 = 1^2 and in this case x is not an integer but if x = 3, then 3x = 9 = 3^2 and in this case x is an integer. Not sufficient.

(2) 2x is divisible by 4 --> 2x = 4k --> x = 2k = even = integer. Sufficient.

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Re: Is the positive number 'x' an integer?  [#permalink]

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12 Jun 2016, 14:36
1
in the secnd statement we have 2x is divisible by 4.Cant we have x=1.6 then also 2x is divisible by 4.In that case x is not an integer,,
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Re: Is the positive number 'x' an integer?  [#permalink]

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12 Jun 2016, 19:43
kplusprinja1988 wrote:
in the secnd statement we have 2x is divisible by 4.Cant we have x=1.6 then also 2x is divisible by 4.In that case x is not an integer,,

Hi,

divisiblity means TO BE COMPLETELY DIV..
here if you have x as 1.6... when div by 4, the answer will be in decimals, which means it is not div by 4..
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Re: Is the positive number 'x' an integer?  [#permalink]

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13 Jun 2016, 11:01
chetan2u wrote:
kplusprinja1988 wrote:
in the secnd statement we have 2x is divisible by 4.Cant we have x=1.6 then also 2x is divisible by 4.In that case x is not an integer,,

Hi,

divisiblity means TO BE COMPLETELY DIV..
here if you have x as 1.6... when div by 4, the answer will be in decimals, which means it is not div by 4..

Thanks Chetan
So can i generalize that whenever completely divisible is given we cannot take decimal values ?
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Re: Is the positive number 'x' an integer?  [#permalink]

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14 Jun 2016, 09:29
There is 1 variable (x) in the original condition. Hence, we need 1 equation to match the number of variables and the number of equations.
Since the condition 1) and the condition 2) each has 1 equation, there is high chance that D is the correct answer.
Condition 1) has 3x=9 yes, 3x=4 no. The condition is not sufficient
Condition 2) has 2x=4t(t is any positive integer) and we get x=2t. Hence, the answer is yes. Thus, the correct answer is B.
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Re: Is the positive number 'x' an integer?  [#permalink]

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19 Feb 2019, 01:18
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Re: Is the positive number 'x' an integer?   [#permalink] 19 Feb 2019, 01:18
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