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# Is x/3 an integer?

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Senior Manager
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19 May 2010, 01:49
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44% (02:13) correct 56% (00:57) wrong based on 183 sessions

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Is x/3 an integer?

(1) 7x/3 = Positive integer
(2) 14x/3 = Positive integer
[Reveal] Spoiler: OA
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19 May 2010, 02:52
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D.
- For 7 is indivisible by 3, then x must be divisible by 3 => x/3 an integer
- 14 = 7*2, neither is divisible by 3, then x must be divisible by 3 => x/3 an integer
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19 May 2010, 03:28
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dimitri92 wrote:
Is x/3 an integer?

(1) 7x/3 = Positive integer
(2) 14x/3 = Positive integer

Is $$\frac{x}{3}=integer$$?

Note that we are not told that x is an integer.

(1) $$\frac{7}{3}x$$ = Positive integer --> x is of a type $$x=\frac{3k}{7}$$, where $$k$$ is an integer $$>{0}$$. Hence x may be multiple of 3 (3, 6, ...) in this case $$\frac{x}{3}=integer$$ OR x can be reduced fraction (3/7, 6/7, ...) in this case $$\frac{x}{3}\neq{integer}$$. Not sufficient.

(2) $$\frac{14}{3}x$$ = Positive integer --> x is of a type $$x=\frac{3n}{14}$$, where $$n$$ is an integer $$>{0}$$. Hence x may be multiple of 3 (3, 6, ...) in this case $$\frac{x}{3}=integer$$ OR x can be reduced fraction (3/14, 6/14=3/7, ...) in this case $$\frac{x}{3}\neq{integer}$$. Not sufficient.

(1)+(2) No new info. If $$x=3$$, answer is YES but if $$x=\frac{3}{7}$$, answer is NO. Not sufficient.

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19 May 2010, 03:30
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Bunuel wrote:
dimitri92 wrote:
Is x/3 an integer?

(1) 7x/3 = Positive integer
(2) 14x/3 = Positive integer

Is $$\frac{x}{3}=integer$$?

Note that we are not told that x is an integer.

(1) $$\frac{7}{3}x$$ = Positive integer --> x is of a type $$x=\frac{3k}{7}$$, where $$k$$ is an integer $$>{0}$$. Hence x may be multiple of 3 (3, 6, ...) in this case $$\frac{x}{3}=integer$$ OR x can be reduced fraction (3/7, 6/7, ...) in this case $$\frac{x}{3}\neq{integer}$$. Not sufficient.

(2) $$\frac{14}{3}x$$ = Positive integer --> x is of a type $$x=\frac{3n}{14}$$, where $$n$$ is an integer $$>{0}$$. Hence x may be multiple of 3 (3, 6, ...) in this case $$\frac{x}{3}=integer$$ OR x can be reduced fraction (3/14, 6/14=3/7, ...) in this case $$\frac{x}{3}\neq{integer}$$. Not sufficient.

(1)+(2) No new info. If $$x=3$$, answer is YES but if $$x=\frac{3}{7}$$, answer is NO. Not sufficient.

wow that was brilliant
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20 May 2010, 17:54
Good one I didn't see that coming...I gotta keep asking the important parameter questions. What info is given about X?
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13 Jul 2010, 01:59
Oh yeah..integer trap thing..it took me weeks to get over that. Still got me sometimes ! Here's another good integer trap with excellent explanation from HRH Bunuel
http://gmatclub.com/forum/odd-even-95982.html
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13 Jul 2010, 08:20
What a trap; hatsoff
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GGG (Gym / GMAT / Girl) -- Be Serious

Its your duty to post OA afterwards; some one must be waiting for that...

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Re: Is x/3 an integer? [#permalink]

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05 Jan 2014, 13:45
dimitri92 wrote:
Is x/3 an integer?

(1) 7x/3 = Positive integer
(2) 14x/3 = Positive integer

Obviously each statement alone is insufficient

Now, both together

x can be 3/7 and will satisfy all conditions, is it an integer no

x can also be any multiple of 3 giving answer as yes

So I'm betting my @ on E here

Cheers!
J
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Re: Is x/3 an integer? [#permalink]

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14 Feb 2014, 02:10
dimitri92 wrote:
Is x/3 an integer?

(1) 7x/3 = Positive integer
(2) 14x/3 = Positive integer

Got wrong.. It tuk around 30 second to choose option D..question shud have mentioned that x is integer :D

A lesson to learn from this question is.. chek..whether question has mentioned that X is integer or not
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Bole So Nehal.. Sat Siri Akal.. Waheguru ji help me to get 700+ score !

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Re: Is x/3 an integer? [#permalink]

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24 Dec 2015, 07:35
Bunuel wrote:
dimitri92 wrote:
Is x/3 an integer?

(1) 7x/3 = Positive integer
(2) 14x/3 = Positive integer

Is $$\frac{x}{3}=integer$$?

Note that we are not told that x is an integer.

(1) $$\frac{7}{3}x$$ = Positive integer --> x is of a type $$x=\frac{3k}{7}$$, where $$k$$ is an integer $$>{0}$$. Hence x may be multiple of 3 (3, 6, ...) in this case $$\frac{x}{3}=integer$$ OR x can be reduced fraction (3/7, 6/7, ...) in this case $$\frac{x}{3}\neq{integer}$$. Not sufficient.

(2) $$\frac{14}{3}x$$ = Positive integer --> x is of a type $$x=\frac{3n}{14}$$, where $$n$$ is an integer $$>{0}$$. Hence x may be multiple of 3 (3, 6, ...) in this case $$\frac{x}{3}=integer$$ OR x can be reduced fraction (3/14, 6/14=3/7, ...) in this case $$\frac{x}{3}\neq{integer}$$. Not sufficient.

(1)+(2) No new info. If $$x=3$$, answer is YES but if $$x=\frac{3}{7}$$, answer is NO. Not sufficient.

Hats off !!
Not a single thought about x values , considered about x/3 only .
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Re: Is x/3 an integer? [#permalink]

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09 May 2017, 02:24
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Re: Is x/3 an integer?   [#permalink] 09 May 2017, 02:24
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