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If y is an integer, is y^3 divisible by 9 ?

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Bunuel
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If y is an integer, is y^3 divisible by 9 ? [#permalink] New post  29 Jan 2014, 01:18
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00:00
A
B
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D
E

Difficulty:

25% (medium)

Question Stats:

77% (01:12) correct 23% (01:38) wrong based on 2165 sessions

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If y is an integer, is y^3 divisible by 9 ?

(1) y is divisible by 4.
(2) y is divisible by 6.
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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink] New post  29 Jan 2014, 02:09
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If y is an integer, is y^3 divisible by 9 ?

(1) y is divisible by 4.
(2) y is divisible by 6.



IMO B
takind A alone, if y is divisible by 4 then y= 4n therefore , y^3 = (4n)^3 = 64n^3 . thus we cant say anything about the divisibility by 9 since it will not depend totally on the value of n
INSUFFICIENT

taking B alone, if y is divisible by 6 then y= 6n therefore , y^3 = (6n)^3 = (2*3*n)^3 = (8* 9*3) n^3. thus we can say that it is divisible by 9.
SUFFICIENT.
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Bunuel
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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink] New post  29 Jan 2014, 01:18
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SOLUTION

If y is an integer, is y^3 divisible by 9 ?

(1) y is divisible by 4. Clearly insufficient: y can be 4 or 9*4.

(2) y is divisible by 6 --> y is divisible by 3 --> y^3 is divisible by 9. Sufficient.

Answer: B.
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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink] New post  29 Jan 2014, 02:07
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From S1:y=4k
y^3=64*k^3.Insufficient as K could take any value and accordingly y^3 could or could not be div by 9.
From S2:y=6k
y^3=216k^3.Regardless of value of k,y^3 will be div by 9 because 216 is div by 9.
Sufficient.
Ans.B
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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink] New post  30 Jan 2014, 02:21
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[quote="Bunuel"]The Official Guide For GMAT® Quantitative Review, 2ND Edition

If y is an integer, is y^3 divisible by 9 ?

(1) y is divisible by 4.
(2) y is divisible by 6.

Statement 1 : It says y is a multiple of 4 i.e. y=4k , but here k may or may not be a multiple of 3 and thus it is not sufficient to say if y^3 will be divisible by 9.

Statement 2 : It says y = 6k and thus y^3=216(k^3) ; 216 being divisible by 9, y^3 is divisible by 9 for sure irrespective of the value of k.It is sufficient.

B it is. :) :)
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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink] New post  02 Jan 2017, 15:01
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Nice Official Question.
Here is what i did in this one ->
Using test cases =>

Statement 1->
y=4
NO
y=12
YES

Hence not sufficient

Statement 2=>
y=> divisible by 12 => y has a 3
Thus y^3 will have a 27
Hence sufficient

Hence B
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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink] New post  23 Jan 2017, 10:29
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Is y = \(\frac{y^{3}}{9}\)
1, \(\frac{Y}{4}\)
For 4(2x2 factors )
For 9 (3x3 factors )
so Insufficient
2, \(\frac{Y}{6}\)
6(2x3 factors)
6^3 (2x2x2x3x3x3)
Divisible by 9(3x3 factors)
B
Bunuel is this a right approach?
Pls help. thanks
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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink] New post  30 Sep 2018, 14:02
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If y is an integer, is y^3 divisible by 9 ?

(1) y is divisible by 4.
(2) y is divisible by 6.

Data Sufficiency
Question: 64
Category: Arithmetic Properties of numbers
Page: 157
Difficulty: 600


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Basically the question is asking for \(\frac{y^3}{3^2}\)

statement 1) says y/4 so y could be 4,8,12 etc.. if y = 4 then it is not divisible by 3^2 however if y = 12 then y^3 is divisible by 9. Insufficient.

Statement 2) y is divisible by 6. This means that y is 6,12,18 etc.. since any multiple of 6 will contain a 3 in it so it will be divisible.

B sufficient.
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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink] New post  23 May 2020, 10:58
Whenever you see language like this "y is divisible by 4"

Always consider Y = 4 A

(4A)^3 = May or may not be divisible by 9

(6A)^3 = is surely divisible by 9
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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink] New post  08 Jan 2021, 20:14
Hi Bunuel - i have a problem with this question. in the stimulus, they only say that Y is an integer, so it could be zero. Isnt zero divisible by any integer but itself?

In case that were true, wouldn't the answer be E? otherwise then it would clearly be B.

Thank you and appreciate the help.
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Bunuel
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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink] New post  08 Jan 2021, 23:26
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ricardorr04 wrote:
Hi Bunuel - i have a problem with this question. in the stimulus, they only say that Y is an integer, so it could be zero. Isnt zero divisible by any integer but itself?

In case that were true, wouldn't the answer be E? otherwise then it would clearly be B.

Thank you and appreciate the help.


Yes, 0 is an integer and it is divisible by every integer except 0 itself. But if y = 0, then still from (2) we have the same yes answer: y^3 = 0^3 = 0 is divisible by 9.
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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink] New post  09 Feb 2023, 06:47
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