If y is an integer, is y^3 divisible by 9 ? : GMAT Data Sufficiency (DS)
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# If y is an integer, is y^3 divisible by 9 ?

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If y is an integer, is y^3 divisible by 9 ? [#permalink]

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29 Jan 2014, 01:18
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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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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink]

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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.

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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink]

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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]

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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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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink]

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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]

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01 Feb 2014, 09:07
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.

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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink]

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07 May 2015, 07:54
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Re: If y is an integer, is y^3 divisible by 9 ? [#permalink]

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30 Nov 2016, 20:16
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Re: If y is an integer, is y^3 divisible by 9 ?   [#permalink] 30 Nov 2016, 20:16
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