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# If A and B are positive integers and A^3 is divisible by 24

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Joined: 03 Mar 2018
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If A and B are positive integers and A^3 is divisible by 24  [#permalink]

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Updated on: 05 Mar 2018, 06:53
1
00:00

Difficulty:

65% (hard)

Question Stats:

55% (01:20) correct 45% (01:54) wrong based on 31 sessions

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If A and B are positive integers and $$A^3$$ is divisible by 24, then is $$AB^2$$ a multiple of 216?

(1) B is a multiple of 6

(2) B is divisible by 30

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

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Originally posted by itisSheldon on 05 Mar 2018, 04:49.
Last edited by itisSheldon on 05 Mar 2018, 06:53, edited 1 time in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7211
Re: If A and B are positive integers and A^3 is divisible by 24  [#permalink]

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05 Mar 2018, 05:09
itisSheldon wrote:
If A and B are positive integers and A^3 is divisible by 24, then is AB^2 a multiple of 216?

(1) B is a multiple of 6

(2) B is divisible by 30

$$A^3$$ div by 24 (means div by $$24=2^3*3$$)...
so A should be div by 2*3 or 6

now $$216 = 2^3*3^3$$...
since A is div by 6, B^2 must be div by $$2^2*3^2$$ or B must be div by $$\sqrt{2^2*3^2}=6$$ for AB^2 to be div by 216

lets see the statements..

(1) B is a multiple of 6
so suff

(2) B is divisible by 30
so B will be div by 6
suff

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If A and B are positive integers and A^3 is divisible by 24  [#permalink]

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05 Mar 2018, 07:01
chetan2u wrote:
itisSheldon wrote:
If A and B are positive integers and A^3 is divisible by 24, then is AB^2 a multiple of 216?

(1) B is a multiple of 6

(2) B is divisible by 30

$$A^3$$ div by 24 (means div by $$24=2^3*3$$)...
so A should be div by 2*3 or 6

now $$216 = 2^3*3^3$$...
since A is div by 6, B^2 must be div by $$2^2*3^2$$ or B must be div by $$\sqrt{2^2*3^2}=6$$ for AB^2 to be div by 216

lets see the statements..

(1) B is a multiple of 6
so suff

(2) B is divisible by 30
so B will be div by 6
suff

D

Thank you for the explanation!

My understanding was if A^3 is divisible by 24, then A^3 must be equal to 24k (multiple of k) and therefore A "must be divisible" by 2*(3^1/3)... Please help me identify where am I going wrong.
Math Expert
Joined: 02 Aug 2009
Posts: 7211
Re: If A and B are positive integers and A^3 is divisible by 24  [#permalink]

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05 Mar 2018, 07:12
1
1
urvashis09 wrote:
chetan2u wrote:
itisSheldon wrote:
If A and B are positive integers and A^3 is divisible by 24, then is AB^2 a multiple of 216?

(1) B is a multiple of 6

(2) B is divisible by 30

$$A^3$$ div by 24 (means div by $$24=2^3*3$$)...
so A should be div by 2*3 or 6

now $$216 = 2^3*3^3$$...
since A is div by 6, B^2 must be div by $$2^2*3^2$$ or B must be div by $$\sqrt{2^2*3^2}=6$$ for AB^2 to be div by 216

lets see the statements..

(1) B is a multiple of 6
so suff

(2) B is divisible by 30
so B will be div by 6
suff

D

Thank you for the explanation!

My understanding was if A^3 is divisible by 24, then A^3 must be equal to 24k (multiple of k) and therefore A "must be divisible" by 2*(3^1/3)... Please help me identify where am I going wrong.

pretty much in the same line BUT A is an integer so it cannot have a value of 3rd root of 3 and minimum value has to be 2*3=6
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Manager
Joined: 03 Mar 2018
Posts: 215
If A and B are positive integers and A^3 is divisible by 24  [#permalink]

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05 Mar 2018, 07:20
urvashis09 wrote:
chetan2u wrote:
itisSheldon wrote:
If A and B are positive integers and A^3 is divisible by 24, then is AB^2 a multiple of 216?

(1) B is a multiple of 6

(2) B is divisible by 30

$$A^3$$ div by 24 (means div by $$24=2^3*3$$)...
so A should be div by 2*3 or 6

now $$216 = 2^3*3^3$$...
since A is div by 6, B^2 must be div by $$2^2*3^2$$ or B must be div by $$\sqrt{2^2*3^2}=6$$ for AB^2 to be div by 216

lets see the statements..

(1) B is a multiple of 6
so suff

(2) B is divisible by 30
so B will be div by 6
suff

D

Thank you for the explanation!

My understanding was if A^3 is divisible by 24, then A^3 must be equal to 24k (multiple of k) and therefore A "must be divisible" by 2*(3^1/3)... Please help me identify where am I going wrong.

Please note that if A^3 is divisible by 24(i.e Factors of A^3 are 2 and 3) the A must have 2 and 3 as their factors. For instance if A^3 is divisible by 343 then A must be divisible by 7. Similarly if A^3 is divisible by 18 then A must be divisible by 2*3.
Hope it helps and correct me if i am wrong.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

If A and B are positive integers and A^3 is divisible by 24 &nbs [#permalink] 05 Mar 2018, 07:20
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