GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Jan 2019, 01:12

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winners of the GMAT game show

January 22, 2019

January 22, 2019

10:00 PM PST

11:00 PM PST

In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.
• ### Key Strategies to Master GMAT SC

January 26, 2019

January 26, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.

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

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

### Show Tags

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

### HideShow timer Statistics

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.

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.

_________________

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]

### Show Tags

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

GMAT online Tutor

Senior Manager
Joined: 15 Oct 2017
Posts: 312
GMAT 1: 560 Q42 V25
GMAT 2: 570 Q43 V27
GMAT 3: 710 Q49 V39
Re: If A and B are positive integers and A^3 is divisible by 24  [#permalink]

### Show Tags

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]

### Show Tags

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]

### Show Tags

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
Display posts from previous: Sort by

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.