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A number that is evenly divisible by 8, 9 and 10 must also be evenly

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A number that is evenly divisible by 8, 9 and 10 must also be evenly  [#permalink]

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New post 07 Oct 2019, 19:55
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EMPOWERgmat PS Series:
Pack 2, Question 5

A number that is evenly divisible by 8, 9 and 10 must also be evenly divisible by which of the following:

A. 55
B. 60
C. 65
D. 70
E. 75



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Re: A number that is evenly divisible by 8, 9 and 10 must also be evenly  [#permalink]

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New post 07 Oct 2019, 23:02
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Any number that is LCM of 8,9,10 or factor of the LCM will fit in.
LCM is 2^3*3^2*5=360
Only 60 is a factor as 60=2^2*3*5

B.
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Re: A number that is evenly divisible by 8, 9 and 10 must also be evenly  [#permalink]

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New post 09 Oct 2019, 09:53
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A number divisible by 8,9,10 must be a multiple of 360(LCM of 8,9,10)

Only choice that evenly divides 360 is B. Hence B is the correct answer choice
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Re: A number that is evenly divisible by 8, 9 and 10 must also be evenly  [#permalink]

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New post 10 Oct 2019, 21:47
OFFICIAL EXPLANATION

Hi All,

We're told that a number that is evenly divisible by 8, 9 and 10. We're asked what that number must ALSO be evenly divisible by. This question can be approached in a couple of different ways, including by Prime Factorization and TESTing VALUES.

The most obvious number that is divisible by 8, 9 and 10 is (8)(9)(10) = 720. If you're comfortable with Prime Factorization, then you could determine that the Least Common Multiple is actually 360 though (since both 8 and 10 are EVEN, the LCM of those two numbers will NOT be the product of those numbers - it will be HALF of that product).

At this point, you can divide each of the 5 answers into either 720 or 360 - only one answer will evenly divide in...

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Re: A number that is evenly divisible by 8, 9 and 10 must also be evenly  [#permalink]

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New post 11 Oct 2019, 10:41
EMPOWERgmatRichC wrote:
EMPOWERgmat PS Series:
Pack 2, Question 5

A number that is evenly divisible by 8, 9 and 10 must also be evenly divisible by which of the following:

A. 55
B. 60
C. 65
D. 70
E. 75



48 Hour Window To Win An $85 EMPOWERgmat Tuition Credit (1 Month Free!)
Share your explanation! The GMAT Club member with the most verified Kudos in total on the 5 question PS Block 2 question pack will win an $85 EMPOWERgmat tuition credit, which will entitle the winner to a full month of complete access to the EMPOWERgmat system. Even if you're not sure about your answer or your rationale, share your explanation to help boost your learning and earn a chance to win.

To be eligible, your explanation must be submitted within the 48 hour window after this post was created and should explain your reasoning why the answer you chose is correct

The OA and official explanation will be held until the 48 hour window has lapsed.


The number that is evenly divisible by 8, 9 and 10 is LCM of the numbers = 360

AMong the given options only (B) 60 can divide it, hence Answer must be (B)
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Re: A number that is evenly divisible by 8, 9 and 10 must also be evenly  [#permalink]

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New post 01 Dec 2019, 13:51
Most common number would be 8*9*10 = 720
Now 720 divisible by all the options.
a) 720/55 = 13.09
b) 720/60=12
c) 720/65=11.08
d) 720/70 =10.28
e) 720/75 = 9.6

Hence, the perfect divisible would be option B.
Hope this helps. :)
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Re: A number that is evenly divisible by 8, 9 and 10 must also be evenly   [#permalink] 01 Dec 2019, 13:51
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