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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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EMPOWERgmatRichC
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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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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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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