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by theCodeToGMAT » Mon Oct 14, 2013 1:09 am
240 = 2 x 2 x 2 x 3 x 5 x 2

We need answer choice which contains at least: two 2's, one 3 and one 5

So, 2 x 2 x 3 x 5 = 60

Answer [spoiler]{C}[/spoiler]
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by sukhman » Mon Oct 14, 2013 1:15 am
I didnt understand it says K^3 (k cube) why not 30
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by theCodeToGMAT » Mon Oct 14, 2013 1:30 am
sukhman wrote:I didnt understand it says K^3 (k cube) why not 30
30 = 3 x 2 x 5

(30)^3 = 3^3 x 2^3 x 5^3

However, for a number to be divisible by 240 we need MINIMUM 2^4 x 3^1 x 5^1

Since, we have one less "2" in 30^3 .. it cannot be divisible by 240
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by GMATGuruNY » Mon Oct 14, 2013 3:15 am
sukhman wrote:If k^3 is divisible by 240 what is the least possible value of integer k
a.12 b.30 c.60 d.90 e.120
Answer is c
An alternate approach is to PLUG IN THE ANSWERS.
The correct answer choice will be the smallest option that, when cubed, is divisible by 24*10 = 24*10 = 2*10*12.

A: (12*12*12)/(2*10*12) = (6*6*1)/(1*5*1).
Doesn't work.
Eliminate A

B: (30*30*30)/(2*10*12) = (15*3*5)/(1*1*2).
Doesn't work.
Eliminate B.

C: (60*60*60)/(2*10*12) = (30*6*5)/(1*1*1) = 30*6*5.
Success!

The correct answer is C.
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