240 = (2) (2) (2) (2) (3) (5), which is (2) (2) (3) (3) (5) (5) short of being a minimum cube for this kind of K.kop wrote:If K to the power of 3 (k cube) is divisible by 240, what is the least possible value of integer K?
a 12
b 30
c 60
d 90
e 120
Please explain?
Let's see what minimum K comes out to be when the supply is made:
K^3 = (2) (2) (2) (2) (3) (5) (2) (2) (3) (3) (5) (5)
Hence the least possible value of integer K = [spoiler](2) (2) (3) (5) = 60
Choose C[/spoiler]
Alternative Approach
We know that 240 = (2) (2) (2) (2) (3) (5)
May be we plug in the answers, start testing from C as usual, see it's
(C) 60 = (2) (2) (3) (5)
If cubed 60^3 = (2) (2) (2) (2) (3) (5) (2) (2) (2) (2) (3) (5) (2) (2) (2) (2) (3) (5) , which contains everything that is required by 240 = (2) (2) (2) (2) (3) (5). Hence, we can eliminate the bigger choices, as we're looking for the least value only. We should plug in a smaller choice to make sure if (C) is correct. Let's plug in
(B) 30 = (2) (3) (5)
If cubed 30^3 = (2) (3) (5) (2) (3) (5) (2) (3) (5), which is (2) short of what is required by 240 = (2) (2) (2) (2) (3) (5). Hence, [spoiler](C)[/spoiler] remains the correct answer.
