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Quant Integer Properties- Optimum Approach

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by ankur.agrawal » Tue Aug 17, 2010 11:49 pm
k is a positive integer and 225 and 216 are both divisors of k. If k = 2a ×3b ×5c, where a, b and c are positive integers, what is the least possible value of a + b + c ?

(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
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by kvcpk » Wed Aug 18, 2010 2:15 am
ankur.agrawal wrote:k is a positive integer and 225 and 216 are both divisors of k. If k = 2a ×3b ×5c, where a, b and c are positive integers, what is the least possible value of a + b + c ?

(A) 4 (B) 5 (C) 6 (D) 7 (E) 8
225 = 9*25
216=9*24
LCM of 225 and 216 is
9*25*24 =216*5(5)

There should be atleast 5 five multiples. hence answer should be greater than 5.

216 = 2a*3b
36=ab
sum of a and b should be minimum.
Hence a=b=6

I get a+b+c = 6+6+5 = 17

What am I missing?
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by anantbhatia » Wed Aug 18, 2010 2:30 am
I presume that you meant k = 2^a X 3^b X 5^c

In that case, LCM of 225,216= 2^3 . 3^3 . 5^2

This will give us the smallest number that will be divisible by both 225 and 216. and hence the smallest value of the sum will be 8. (E)
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by gmatmachoman » Wed Aug 18, 2010 2:47 am
praveen ..u have nailed it..it has to be 17...

U can get 18 if u use a= 4, b=9,c=5

But we are looking for least so u get ur point....
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by ankur.agrawal » Wed Aug 18, 2010 2:57 am
OOPS! SORRY FOR MISTAKE IN COPY PASTE. I MEANT


I meant k = 2^a X 3^b X 5^c .
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by kvcpk » Wed Aug 18, 2010 3:19 am
ankur.agrawal wrote:OOPS! SORRY FOR MISTAKE IN COPY PASTE. I MEANT


I meant k = 2^a X 3^b X 5^c .
Hi Ankur,

Excused :)

Request to recheck your psost after/before posting. Because I spent much time thinking what I am doing wrong.
We all do mistakes. But just wanted to let you know.

Cheers!!
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
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by ankur.agrawal » Wed Aug 18, 2010 3:23 am
kvcpk wrote:
ankur.agrawal wrote:OOPS! SORRY FOR MISTAKE IN COPY PASTE. I MEANT


I meant k = 2^a X 3^b X 5^c .
Hi Ankur,

Excused :)

Request to recheck your psost after/before posting. Because I spent much time thinking what I am doing wrong.
We all do mistakes. But just wanted to let you know.

Cheers!!
I am real sorry. Wont let it happen again.
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by bdevas01 » Wed Aug 18, 2010 5:43 am
Why didn't anyone post the answer?

Its 7 right?

The LCM of both numbers is 5400, which can be broken down into prime numbers: (2^2)x(3^3)x(5^2) and the values of a, b and c are 2, 3 and 2 respectively.

2 + 3 + 2 = 7, so D. 7.
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by kvcpk » Wed Aug 18, 2010 6:02 am
bdevas01 wrote:Why didn't anyone post the answer?

Its 7 right?

The LCM of both numbers is 5400, which can be broken down into prime numbers: (2^2)x(3^3)x(5^2) and the values of a, b and c are 2, 3 and 2 respectively.

2 + 3 + 2 = 7, so D. 7.
5400 = 2^3*3^3*5^2
answer should be 3+3+2 = 8

HTH!!
"Once you start working on something,
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People who work sincerely are the happiest."
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