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If k^3 is divisible by 240 what is the least possible value

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If k^3 is divisible by 240 what is the least possible value [#permalink] New post 26 Apr 2012, 02:14
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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
[Reveal] Spoiler: OA
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Re: Different ways to solve the problem : If K^3 is divisible [#permalink] New post 26 Apr 2012, 02:24
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sugu86 wrote:
If K^3 is divisible by 240, wat is the least possible value of integer k?

A) 12 B) 30 C) 60 D)90 E)120


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

Make prime factorization: 240=2^4*3*5.

Now, all primes of k^3 must be multiples of 3 (because of 3), so the least value of k^3 so that it's divisible by 2^4*3*5 is k^3=2^6*3^3*5^3 --> k=2^2*3*5=60.

Answer: C.

Hope it's clear.
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Re: If k^3 is divisible by 240 what is the least possible value [#permalink] New post 29 May 2012, 06:30
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hi Buneal your works are just grate

would you please explain
k^3=2^6*3^3*5^3
how power of 2 got 6

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Re: If k^3 is divisible by 240 what is the least possible value [#permalink] New post 29 May 2012, 06:37
marzan2011 wrote:
hi Buneal your works are just grate

would you please explain
k^3=2^6*3^3*5^3
how power of 2 got 6

Posted from my mobile device Image


We have that:
(i) k^3 is divisible by 2^4*3*5;
(ii) primes of k^3 must be multiples of 3;

Now, k^3 is divisible 2^4, so the power of 2 in k^3 must be multiple of 3 and more that 4: the least multiple of 3 which is more that 4 is 6.

Hope it's clear.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!

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Re: If k^3 is divisible by 240 what is the least possible value   [#permalink] 29 May 2012, 06:37
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