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If n is a positive integer and n^3 is a multiple of 550, what is the

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Bunuel
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If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink] New post   11 Feb 2015, 06:38
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If n is a positive integer and n^3 is a multiple of 550, what is the least possible value of n?

A. 8
B. 27
C. 81
D. 110
E. 125


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D
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Re: If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink] New post   12 Feb 2015, 00:16
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If n is a positive integer and n^3 is a multiple of 550, what is the least possible value of n?

A. 8
B. 27
C. 81
D. 110
E. 125



Since n^3 is multiple of 550 so unit digit of n must be "0".
OA = D
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Re: If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink] New post   11 Feb 2015, 22:40
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Answer = D. 110

\(550 = 2^2 * 5^1 * 11^1\)

Out of the OA, only option D has 2, 5 & 11 as the constituents.
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Re: If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink] New post   12 Feb 2015, 01:23
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IMO its D
simple.. 5^2 * 2 *11=550
k(n^3)=550
all we need 5,2 and 11
hence 110


kudos to me if its a right one
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Re: If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink] New post   16 Feb 2015, 05:58
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Bunuel wrote:
If n is a positive integer and n^3 is a multiple of 550, what is the least possible value of n?

A. 8
B. 27
C. 81
D. 110
E. 125


Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION

Correct Answer: D

To begin this question, factor 550 into its primes: 550 = 2 * 5 * 5 * 11. If we multiply this number by 2 * 2 * 5 * 11 * 11, we'll have 2^3 * 5^3 * 11^3 , which is the same as (2∗5∗11)^3. This is the smallest multiple of 550 that is a perfect cube (an integer cubed) and thus n = 110.

The correct answer is D.
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If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink] New post   25 Apr 2016, 01:56
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ranaazad wrote:
Bunuel wrote:
Bunuel wrote:
If n is a positive integer and n^3 is a multiple of 550, what is the least possible value of n?

A. 8
B. 27
C. 81
D. 110
E. 125


Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION

Correct Answer: D

To begin this question, factor 550 into its primes: 550 = 2 * 5 * 5 * 11. If we multiply this number by 2 * 2 * 5 * 11 * 11, we'll have 2^3 * 5^3 * 11^3 , which is the same as (2∗5∗11)^3. This is the smallest multiple of 550 that is a perfect cube (an integer cubed) and thus n = 110.

The correct answer is D.


l was looking for an answer choice with a number greater than 550. As l knew, a multiple of any number is equal to or greater than the number itself. Could someone please clarify what l'm missing here?
Almost 90% people got this question correct. :oops: My apologies for the silly question.

Regards,
Rana


Hi,
if it was N is multiple of 550, yes you should have been looking for N>550..
But here N^3 is to be made multiple of 550...
N^3 means there should be atleast three of each prime factors in it..
\(550 = 2*5^2*11\)...
so we require 2*5*11..
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Re: If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink] New post   31 Jul 2020, 07:28
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Bunuel wrote:
If n is a positive integer and n^3 is a multiple of 550, what is the least possible value of n?

A. 8
B. 27
C. 81
D. 110
E. 125


Kudos for a correct solution.


Solution:

Let’s prime factorize 550:

550 = 55 x 10 = 5 x 11 x 5 x 2 = 2 x 5^2 x 11

Since n^3 must have its prime factors in multiplicities of 3, the least possible value of n^3 is 2^3 x 5^3 x 11^3 (i.e., n = 550 x 2^2 x 5 x 11^2) and hence the least possible value of n is 2 x 5 x 11 = 110.

Answer: D
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Re: If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink] New post   11 Feb 2015, 07:29
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Bunuel wrote:
If n is a positive integer and n^3 is a multiple of 550, what is the least possible value of n?

A. 8
B. 27
C. 81
D. 110
E. 125


Kudos for a correct solution.


cube of a number entails having 3 copies of the original prime factors. Since 550 is a facor of \(n^3\) the least possible value of n is 5(11)2 = 110 and the answer is D.
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Re: If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink] New post   25 Apr 2016, 01:48
Bunuel wrote:
Bunuel wrote:
If n is a positive integer and n^3 is a multiple of 550, what is the least possible value of n?

A. 8
B. 27
C. 81
D. 110
E. 125


Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION

Correct Answer: D

To begin this question, factor 550 into its primes: 550 = 2 * 5 * 5 * 11. If we multiply this number by 2 * 2 * 5 * 11 * 11, we'll have 2^3 * 5^3 * 11^3 , which is the same as (2∗5∗11)^3. This is the smallest multiple of 550 that is a perfect cube (an integer cubed) and thus n = 110.

The correct answer is D.


l was looking for an answer choice with a number greater than 550. As l knew, a multiple of any number is equal to or greater than the number itself. Could someone please clarify what l'm missing here?
Almost 90% people got this question correct. :oops: My apologies for the silly question.

Regards,
Rana
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Re: If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink] New post   25 Apr 2016, 03:01
Hi,
if it was N is multiple of 550, yes you should have been looking for N>550..
But here N^3 is to be made multiple of 550...
N^3 means there should be atleast three of each prime factors in it..
\(550 = 2*5^2*11\)...
so we require 2*5*11..[/quote]


Thank you for the instant reply! lt's understandable now. :-D
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Re: If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink] New post   02 Aug 2020, 17:11
Bunuel wrote:
If n is a positive integer and n^3 is a multiple of 550, what is the least possible value of n?

A. 8
B. 27
C. 81
D. 110
E. 125


Kudos for a correct solution.


550=5*11*10

For n^3 to be multiple of 550 we need at least 5*2*11. Only option D has all 3 elements. 110=11*10=11*2*5

Answer B
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Re: If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink] New post   13 Jul 2022, 02:54
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