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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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Math Expert
Joined: 02 Sep 2009
Posts: 46264
If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink]

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11 Feb 2015, 06:38
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Question Stats:

91% (01:00) correct 9% (01:37) wrong based on 127 sessions

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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

Kudos for a correct solution.

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Re: If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink]

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11 Feb 2015, 07:29
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]

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11 Feb 2015, 22:40
1

$$550 = 2^2 * 5^1 * 11^1$$

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]

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12 Feb 2015, 00:16
3
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]

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12 Feb 2015, 01:23
1
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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Posts: 46264
Re: If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink]

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16 Feb 2015, 05:58
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

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.

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Re: If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink]

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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

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.

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. My apologies for the silly question.

Regards,
Rana
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Math Expert
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Posts: 5911
If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink]

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25 Apr 2016, 01:56
1
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

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.

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. 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]

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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.
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Re: If n is a positive integer and n^3 is a multiple of 550, what is the [#permalink]

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15 Aug 2017, 08:42
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Re: If n is a positive integer and n^3 is a multiple of 550, what is the   [#permalink] 15 Aug 2017, 08:42
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