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# In the expression 51840/x^4 for which of the following values of x wil

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Manager
Joined: 02 Jun 2015
Posts: 184
Location: Ghana
In the expression 51840/x^4 for which of the following values of x wil  [#permalink]

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25 Oct 2016, 15:48
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In the expression 51840/x^4, for which of the following values of x will the expression NOT be an integer?

A 1/2
B) 1
C) 2
D) 3
E) 5

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Manager
Joined: 28 Jun 2016
Posts: 216
Concentration: Operations, Entrepreneurship
In the expression 51840/x^4 for which of the following values of x wil  [#permalink]

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25 Oct 2016, 16:02
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duahsolo wrote:
In the expression 51840/x^4, for which of the following values of x will the expression NOT be an integer?

A 1/2
B) 1
C) 2
D) 3
E) 5

We can straightaway eliminate A & B, since the expression will always yields an integer for those values

Out of C, D, and E. Let us consider option E. 51840 has only one trailing zero and tens digit is not 5, so It has just one 5 in it. But for the expression to be an integer numerator should have 5^4.

So option E
##### General Discussion
Manager
Joined: 04 May 2014
Posts: 158
Location: India
WE: Sales (Mutual Funds and Brokerage)
In the expression 51840/x^4 for which of the following values of x wil  [#permalink]

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25 Sep 2017, 01:03
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Factorize 51840.
51840=5X10368. We can stop here as 10368 will not contain anymore 5.
In order for 51840 to be divisible by $$5^{4}$$ it should contain 4 no of 5"s.
Manager
Joined: 12 Feb 2017
Posts: 70
Re: In the expression 51840/x^4 for which of the following values of x wil  [#permalink]

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04 Sep 2017, 22:44
We can eliminate option A and B, as in any case these options will give us an integer value.
Now to solve further problem we need to factorize the given number.
51840= 2^7 * 3^4 * 5
Option C=2
(2^7 * 3^4 * 5) / 2^4 ---- Integer
Option D=3
(2^7 * 3^4 * 5) / 3^4 ---- Integer
Option E=5
(2^7 * 3^4 * 5) / 5^4 ---- Not an Integer

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Re: In the expression 51840/x^4 for which of the following values of x wil  [#permalink]

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26 Sep 2017, 16:27
duahsolo wrote:
In the expression 51840/x^4, for which of the following values of x will the expression NOT be an integer?

A 1/2
B) 1
C) 2
D) 3
E) 5

Let’s break down 51,840:

51,840 = 20 x 2,592

From this factorization of 51,840, we see that 20 has just one factor of 5. We see that 2,592 does not have a units digit of 5 or 0, and so it has no factors of 5. Therefore, 51,840 itself has only one factor of 5.
Note that 51,840/x^4 can be an integer only if x^4 divides equally into 51,840. If x = 5, we know that 5^4 does not divide equally into 51,840 because 51,840 contains only one factor of 5. Thus, 51,840/5^4 will not yield an integer answer.

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Intern
Joined: 16 Dec 2018
Posts: 10
Re: In the expression 51840/x^4 for which of the following values of x wil  [#permalink]

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11 Jan 2019, 10:13
Ans is E. I just used elimating the options process atleast i left with E.

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Re: In the expression 51840/x^4 for which of the following values of x wil   [#permalink] 11 Jan 2019, 10:13
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