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

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

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New post 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
[Reveal] Spoiler: OA

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

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New post 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

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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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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

Hence Answer is option E.

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

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New post 25 Sep 2017, 01:03
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Factorize 51840.
let us start with the largest no.
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.

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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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New post 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.

Answer: E
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Re: In the expression 51840/x^4 for which of the following values of x wil   [#permalink] 26 Sep 2017, 16:27
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