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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: 190

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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, 14:48
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63% (01:24) correct 37% (00:51) wrong based on 153 sessions

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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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Kudos [?]: 324 [1], given: 407

Manager
Joined: 28 Jun 2016
Posts: 207

Kudos [?]: 94 [3], given: 63

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, 15:02
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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

Kudos [?]: 94 [3], given: 63

Manager
Joined: 12 Feb 2017
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Kudos [?]: 30 [2], given: 47

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

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04 Sep 2017, 21:44
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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

Kudos if it helps.

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Manager
Joined: 03 May 2014
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Kudos [?]: 20 [1], given: 126

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, 00:03
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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.

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Target Test Prep Representative
Affiliations: Target Test Prep
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Kudos [?]: 1046 [0], given: 5

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

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26 Sep 2017, 15:27
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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Kudos [?]: 1046 [0], given: 5

Re: In the expression 51840/x^4 for which of the following values of x wil   [#permalink] 26 Sep 2017, 15:27
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