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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