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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