sandy wrote:
If x is divisible by 78, which of the following must be divisible by x?
Indicate all possible values.
A. \(\frac{x}{78}\)
B. \(x\)
C. \(x+78\)
D. \(78-x\)
E. \(78x\)
F. \(78x+78\)
sandyI think it must be B and E only
Here is why:
If \(x\) is divisible by \(78\) then \(x\) must have all the factors of \(78\) i.e. \(2, 3\) and \(13\)
Let \(x = 78a = (1)(3)(13)a\)
A. \(\frac{x}{78x} = \frac{1}{78}\) - NO
B. \(\frac{x}{x} = 1\) - YES
C. \(\frac{(x+78)}{x} = \frac{(78a + 78)}{78a} = \frac{(a + 1)}{a}\) - NO
D. \(\frac{(78 - x)}{x} = \frac{(78 - 78a)}{78a} = \frac{(1 - a)}{a}\) - NO
E. \(\frac{78x}{x} = 78\) - YES
F. \(\frac{(78x+78)}{x} = \frac{78(x + 1)}{78a} = \frac{(x + 1)}{a}\) - NO
Hence, option B and E