sahuamit91 wrote:
If x and y are positive integers, is x a multiple of y?
(1) y^2 + y is not a factor of x.
(2) x^3 + x is not a multiple of y.
Got some enlighment here
Question ask whether \(\frac{x}{y}=integer\).
Statement 1- We can write the statement into \(\frac{x}{(y^2)+y}=non integer\)
- Simplify equation, we get \(\frac{x}{y(y+1)}=non integer\) --> we isolate \(\frac{x}{y}\) --> \(\frac{x}{y}=non integer*(y+1)\)
- From here, we can conclude that \(\frac{x}{y}\) can be either an integer or not an integer.
- Case 1 : let say we have non integer \(\frac{1}{3}\) and \(y=2\), so \(\frac{1}{3}*(2+1) = integer\).
- Case 2 : let say we have non integer \(\frac{1}{3}\) and \(y=3\), so \(\frac{1}{3}*(3+1) = non integer\).
- INSUFFICIENT.
Statement 2- We can write the statement into \(\frac{x^3+x}{y}=non integer\)
- Simplify equation, we get \(\frac{x(x^2+1)}{y}=non integer\) --> we isolate \(\frac{x}{y}\) --> \(\frac{x}{y}=\frac{non integer}{(x^2+1)}\).
- From here, we can conclude that the result of \(\frac{x}{y}\) always non integer.
There is no way a non integer when divided by integer become integer.
- Thus, we got the definite answer here!
- SUFFICIENT
B
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