OCDianaOC wrote:
Bunuel wrote:
SOLUTION
If x is an integer, is y an integer?
(1) The average (arithmetic mean) of x, y and y – 2 is x --> \(\frac{x+y+(y-2)}{3}=x\) --> \(x+2y-2=3x\) --> \(y=x+1=integer+integer=integer\). Sufficient.
(2) The average (arithmetic mean) of x and y is not an integer --> if \(x=1\) and \(y=2\) the answer is YES but \(x=1\) and \(y=\frac{1}{2}\) the answer is NO. not sufficient.
Answer: A.
With the limited time constraints, how can you tell if it's best to try out alegebra or to plug in numbers?
I tried to plug in numbers for statement 1, but didn't seem to plug in correctly. I then proceeded to plug in #'s for number #2, and this one was much easier to solve!
Hi
I think this comes best with practice. The more we practice various questions and the more you try to apply both algebra and number plug-in methodology in those questions, the more our understanding will increase steadily.
Eg., in this question only substitution works better in statement 2 but algebra works better in statement 1.
Sometimes we will see that when there are only 1/2 variables, substitution works out well and when more variables are given in a question, generally algebra or some conceptual application fits in better towards a solution. (That is not true all the time though)