If x and y are positive integer and xy is divisible by 4, which of the

Thank you for the reply Mike. When I saw \(xy\), I didn't think that it is \(x*y\). I thought it might be below

\(x\) --> 1
\(y\) --> 4

then \(xy\) is 14. Is this not the case? If not, can you explain when the expression indicates \(x*y\)?

Dear gmatchase

First of all, I'd like to suggest --- don't over-do the "math" notation. That's useful for fractions & exponents, but for ordinary x+y, we don't need the special notation.

The blanket assumption throughout all of algebra is that writing two variables next to each other (mx) or writing a number directly next to a variable (5y) always means multiplication. That's the meaning 100% of the time, unless something different is very explicitly specified. If the problem wanted the variables to represent digits, first of all, it probably would have used letters from the beginning of the alphabet, certainly not x & y (the standard algebraic variables), and it would have to say, quite explicitly, something like "Let a and b be digits in a the two-digit number ab." In other words, because the blank assumption is --- two variables next to each other always means multiply --- when a problem wants to indicate digits or anything else, it practically has to set up traffic cones and flashing signs to indicate the change. For a digits problem, it would have to explain, explicitly, what each variable represented. Any problem that just tosses an xy at you with no verbiage will never be using those variable as digits --- that xy will be multiplication 100% of the time.

Here's an example of a rare digit problem.
https://gmat.magoosh.com/questions/54
When you submit you answer, the following page will have a full video explanation.

Does all this make sense?

Mike

What if xy= 44 ( x=11, y= 4 or x=4 and y= 11)

Option B, C and D hold true then....i know in must be true questions picking numbers can be confusing..

Dear prateekbhatt
Yes. Remember that in any "must be true" math question, one answer has to be true, and most of the time, the other four will be usually be true --- some will be things that seem like they should be true. The GMAT simply is not going to give you one 100% true choice and four 100% false choices ---- it's going to be something more like one 100% true choice and four 90-95% true choices.

This means that, for any pair of numbers you pick, unless you are exceedingly lucky (or exceedingly skillful at picking numbers), more than one answer choice will still be true. The value of any single pair of numbers lies in [b]the choices you can eliminate[/b] ---- you pick one pair, eliminate some choices, then pick another pair, eliminate more choices, and whittle down the options. You are in the wrong frame of mind if you are trying to find the idea choice so that you can eliminate the four incorrect options all at once. If that happens by chance, great, but don't spend any time striving for that. Instead, think simplicity and speed. If I were plugging in numbers for this, my first choices would be the simplest kindergarten possibilities --- x = 1 & y = 4, then x = 4 & y = 1, then x = 2 & y = 2 --- in the first 10-20 seconds, you should be able to eliminate at least three answer choices with very easy selections for the variable values. Focus speed & efficiency, not on making ideal choices. Once you are down to two answers, you may need a more sophisticated choice --- for example, none of those choices would eliminate (D), so you would have to choose something like x = 2 & y = 8. That eliminates everything except the OA, (B), and I didn't use anything other than single-digit choices. Often you can remain with single digit math and get everything you need.

Does all this make sense?
Mike