Hey! I have a question from the Oct 2015 test, section 2 Q#17

Could you explain the thought process? (The parentheses are for the square root, anything in the parentheses next to the square root are meant to be included in the square root )√(y-3) = √(x-2) +x

In the equation above, X and Y are positive integers. What is the least possible value of Y?

You’ll get the least value of *y* when you *x* is as small as possible, too. The smallest possible value of *x* is 2, because if *x* were any smaller then the square root on the right would have a negative in it. So let’s say *x* = 2.

From there, it’s only a few more steps to the answer. Square both sides:

*y* – 3 = 4

*y* = 7

## Comments (2)

So in general, in the SAT, things will always pan out well in that way? There wouldn’t be a case where, say, putting x as 2 would give a non-integer y value? For my part, I tried going from y straight away, and it took me a while to understand that it had to be something (y value) which, when y-3, gave something which would be a square (for x to be an integer). However, it would have taken me too long to understand that during test day, and your solution seems far superior. I just find that thinking of plugging x as 2 doesn’t and won’t always come to mind during test day, and I don’t know what approach I should take to solve these questions consistently and be confident when I see them. Thanks Mike.

There’s no such thing as “always” with the SAT. That’s why it’s important to develop a bag of tricks—techniques that work fairly often, like plugging in. That way, if you’re stumped on a problem, you have a few things you can try. If you practice it now, then maybe by the time test day comes around plugging in 2 WILL occur to you on test day.