Hi vikasp99,
This question can be solved in a couple of different ways. It's also built around some specific Number Properties, so if you're not sure how to approach the question, you can take advantage of those patterns and take a great guess.
We're told that X and Y are CONSECUTIVE INTEGERS (0 < X < Y) and that Y^2 - X^2 = 12,201. We're asked for the value of X.
To start, it's interesting that the DIFFERENCE ends in a 1. When subtracting the squares of consecutive integers, there are only a couple of ways that this can occur:
Y ends in a 1 and X ends in a 0
Y ends in a 6 and X ends in a 5
From the answer choices, we can clearly see that it's the first option - and that the correct answer is either Answer A or Answer C. If you're not sure what to do next, then you could guess and move on. However, if you want to continue working, you don't actually have to square two big numbers to find the solution to this question.
Since the two variables are consecutive, we can rewrite Y as (X + 1), so the original equation can be written as...
(X+1)^2 - X^2 = 12,201
X^2 + 2X + 1 - X^2 = 12,201
2X + 1 = 12,201
2X = 12,200
X = 6,100
Final Answer:
GMAT assassins aren't born, they're made,
Rich
When I first did the problem, I didn't actually come up with an answer, but did end up with a 61 while trying to figure out an approach. So I figured out that it had to be y^2 - x^2 = 12,201. So, I simplified 12,201 to 12,200 to make it more manageable (without doing the algebra). I then divided 12,200 by 2 which gave me 6,100 (just because I needed to try something). I thought this was a trick or some flaw in my thinking so I actually eliminated that choice. Was I just lucky in getting the 6,100 or is there an avenue to the solution somewhere in that train of thought without realizing the substitution method of y=x+1?