If x and y are integers and xy ≠ 0, is x - y > 0 ?
(1) x /y < 1/2
(2) Sqrt(x^2) = x and ) Sqrt(y^2) = y
My answer was A, but that is not the OA ?
Hi all,
Step one of the Kaplan method tells you to think about the question; know that yes/no questions can often be rephrased.
The question asks you whether the difference between x and y is positive.
A difference between any two numbers is positive only and always when the number being subtracted is smaller than the number being subtracted from. This must be true because if the number being subtracted were larger than the number being subtracted from, then the difference would be negative.
In other words:bigger-smaller = +ve
and............smaller-bigger = -ve
Accordingly, the question is really just asking us whether we can determine which one is bigger (or smaller) than the other. Once we know that, we will be able to figure out whether that difference is positive or negative. And, really all you need to rephrase the question is the big/small rule as I summarized it, and some good data sufficiency technique (ie, method). Before going to the statements, say to yourself "hey it is asking me aboue size difference, how would that be easy to figure out?...if I knew one was positive and the other negative...will the statements allow me to figure that out?"
Statment 1: x/y can be smaller than 1/2 by being positive or negative. Pick some numbers that satisfy the statement. If x/y is 1/3, then either both x and y are positive or else both are negative. This is, in fact, enough to know that the statement is not sufficient because knowing that either both are positive or both negative is not enough to know which one is bigger (or smaller) than the other. ( If both are positive, then x is smaler than y but if both are negative then y is smaller than x). But even if x/y is (-1/3), then one is positive, the other negative, but you don't know which one is which (x could be pos and y could be neg or other way around). Insufficient.
Statement 2: Again, some crtiical thinking. A good rule in DS is "think before math."
sqrtx^2=x and sqrty^2=y
Because these equations are the same, let's just think about one of them. The right hand side does not give us much information so let's look to the left. The left hand side involves a square. You should now say "I am trying to figure out about pos and neg...what does a square have to do with that?" and then you are likely to remember that squares are always positive. And, on the GMAT, the sqrt symbol literally means "just the positive square root." And of course the (positive) square root of a positive number is...positive...
...Therefore, the left hand side is positive. Therefore, the right hand side is positive. Therefore, both x and y are positive...
but we don't have any information about size difference...Insufficient.
Both statements insufficient. This is the only time we combine the statements (step 3 of Kaplan method). And we combine the statments every time they are independently insufficient.
In combo, you know that they are both positive and that x/y<1/2. Because they are both positive you don't have to worry about sign changing, and you can just rewrite this is as 2x<y. If two xs are smaller than y, then one x is definitely smaller than y, and we now know their relative size difference.
Both statements insufficient by themsleves but sufficient in combination. Choice C.
...and just to be clear because x is smaller than y, we have smaller - bigger and x- y is definitely negative. Therefore, the answer to the question is "definitely no", which is just as sufficient as "definitely yes" (what matters is the confidence of the response, not its direction.)
For pandyvineet: You can treat an inequaliy symbol the exact same way you would treat an equal sign except for one big difference: when multiplying or dividing by negative one, you have to flip the sign. In statement one, because we don't know whether x and y are pos and neg, we don't know whether or not to flip the sign.
