MathRevolution wrote:
Is x > y?
1) x + a > x - a
2) ax > ay
Target question: Is x > y? Statement 1: x + a > x - a This statement doesn't include any information about y, so there's no way to answer the
target question.
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: ax > ay Some students will divide both sides by a and
incorrectly conclude that x > y.
However, before we divide by a variable, we must ensure that the variable is EITHER positive OR negative, because if we divide by a
negative value, we must reverse the direction of the inequality, and if we divide by a
positive value, the direction of the inequality stays the same. As it stands, we don't know whether a is positive or negative.
To see what I mean, consider these values of a, x and y that satisfy the given condition:
Case a: a = 1, x = 3 and y = 2, in which case
x > yCase b: a = -1, x = 2 and y = 3, in which case
x < ySince we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that x + a > x - a
Add a to both sides to get: x + 2a > x
Subtract x from both sides to get: 2a > 0
Divide both sides by 2 to get: a > 0. In other words,
a is POSITIVEStatement 2 tells us that ax > ay
Now that we know that
a is POSITIVE, we can take ax > ay and safely divide both sides by a to get:
x > y PERFECT!
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
RELATED VIDEO FROM OUR COURSE
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Students often get questions wrong NOT because they lack the skills to solve the question, but because they don’t understand what the GMAT is testing Learn more