rahul16singh28 wrote:
Bunuel wrote:
If x > 2 and y < -2, then which of the following must be true ?
A) x/y > 1
B) x/y < -1
C) x/y < 0
D) x + y > 0
E) xy > 0
Kudos for a correct solution.
Hi
chetan2u &
genxer123,
For this question its obvious that the answer will be C. But I am unable to justify why D is wrong even though we can prove that D is wrong by plugging in some numbers. From the given question x > 2 and -2 > y. As I understand we an add and substract inequalities provided we know their sign. So, when we subtract the above two equation we get x + 2 > 2 - y or x+y > 0. Can you please advise where I am wrong in my thinking.
rahul16singh28 , you just got a little mixed up about the direction of the sign. (Take comfort: the answer is there because plenty of others will do exactly what you did.)
It looks to me as if you subtracted inequalities with the same sign.
You said you subtracted these: x > 2 and -2 > y
Not allowed. Their signs face the same direction.
We can
add inequalities whose signs are the
same direction.
We can
subtract inequalities whose signs are in
opposite directions.
So you can
add the two you listed. And: You are adding a negative number (-2) on LHS, i.e., subtraction. 3 + -2 = (3-2) = 1
····· x > 2
(+)-2 > y
------------------------
= x - 2 > 2 + y
Can you take it from there?
If not, you might want to take a look at
Bunuel ,
Tips and Hints on InequalitiesAnd here,
Inequalities Made EasyJust in case you haven't seen it, the GMATclub Math Book,
IS HEREDoes that help?