If x 2 and y

Question

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 .

haritha177 · Answer

It should be C 
A is not possible cuz y is -ve & x is +ve
B - the ans can be -1 ex. (3/-3)
D x+y can be negetive
E xy is always -ve

BrainLab · Answer

x > 2 and y < -2

A) x/y > 1 -> Answer cannot be positive as we are dealing with opposite signs by x,y
B) x/y < -1 -> let's pick some extreme numbers x=2,1 and y=-1,9 than x/y =-1.1 YES , but x=5, y=-10 x/y=-0.5 NO
C) x/y < 0 -> CORRECT
D) x + y > 0 -> X=3, y=-1 YES, x=3, y=-100 NO
E) xy > 0 -> same as A

longfellow · Answer

The answer is C

x equals any value from 2 to infinity while y includes values from -2 to -infinity. this value will always be less than zero as their signs will always be different irrespective of values.

ravieee1 · Answer

Pick x=3, y = -3
A) x/y > 1 - Incorrect as x/y = -1
B) x/y < -1 - Incorrect as x/y = -1
C) x/y < 0 - Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0
D) x + y > 0 - Incorrect. x + y = 0
E) xy > 0 - Incorrect. XY = -9 which is less than zero.

C should be the answer.

AkshdeepS · Answer

My solution:

Stem says:- x is +ve and greater than 2, y is -ve and less than -2.

A) x/y>1 (can never be greater than 1 as expression will always be negative as y is negative. Not true )

B) x/y < -1 (can be equal to -1 when x is 3 and y is -3. Not true always)

C) x/y < 0 (will always be less than zero as only one value is negative i.e, "y". Always true.

D) x+y>0 (can be equal to zero or less than zero [3+(-3)=0] or [4+(-5)=-1] Not always true)

E) xy>0(As y is negative xy can never be greater than zero. Not true)

Jonas84 · Answer

I believe the answer is C. Please see below for explanation.

If x > 2 and y < -2, then which of the following must be true ?

if x= 3 and y =-3 and we plug in the numbers we get

A) x/y > 1---------- 3/-3=-1 not true
B) x/y < -1--------- 3/-3=-1 not true
C) x/y < 0---------- 3/-3=-1 a positive number divided by a negative number will always be negative True
D) x + y > 0-------- 3-3=0 not true
E) xy > 0----------- 3*-3<0 not true

Answer C

rahul16singh28 · Answer

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 can 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.

generis · Answer

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 Inequalities And here, Inequalities Made Easy Just in case you haven't seen it, the GMATclub Math Book, IS HERE Does that help?

chetan2u · Answer

Already explained above ....
Just remember that you do not know the signs of variables..
So look at the sign and add the greater quantities and add the smaller quantities, ofcourse sum of greater quantities will be MORE than the sum of smaller quantities..
So x>2 and -2>y tells you x ia POSITIVE and y is NEGATIVE..
So 2-y will become a positive value.

If x > 2 and y < -2, then which of the following must be true ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions