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

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Re: If x > 2 and y < -2, then which of the following must be true ? [#permalink]

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.
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Re: If x > 2 and y < -2, then which of the following must be true ? [#permalink]
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.

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If x > 2 and y < -2, then which of the following must be true ? [#permalink]
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.

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)
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If x > 2 and y < -2, then which of the following must be true ? [#permalink]

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

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Re: If x > 2 and y < -2, then which of the following must be true ? [#permalink]
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 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.
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If x > 2 and y < -2, then which of the following must be true ? [#permalink]
1
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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 Inequalities

Just in case you haven't seen it, the GMATclub Math Book, IS HERE

Does that help?
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Re: If x > 2 and y < -2, then which of the following must be true ? [#permalink]
1
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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 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.