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

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29 Sep 2015, 03:02

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

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29 Sep 2015, 03:15

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.

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

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29 Sep 2015, 05:28

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.

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

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30 Sep 2015, 10:08

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

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.

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

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.

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.
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