Question asks whether X & Y have the same sign. If they do XY>0. If they have different signs, then XY<0

from 1:
x-y>-2 it follows: x > y-2
This is not sufficient. All it says is that X>Y

from 2:
x-2y<-6 it follows: X < 2y-6
Also not sufficient. If X is negative Y could be positive or negative

Combine 1 & 2

y-2 < 2y-6 (you can do this since X is greater than Y-2. So if X is less than 2Y-6 ... then by definition Y-2 will be less than 2Y-6)

Simplify
y-2 < 2y-6
y < 2y - 4
y>4

From statement 1we know that
x > y-2 .. so X>2

both X & Y are positive. XY must be positive. Answer is C

Thanks for the detailed explanation. Very helpful

I'm not sure if anybody is still watching this post, but if so,

what if this weren't so convenient and we weren't able to combine the inequalities as done by LSB for part C. would it be best to plug numbers? whats the fastest way to tackle this?

thanks.

In most of the inequality problems you can just combine the statements and find the solution.But never forget the basic rule that whenever both sides of an inequality is multiplied or divided by a negative number the sign is reversed..All you have to worry about is absolute value problems which can sometimes pose a problem..Even problems of such type can be easily tackled using Ian Stewart's approach..

you can also make substraction (1) from (2)
1. x-y>-2
2. x-2y<-6


(1)
x+2<y
(2)
x+6<2y

Substracting:
4<y

Some variation to LSB's approach

@ 4meonly....I think inequalities can be altered only by addition....Please correct me if I am wrong..

And the equations you have posted are incorrect

The 1st statement is x-y>-2 which can be altered to -x+y<2 (1) and not x+y<2 as you had posted earlier

The 2nd statement is x-2y<-6 (2)

Adding both the statements we get -y<-4 which is nothing but y>4

From the 1st statement we know that x>y-2 so x is also positive

Hence the ans is C

I would also request a piece of advice from the experts regarding altering the inequalities to deduce a solution...Kindly help

I still haven't got a response..Can the inequalities be altered only by addition or can subtraction be used in some cases?....I kindly request the experts to share their thoughts on this...Pls help

raju232007 wrote:I still haven't got a response..Can the inequalities be altered only by addition or can subtraction be used in some cases?....I kindly request the experts to share their thoughts on this...Pls help

Inequalities can only be added to each other, they cannot be subtracted to each other in any case.

suppose you have

1 x < ay +c
2 x> by +k

to substract

first make 2 like

-x < -(by +k)

and then add , remember for addition you need both the inequalities to have same gt or lt sign.

hope that helps.