Mike@Magoosh wrote:

gmattesttaker2 wrote:Hello,

I was wondering why this would be wrong since I thought that we can add/subtract inequalites as long as they have the same sign:

If w + x < 0, is w - y > 0?
(1) x + y < 0

So, w + x < 0
& y + x < 0

So, w - y < 0

Thanks,
Sri

Sri,
I'm responding to your private message. Sometimes the best way to think about what's true for inequalities is to think in terms of ordinary numbers.

Inequality A: 15 < 17
Inequality B: 3 < 100
Both true. Both are in the same direction.

If we add them, all is well,
A + B: 18 < 117

BUT, if we subtract them ....
A - B: 12 > -83
Here, the direction of inequality reverses when we subtract (A - B). Notice that the direction wouldn't reverse if we subtracted (B - A). There's no predictable pattern --- subtracting inequalities is trouble!

It's NEVER a good idea to subtract two inequalities. Again, adding them is perfectly legit. You are also allowed to add or subtract any constant to both sides, and the inequality would still work. BUT, subtracting one inequality from another is just asking for big problems. That's what's so tempting about this brilliantly designed DS ---- it just lures the unsuspecting test taker into making a very predictable mistake. It's so good for you to learn about these predictable mistakes, so you can learn to avoid them.

Does all this make sense?
Mike

rakeshd347 wrote:

gmattesttaker2 wrote:Hello,

I was just wondering why this would be wrong since I thought that we can add/subtract in-equalites as long as they have the same sign:

If w + x < 0, is w - y > 0?
(1) x + y < 0

So, w + x < 0
& y + x < 0

So, w - y < 0


Thanks,
Sri

Hi Sri,

Here is the golden rule of inequality:

A>C and B>D then you can add both inequality: A+B>C+D.
However you can't subtract both inequality A-B>C-D....this is wrong.
If you want to subtract then you have to have the opposite sign.

Let me explain you here:

A>C and B>D...or we can say A>C and D<B....one and same thing right.
Now you can subtract A-D>C-B ( now the main point here to note is inequality sign will take the sign of the inequality from which we are subtracting)

A>C and D<B now suppose you want to get D-A<B-C....in this case it will take the sign of D inequality because you are subtracting from D. In the above inequality you were subtracting from A.

Suppose
3>2 and 3>1...now if you subtract 3-3>2-1 or 0>1 no this is wrong
but if you were to do.

3>2 and 1<3 then you can do 3-1>2-3 which is 2>-1

This Rule will always hold true. Not many people know it but this is a good tool to tackle inequality questions.