torofish wrote:It's from CAT

x<20, Yes or No
1.) X+Y<20
2.) Y<20

I get that 1 and 2 are not sufficient.
For 1+2) I did like this

X+Y<20 [minus]
Y<20
X < 0 Therefore X < 20

But think again, it's not always the case for example
Y = -5 then X < 25

Therefore it's E.

But why two equations operations doesn't work in this case?
I thought we can do like
X+Y = 20
Y = 15
X = 5

or we can only do with equality only?

I dont think you can even get x< 0 in the above question .

X+Y<20 [minus]
Y<20
X < 0 Therefore X < 20

This is not correct since Y is always less than 20 .


Lets look at the question .

x<20, Yes or No?

1.) X+Y<20

2.) Y<20


Rephrase (1) : X + Y < 20

X < 20 - Y

Don't know any thing about Y . Not Sufficient

Rephrase (2) : Y < 20 .

says nothing about X . Not sufficient .

Combine 1 and 2 .

Y < 20 .

And X < 20 - Y .

Now you can get an answer . And the only case when X will be less than 0 will result when Y = 20 and this can not happen since Y < 20 .


But if Y = -5

X < 25 . Is X<20 ,NO

And if Y = 19

X < 1 and Is X < 20, Yes .

Hence E.

x<20, Yes or No
1.) X+Y<20
2.) Y<20

2) Y < 20 cannot say anything about X Insuff.
1) Even if Y >= 0 X will be < 20
but, if Y<0 then say -1 then X < 21 but not < 20
Insuff.

IMO E.

torofish wrote:
I get that 1 and 2 are not sufficient.
For 1+2) I did like this

X+Y<20 [minus]
Y<20
X < 0 Therefore X < 20

I am not sure you will get X<0 , when you subtract the second inequality from the first. Because if you multiply both sides of an equality with -ve sign , the inequality sign changes, so the second inequality becomes - Y > -20 . And you cannot subtract two inequalities which are not of the same sign ( < or > ).

hi thanks for your answer.
For this case, we can prove it by picking number.

But what I really doubt is that can we (+ | -- | * | / ) inequality equations?
I posted a picture
case 1, and 2 is for sure OK.

But in case 3, is it OK to do like that?
If no, from now on, if I see this kind of question, I'll just don't do another equation operations rather just simply pick numbers.

If yes, clearly, it cannot be done every time, for example, the question I asked.
So, the next question is what should I look for as a warning that these two inequalities are not operable.

torofish wrote:hi thanks for your answer.
For this case, we can prove it by picking number.

But what I really doubt is that can we (+ | -- | * | / ) inequality equations?
I posted a picture
case 1, and 2 is for sure OK.

But in case 3, is it OK to do like that?
If no, from now on, if I see this kind of question, I'll just don't do another equation operations rather just simply pick numbers.

If yes, clearly, it cannot be done every time, for example, the question I asked.
So, the next question is what should I look for as a warning that these two inequalities are not operable.

Hi,

there are so many times that we're not[/u] allowed to add and subtract inequalities that it's just not worth the trouble to do so. You're definitely better off using logic/common sense to reason out the answer or picking numbers.

With equations, it's safe to add/subtract them.

torofish wrote:hi thanks for your answer.
For this case, we can prove it by picking number.

But what I really doubt is that can we (+ | -- | * | / ) inequality equations?
I posted a picture
case 1, and 2 is for sure OK.

But in case 3, is it OK to do like that?
If no, from now on, if I see this kind of question, I'll just don't do another equation operations rather just simply pick numbers.

If yes, clearly, it cannot be done every time, for example, the question I asked.
So, the next question is what should I look for as a warning that these two inequalities are not operable.

Dude ,

Here is the mantra , when you see inequalities in equations only two operations are allowed .

1. Addition of variable
2. Subtraction of variable


So to answer your questions YES (3) is allowed and you can line up inequalities and add or subtract variables .

BUT

You can never - never multiply OR divide variables .

Reason : We never know what sign the variable has is it + ve or - ve .

And as far as multiplying / divining by - ve number is concerned you need to flip the inequality sign .

So : never multiply / divide variables in inequality .

You can add or subtract variables in equality .

Hope this helps