X greater than Y - Doubt in sign

[rahulvsd]

Is x < y ?

STATEMENT 1:

10x > 10y

STATEMENT 2:

x + ab > y + ba
[spoiler]
OA: D. Can we actually say that St 1 will be sufficient on its own, cos after dividing by 10 we get x < y. Now dont we need to know the sign of x and y to say which is greater? [/spoiler]

[aneesh.kg]

Is x < y ?

STATEMENT 1:

10x > 10y

STATEMENT 2:

x + ab > y + ba
[spoiler]
OA: D. Can we actually say that St 1 will be sufficient on its own, cos after dividing by 10 we get x < y. Now dont we need to know the sign of x and y to say which is greater? [/spoiler]

By dividing
10x > 10y by 10 on both sides you get
x > y
and NOT
y < x.

The sign of the inequality reverses only when you multiply or divide both sides of the inequality by a negative number. If you multiply or divide both sides by a positive number (such as 10), the sign of the inequality does not change.

Take the example of
3 > 2
If we divide by 10 on both sides, we get
0.3 > 0.2
which is true. The sign of the inequality does not change,

If we divide by -10 on both the sides, we get
-0.3 < -0.2
The sign of the inequality reverses.

This is a very important concept and I hope you've understood.

Statement(1) answers the question with a 'NO', so does Statement (2).

[rahulvsd]

Thanks. I did realize this basic concept after I posted the question. Guess I was half asleep while doing this problem.