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## Comment on

2x over y## Why do we have (y -ve for

## The problem with that

The problem with that approach (multiplying both sides by y) is that we don't know whether y is positive or negative.

If y is negative, we must reverse the inequality sign. If y is positive, the direction of the inequality sign stays the same.

For more see https://www.gmatprepnow.com/module/gmat-algebra-and-equation-solving/vid...

## So is it safe to say you

## That's correct. Having or not

That's correct. Having or not having a negative symbol in front of a variable doesn't tell us anything about whether that variable is positive or negative.

For example, x can be negative or positive.

Likewise, -x can be negative or positive.

## then in the second case how

## While rewriting the

While rewriting the inequality in statement 2, we are able to avoid multiplying or dividing both sides of the inequality by a variable. So, in the end, we can be certain that y is greater than zero.

## If in above problem assume it

## IF we had been able to

IF we had been able to conclude (from statement 2) that y is negative, then the answer would be E.

From statement 1, we learned that, if y is negative, then x < 5

So, when we combine the two statements, we can conclude that x < 5

The target question asks "Is x negative?"

So, if x < 5, then x COULD equal 4, which means x IS positive.

Conversely, if x < 5, then x COULD equal -1, which means x is NOT positive.

Since we cannot answer the target question with certainty, the combined statements are not sufficient.

## Brilliant explanation in

## Great question, I completely

## You're not alone. Many

You're not alone. Many students will forget that y can be either positive or negative.

## Great video Brent. If using a

## Think I get it now Brent to

## That's correct.

That's correct.

The target question, "Is x > 0?" contains no given information.

So, if we know that x > 5, then we can be certain that x > 0.

In other words, the answer to the target question is a definite YES (x IS greater than 0), which means the statement is sufficient.

## Brilliant thanks Brent for