Question: 2x over y

Comment on 2x over y

Why do we have (y -ve for first statement) --if we multiply both sides by y (-ve or +ve) we get rid of Y and we are left with 2x > 10 ---which gives unique result i.e. x> 5
gmat-admin's picture

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

So is it safe to say you shouldn't assume +/- for a variable in a DS question? I just assumed y was positive because it was written as y, and not -y.
gmat-admin's picture

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 do we know y is positive?
gmat-admin's picture

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 turns out that y is negative as the outcome of second equation, answer still be C, right? Logic is by combining we can arrive to a conclusion that x is not positive. Please correct if wrong.
gmat-admin's picture

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 simplest way.

Great question, I completely ignored the Y after solve the first equation, incorrectly chose A because if x is greater than 5 of course it is greater than 0...
gmat-admin's picture

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

Great video Brent. If using a number line here, x>0? mean x = 1,2,3,5,6...etc. Combined result is x > 5. So that mean x could be 6,7,8... and there's a gap between 0 ~ 5 on the number lines. So shouldn't this be E. Did I miss something here? Thanks Brent.

Think I get it now Brent to my previous question. To clarify x>0 is a question and not a statement. Therefore x>5 is sufficient to say x is positive. Is this corrent? Thanks Brent
gmat-admin's picture

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 confirmation.

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