When to cancel out variables in Quantitative Comparison

[safirshahbaaz90]

Hi,

I was trying out the following quantitative comparison question

Quantity A: x + y - 1
Quantity B: x - y + 1

I was wondering if it is possible to cancel out x from both equations since the sign and value will be the same regardless.

Would it be OK to do so? Also, could you please let me know in what scenarios would it be possible to cancel out variables?

Regards,
Safir

[tommywallach]

Hey Safir,

Indeed, this is a very important method for dealing with QC questions. You are always allowed to treat the two columns as if they were a giant inequality. Remember, however, what you can and cannot do with an inequality. You CAN: add/subtract the same thing to both sides, square or square root both sides, multiply/divide both sides by a known quantity. You CANNOT: multiply or divide both sides by a variable if you don't know it's sign (because the sign might flip).

So in this case:

A: x + y - 1
B: x - y + 1

We begin by subtracting x from both columns:

A: y - 1
B: - y + 1

Next, we add y t both columns:

A: 2y - 1
B: 1

Next, we add 1 to both columns:

A: 2y
B: 2

Next we divide both columns by 2:

A: y
B: 1

Assuming the question hasn't told us anything about y, the answer is D, because we don't know if y is greater than, equal to, or less than 1.

Hope that helps!

[safirshahbaaz90]

Hi Tommy,

Thanks for the reply!

So just to clarify the concept, I have another QC question:

Condition: x > 0

Quantity A: x^2

Quantity B: x^3

Here since x will always be positive, we can divide by x^2 on both sides resulting in:

Quantity A: 1
Quantity B: x

The answer is D. Plugging in x = 1 results in equal. Plugging in x = 1/2 results in A > B. Is the reduction and problem solving correct?

Regards,
Safir

[tommywallach]

Hey Safir,

Yep. That's a legal move there! (And you can see that from the original situation: plugging in 1 would create an equal situation, just as it does in the situation after you've done the division, and plugging in 1/2 would still mean column A is bigger, because it's 1/4 versus 1/8).

-t