GMAT math versus high school math

By Brent Hanneson - November 11, 2020

This is one of my favorite questions on GMAT Club. So, put on your test-taking pants and see if you can plow through it:

If you weren’t able to answer the question, you’re not alone.  The question’s stats (on GMAT Club) tell us that this is a 700+ level question that only 54% of students answered correctly.

Judging from the average solution time (1:36), most people who correctly answered the question squared both sides, rearranged the terms to get a quadratic equation set equal to zero, factored the quadratic, identified two possible solutions, plugged those solutions back into the original equation to learn that x = -1 is an extraneous root, leaving only x = 9 as the valid solution. Presumably, many others followed the exact same steps, but neglected to check for extraneous roots, yielding an incorrect response of D.

If your approach was similar to the one described above, then you’re still doing math the same way you did in high school.

When you switch to GMAT math mode, you'll ask the same question you ask when encountering any Problem Solving question: "Can I use the answer choices to my advantage?" In this case, the answer to your question is a resounding "Yes!", and when you test each possible solution, this 700+ level question can be solved in 10 seconds (11 if you stop to gloat in private for 1 second).

I. x  = -1

Plug x = -1 into the left side of the equation to get -4, which is negative.

Since the square root on the right side will always evaluate to be greater than or equal to 0, we know that x = -1 is definitely not a solution to the equation.

And now you’re done!

Since x = -1 is not a solution, we can eliminate answer choice A, because it says x = -1 is a solution. While we’re at it, we can eliminate C, D and E, since they also say that x = -1 is a solution.

Answer: B

If you still need more reasons to use the answer choices to your advantage, here’s an earlier article.