One third of the attendees at a concert left the show before the encore. Twenty more people left during the encore. After the encore, half as many people as had left before the encore left. If 76 people remained in the theater after the concert was over to try to get autographs from the band, how many people, in total, attended the concert? Please write it out step by step. Thank You.

I wrote this question to encourage you to backsolve, which means you take the answer choices, starting in the middle, and you work them through the question until one fits. (Note: this question was in my old book for the old test—hopefully you’re not using that as your main prep resource because it doesn’t address many topics that appear on the new test.)

Answer choice C for the question is 192. Since that’s the middle choice, try it first:

If there were 192 people at the concert and 1/3 left before the encore, then 64 left. 192 – 64 = 128.

Twenty more people leave: 128 – 20 = 108.

Half as many people as had left before the encore (64) leave: 108 – (64/2) = 76.

Sure enough, the question said 76 people were left at the show, and answer choice C just landed us at 76, so C is the right answer.

Algebraically, here’s how it works: