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.

# Can you elaborate more on question 18 (Backsolve)?

Can you elaborate more on question 18 (Backsolve)? I am having trouble understanding how you got 1683000 and 1717000.

# Solving systems of linear equations

The new SAT places a heavy emphasis on the “Heart of Algebra,” which is a bizarre and tortured euphemism for, mostly, working with linear equations. One of the kinds of questions you know you’re going to see, probably more than once, on your SAT is solving systems of linear equations. For example: Which ordered pair satisfies (more…)

# Two-category Venn diagram problems

I made a video today that I hope will help you understand something I get asked about an awful lot. The SAT loves asking a particular kind of Venn diagram question—not so common that it appears on every test, but common enough that high scorers need to know it. The test writers keep coming back (more…)

# Backsolve, or figure out a much more difficult way to solve these backsolve problems.

It’s important to be ever-cognizant of the fact that on a multiple choice test, one of the 5 answers has to be right. Because of this, it’s sometimes possible to answer a question correctly by starting at the end, and ending at the start. Most in the prep world call this “backsolving,” and it’s even more (more…)

# Try this hard function/exponent question.

For all positive integers p and q, let the function p♮q be defined as p♮q = 2p-q. If g♮12 = g, then g = (A) 2 (B) 4 (C) 8 (D) 16 (E) 76 Answer below. The cardinal rule of function questions is this: FOLLOW THE DIRECTIONS EXACTLY. If p♮q = 2p-q, then g♮12 = 2g-12. We know (more…)