For some of the more difficult, abstract questions on the ACT Math test, the “real” math that the test takers have in mind can be quite tricky. But for some of these problems, there might be a way to make the rather abstract problem more concrete, and thus easier. That leads us to an important ACT Math strategy: Picking Numbers.
Consider the following difficult problem which has previously appeared on the ACT.
For every positive two-digit number, x, with tens digit t and units digit u, let y be the two-digit number formed by reversing the digits of x. Which of the following is equivalent to x – y?
A. 9(t – u)
B. 9(u – t)
C. 9t – u
D. 9u – t
Continue reading ACT Math Strategy: Picking Numbers
Our first post, written ten months ago, had to do with a very important SAT Math strategy: Picking Numbers. If you’d like some more practice on this type of problem, here are seven more that you can try. The answers appear at the bottom of this post.
1) In rectangle ABCD, Point E lies 4/7 of the way from A to B. The area of triangle EBC is what fraction of the area of rectangle ABCD?
Continue reading SAT Math: Some More Picking Numbers Problems
If you’ve read my recent post on Picking Numbers and you’re looking to try a few more problems on this very important SAT Math strategy, check out these problems. You may see a way to solve the problem that doesn’t involve picking numbers and that’s great! If it seems easier to you to actually “do the math,” then go for it. But for each of these problems, picking numbers can be used as a strategy to get the correct answer. The solutions appear at the bottom of this post.
1) If a is an odd integer and b is an even integer, which of the following must be even?
(A) ab – 1
(B) ab + 1
(C) (a + b)2
(D) a2 + b + 1
(E) a + b + 2
Continue reading SAT Math: More “Picking Numbers” Problems
It turns out that on some of the problems in the SAT math sections, you don’t really need to do the math (at least not the math they want you to do). Crazy, right? One of the most important strategies that you should master if you want to score higher on SAT math is “picking numbers.” If a student were to come to me a week before the test and say “I know it’s late, but I’m desperate. Show me something!” this technique is what we’d work on.
Consider this example:
If a is an odd integer and b is an even integer, which of the following must be odd?
(B) ab + b
(C) (a + b)2
(D) ab + 2
(E) ab – 2
Continue reading SAT Math Strategy: Picking Numbers