These solutions are for the 2008-2009, 2009-2010 and 2010-2011 SHSAT Handbook Form A tests, which were all identical. Here are my fully worked out solutions to the math section. The test can be found here.
Scrambled paragraphs are some of the trickiest problems on the SHSAT. The scrambled paragraph section in the Barron’s SHSAT book gives you a pretty good idea of what to look for in these problems. I will not try to replicate that full lesson here. The purpose of this post is to give an idea of the thought process you should go through when you’re solving scrambled paragraphs. We will do two examples: paragraphs 1 and 2 from Form A of the 2015-2016 Department of Education SHSAT handbook.
In part 1 we learned how to solve basic if/then questions. A few key points: Put all statements into if/then form. The contrapositive of a true if/then must also be true. The converse and inverse do not have to be true and are often wrong answer choices. Now we will learn some techniques for dealing with trickier questions where you are given more than one if/then.
The Chain Rule
When we have two if/then statements, sometimes we can connect them. For example, suppose these two statements are true:
If I go to Roma’s restaurant, then I get pizza. If I get pizza, then I get a soda.
This is a chain of events: when I go to Roma’s, I get pizza, and when I get pizza I also get a soda. So whenever I go to Roma’s I end up getting a soda! We can get a new if/then by skipping over the middle step: If I go to Roma’s restaurant, then I get a soda. This must be true!
On the SHSAT, you may see a logical reasoning question like this:
q) Suppose the following statement is true: If it is Monday, then Bob goes to the park. Which of the following must also be true?
A) If it is not Monday, then Bob does not go to the park
B) If Bob goes to the park, then it is Monday
C) Bob’s favorite place is the park
D) If Bob doesn’t go to the park, then it is not Monday
E) Bob doesn’t like going to the beach
Ratios and proportions show up a lot on the SHSATs! Mastering them will give you a nice score boost.
Take special notice of this hint from the Regents Prep ratios lesson: When working with ratios such as 2 : 3 : 5, use 2x, 3x, and 5x to write an equation!
Basic lesson and practice on averages:
There are a couple types of tricky problems related to averages that often show up on the SHSATs:
Finding the average from a frequency table:
Practice 2- don’t worry about the second half of the page, which is more advanced:
Missing numbers in averages:
Lesson/ practice 1: