SAT Technique #1: Make it Concrete
When to use this technique: When there is a variable in both the question and the answer.
How often can it be used: About twice per math section or six times per test. Which makes this technique worth about 60 points.
Why it helps: It reduces problems from Algebra to Arithmetic (which after hours of testing is a big help)
How to do it: In a question where the variable is in both the question and the answer, choose a number for the variable that meets all conditions set in the problem and substitute that number in wherever you see the variable (sometimes this method is called substitution but I try to avoid that name because it can mean other similar things as well).
Putting it to work:
Example 1
Question 16 out of a section of 20 (Which would indicate a high difficulty level)
If a is divisible by 5 and b is divisible by 3 which of the following must be divisible by 30
I. 2ab
II. 2(5a+3b)
III. 2(3a+5b)
A) I Only
B) III Only
C) I and II Only
D) I, II, III
E) I, II and III
SAT Technique #1: Making it Concrete
Step 1) Is the variable in both the question and answer? If yes, move on, if no, try something else.
It is, so we can use this SAT technique.
Step 2) Pick numbers that are easy to work with that meet the conditions.
For a my only condition is that it is divisible by 5 so I’m going to say that a=10 because 10 is easy to work with.
I know that b has to be divisible by 3 so I’m going to choose 6 since its a small number (I don’t want to have to calculate with large numbers)
Step 3) Plug in (substitute in) your numbers
10 is divisible by 5 and 6 is divisible by 3 which of the following is divisible by 30
I. 2(10)(6) =120 (which is divisible by 30)
II. 2(5*10+3*6)=2*68=136 (not divisible by 30)
III. 2(3a+5b)=2*60=120 (which is divisible by 30)
D) I and III Only
Step 4) If only one answer choice remains, you’re done circle it. If more than one choice remains, try different numbers but just check it on the remaining answers.
We only had one choice that worked for these numbers so we are done.
Example 2
Question 20 out of a section of 20 (Very Hard!)
If h>0 and an integer, which of the following represent an even integer that equals 2k for a certain odd integer k.
A) 2h
B) 2h+3
C) 2h+4
D) 4h+1
E) 4h+2
SAT Technique #1: Making it Concrete
Step 1) Is the variable in both the question and answer? If yes, move on, if no, try something else.
Notice that h is in both and k is not. We will be using the technique just on h…but if we parse the SAT’s babble speak we can see that we are looking for an even number that is twice an odd number.
Step 2) Pick numbers that are easy to work with that meet the conditions.
I picked h=3, other good choices are 1,5,10. 1,251 would work but we are trying to make things easy on ourselves.
Step 3) Plug in (substitute in) your numbers
h=3, which of the following is an even number that is twice an odd integer.
A) 2*3=6 6 is twice 3 so that works
B) 2*3+3=9 9 is twice 4.5 so that doesn’t work.
C) 2*3+4=10 10 is twice 5 so that works
D) 4*3+1=13 13 is twice 6.5 so that doesn’t work
E) 4*3+2=14 14 is twice 7 so that works.
Step 4) If only one answer choice remains, you’re done circle it. If more than one choice remains, try different numbers but just check it on the remaining answers.
Unfortunately we have three choices that work. So we need to pick again. If you are out of time, you can guess at this point and it will benefit you.
Repeat Step 2) Pick numbers that are easy to work with that meet the conditions.
Lets try h=10
Repeat Step 3) Plug in (substitute in) your numbers
h=1, which of the following is an even number that is twice an odd integer.
A) 2*10=20 20 is twice 10 so that doesn’t work
C) 2*10+4=24 24 is twice 12 so that doesn’t work
E) 4*10+2=42 42 is twice 21 so that works.
(notice I just have to look at A, C and E because I already eliminated the other choices).
Repeat Step 4) If only one answer choice remains, you’re done circle it. If more than one choice remains, try different numbers but just check it on the remaining answers.
E is my only remaining answer so I’ve just successfully finished the hardest question on the math section.