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#1 SAT math strategy May 31, 2008

Posted by Jason McDonald in : SAT tips , trackback


SAT problems rarely provide information or ask questions in a straightforward fashion. One of the most useful ways to cut through the confusion the test writers provide is to display the information your own way. Forming this habit serves three purposes:

     1. It wakes you up from the SAT trance that zaps your time.
     2. It often displays the key relationship to solve the problem.
     3. It helps you avoid or even catch mistakes that are most common when doing work in your head.

This can be done through a table, ratio box, average pie, rate pie, Venn diagram, tree diagram, list of numbers, graph, or a sketch.  It doesn’t have to be pretty, just do it fast.

Here are a couple video mini lessons you should view as you probably haven’t seen them in school (They’re just a couple minutes each).

     Average pie video lesson.
     Rate pie video lesson.

Example 1 (easy):

If the average (arithmetic mean) of the below six numbers is 2x, what is the value of x?
5, x, x, 20, 35 and 40

After trying the problem on your own (hint: make an average pie), watch the video solution on how to get the right answer in 30 seconds.

Example 2 (medium difficulty): 

Machine A makes 1500 newspapers per hour and works for 6 hours.  If Machine B makes 1000 newspapers per hour, how many hours would it take Machine B to make the same amount of newspapers Machine A made in 6 hours?

(A)  1.5
(B)  5
(C)  6.7
(D)  7.5
(E)  9

After trying the problem (hint: make a rate pie), watch the video solution on how to get the right answer in 30 seconds.

Example 3 (medium difficulty):

A stock rose 60 points in a year.  It gained one-third of those points in the first quarter, one-fifth in the second quarter, one-fourth in the third quarter and the rest in the fourth quarter.  How many points were gained in the second half of the year?

(A)  12
(B)  13
(C)  15
(D)  20
(E)  28

After trying the problem (hint: make a table), watch the video solution on how to get the right answer in about 30 seconds.

Could you have done the above problem without a table? 

Of course you could.  Most people would do this problem without a table.  In fact, many people would try to do this problem without even writing anything down.  Keep in mind though most people score around average on the SAT.  You don’t want to be “most people.” 

Contrary to popular belief, making a table actually saves time.  You won’t spend a second thinking about what to do.  You’ll just do it.  As you can see in the video solution, it only takes 30 seconds to get the answer!

Using a table also keeps you from doing unnecessary math like adding the fractions in this case.

Example 4 (more difficult): 

The least integer in a set of consecutive even integers is
-100.  What is the greatest integer in this set if the sum of these integers is 206?

(A)  52
(B)  54
(C)  104
(D)  106
(E)  108

After trying the problem, watch the video solution on how to get the right answer in less than 30 seconds.


As you can see, making a visual doesn’t take long.  It leads you to the right answer in less than 30 seconds even on “difficult” problems.  Now it’s your turn.  Prove to yourself this strategy works on real SAT problems from The Official SAT Study Guide

Video solutions to all of the below problems are posted in the members forum.

pg. 670, #6 (average pie)
pg. 716, #2 (sketch)

pg. 842, #11 (rate pie)
pg. 793, #7 (average pie)
pg. 671, #8 (table)
pg. 489, #10 (sketch)
pg. 735, #7 (Venn diagram)

More difficult
pg. 843, #16 (ratio box)
pg. 807, #14 (sketch)
pg. 412, #18 (rate pie)


1. Jason McDonald - June 11, 2011

Thanks for all of your feedback, Sora. Glad you found these examples and methods helpful!

2. Sora - June 11, 2011

Yah! thnx so much! tho I wish I watch this before my test QQ

3. johnny - June 22, 2010

its really helps thanks