S.A.T. Math Testing Tactics

Tactic 10: Don’t Do More Than You Have To

Don’t Do More Than You Have To!

Look for shortcuts

Many problems have more than one correct way to obtain the right solution

Think: Quick, Efficient, Accurate

Example 10.1

If , what is ?5(3 7) 20x 3 8x

First: Notice that there is a 3x in the given equation AND the expression we are evaluating.

This means we can solve for 3x instead of x. This will save time!

5(3 7) 20x

3 7 4x

3 11x

3 8x 11 83

3

Example 10.2

If and , what is the average (arithmetic mean) of x and y?

7 3 17x y 3 7 19x y

First, what does the average of x and y look like?2

x y

Ex 10.2 (continued)Next, since we have two equations, let’s try adding them together (Tactic 17):

7 3 17x y ( )3 7 19x y

10 10 36x y

10 10 36

10 10

x y

3.6x y

3.6

2 2

x y

1.82

x y

Average of x and y= 1.8

Example 10.3If , what is the value of ?

5 13 31x 5 31x

Notice the equation and the expression both have a 5x

5 13 31x 5 18x

5 31x

18 31497

7

In conclusion: EVERY SECOND IS PRECIOUS–

WORK SMARTER, NOT HARDER!

ALWAYS LOOK FOR SHORTCUTS!

Don’t find 20% and 30% separately if you can find 50% once.

Don’t find x if you really only need 5x.

Don’t find individual numbers if you only need their sum.

DON’T WASTE PRECIOUS TIME!