SAT Math Study Tip # 3

Sat Math

If there is one thing that students can count on when writing the Math section of the SAT, it’s that there will be a question (and maybe two) involving averages (arithmetic mean).

The second thing that they can count on, is that the question won’t be the easy type, such as “what is the average of 40, 26 and 54?” (adding up the numbers and then dividing by 3 – too easy!). So, a smart study routine plans for this – these are marks on the math test that you don’t want to miss getting.

Here is a simple but effective way to solve these problem types every time. It’s a “no formula” method because all it takes is multiplying, adding and subtracting (and sometimes dividing). And, best of all, the first step is always the same.

Sat Math Test Prep

Here’s how it works:

Q:  John averaged $70 of earnings per day on the first four days of his summer job. If he made $55 the first day, $65 the third day, and $85 the fourth day, how much did John earn on the second day of his summer job?

The key idea here is to find the total money John made right away, by multiplying. Since he averaged $70 per day for 4 days, his total earnings are 4 x $70 = $280. 

Then, find what’s missing. If his total is $280 and he made $55 + $65 + $85 = $205 on the three days given, then he must have made $280 – $205 = $75 on the second day.

The correct answer that will appear on the list of choices will be:  $75

 

Q:  The average height of the five students that form the starting line-up of a basketball team is 73 inches. If the heights of three players are 75 inches, 80 inches and 70 inches, what are the combined heights of the remaining two players?

First: Find the total number of “inches of height” of the players on the team. If the average height is 73 inches and there are five players, then the total “inches of height” is 5 x 73 = 365 inches.

Then: Find what’s missing. If  the total inches of height is 365, and the three players heights given  are 75 + 80 + 70 = 225 inches, then the remaining two players must “use up” the remaining inches:  365 – 225 = 140 inches.

The correct answer that will appear on the list of choices will be:  140 inches

 

Q:  Twenty-four students write the same test, and the overall average is 85%. If the first fourteen students achieve an average of 80% on the test, what must be the average of the remaining 10 students who wrote it?

This is a trickier one, because there are three averages involved. Don’t be distracted from our method. As always, let’s find the total number of correct answers from everybody who wrote the test. Remember 80% on a test means 80 questions correct out of 100 questions.

First: Find the total number of correct answers:  24 students averaging 85 correct answers each means 24 x 85 = 2040 correct answers.  

Then: Find what’s missing.  If the first fourteen students averaged 80 correct answers each, then they’ve used up  14 x 80 = 1220 correct answers. That leaves 2040 – 1120 = 920 correct answers for the remaining ten students to score.

This problem is a little more difficult than the previous two examples, because it also asks you for an average, which is the final step. If ten students score a total of 920 correct answers, then their average is 920 / 10 = 92 correct answers each.

The correct answer that will appear on the list of choices will be:  92%

 

Remember that anytime a problem gives you the average, it’s easy to find the total, and then find what’s missing. Using your calculator makes this method even faster. This is one of those strategies that, if you take the time to make it part of your study plan, you will have a hard time finding an averaging problem that you can’t do. You will go into the SAT Math test hoping to see problems involving averages – now that is a mission accomplished.


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