Cracking the SAT subject test in math 2, 2nd edition

Cracking the SAT Subject Test in Math 2, 2nd Edition (D) 5 4 × 107 (E) 2 6 × 108 28 In 1995, Ebenezer Bosticle created a salt sculpture that weighed 2,000 pounds If this sculpture loses 4 percent of i[.]

(D) 5.4 × 107 (E) 2.6 × 108

28 In 1995, Ebenezer Bosticle created a salt sculpture that

weighed 2,000 pounds If this sculpture loses 4 percent

of its mass each year to rain erosion, what is the last year

in which the statue will weigh more than 1,000 pounds?

(A) 2008 (B) 2009 (C) 2011 (D) 2012 (E) 2013

40 A savings bond pays 2.5 percent interest per year In

approximately how many years will the value of the savings bond be twice the original value?

(A) 3 (B) 22 (C) 25 (D) 28 (E) 40

AVERAGES

The SAT Subject Test in Math 2 uses average in a variety of ways Remember, the average is the sum of all the values divided by the number

of values you’re adding up Looking at this definition, you can see that every average involves three quantities: the total, the number of things being added, and the average itself

The chart above is called an Average Pie It’s The Princeton Review way of organizing the information found in an average problem Cover up the

“average” section with your thumb In order to find the average, you divide the total by the “number of things.” Now cover up the “number of things” section You can find it by dividing the total by the average Finally, you can find the total by multiplying the number of things by the average

When you encounter averages on the SAT Subject Test in Math 2, you will

be given two of the three pieces of the pie Finding the missing piece will

be the key to solving most of these questions

Ways to Remember

Remember that in order to find the average, you divide the total by the number of things Think of the horizontal line in the Average Pie

as one big division bar!

DRILL 5: AVERAGES

Test your understanding of averages with the following questions The answers can be found in Part IV

1 People at a dinner paid an average of $25.00 each The total bill for dinner was $225.00

What else do you know? _

2 The average fruit picker on Wilbury Ranch picked 300 apples on Tuesday There are 15 fruit pickers at Wilbury Ranch

What else do you know? _

3 If the 34 students in the chess club lie down end to end, they would form a line 187 feet long

What else do you know? _

The Average Pie becomes most useful when you’re tackling a multiple-average question—one that requires you to manipulate several averages

in order to find an answer Here’s an example:

17 Sydney’s average score on the first 5 math tests of the

year was 82 If she ended the year with a math test average of 88, and a total of 8 math tests were administered that year, what was her average on the last three math tests?

(A) 99.5 (B) 98.75 (C) 98.0 (D) 96.25 (E) 94.0

Here’s How to Crack It

In this question, there are three separate averages to deal with: Sydney’s average on the first five tests, her average on the last three tests, and her final average for all eight In order to avoid confusion, take these one at a time Draw the first Average Pie

You have the number of things and the average, so you can find the total You know that Sydney’s total for the first test is 410 Fill in that information and draw another pie For your second pie, the question tells you that Sydney’s average on all 8 tests was 88, so you can multiply those

numbers to find the total of her 8 scores, or 704 Fill in your second Average Pie below

Since you know the total of all 8 tests and the total of the first 5 tests, you can figure out the total of the last three tests:

704 − 410 = 294 Draw one last pie, using the information that you have:

As it turns out, Sydney averaged a 98 on her last three math tests; so the answer is (C)

Multiple-average questions are never terribly difficult Just draw an

Average Pie every time you see the word average in the question.

Organization is everything on these questions It’s easy to make careless errors if you get your numbers scrambled, so make sure you label the parts of the Average Pie Notice that you can always add or subtract totals and numbers of things, but you can never add or subtract averages

Try these problems The answers can be found in Part IV

18 At a charity fund-raiser, the average of the first 19

donations is $485.00 In order for the average of the first 20 donations to be $500.00, what must the amount

of the twentieth donation be, in dollars?

(A) $300 (B) $515 (C) $650 (D) $785 (E) $800

20 During the first 20 days of September, the Tribune

received an average of 4 complaint letters per day

During the last 10 days of September, the Tribune received an average of 7 complaint letters per day What was the Tribune’s average number of complaint letters per day for the entire month of September?

(A) 5.0 (B) 5.33 (C) 5.67 (D) 6.0 (E) 6.25

21 Over a year, Brendan sold an average of 12 umbrellas per day on rainy days, and an average of 3 umbrellas per day

on clear days If the weather was rainy one day in five, and this was not a leap year, what was Brendan’s average daily umbrella sales for the year?

(A) 4.8 (B) 5.2 (C) 6.75