Cracking The SAT Premium

you know. 100 is the original amount, and the rate is 4%, or 0.04. The account is increasing, so you add
the rate, and you can put in “years” for the number of changes. The formula becomes

final   amount  =   100(1   +   0.04)years

Now you need to figure out what you want the final amount to be. Translate the English to math: the value
of her account (100) will increase (+) by 60 percent (0.6) of the current value (×100). This becomes 100

• (0.6)(100) = 100 + 60 = 160. Now the formula is

160 =   100(1.04)years

The answer choices represent the number of years Becca keeps her money in the account. Now you are all

set to easily plug in the answers. Start with (B), so years = 15. Is 100(1.04)^15 = 160? Use your calculator
to check, making sure to follow PEMDAS rules and do the exponent before you multiply by 100. The
result is $180.09. That is a bit too much money, so the answer will likely be (A), but let’s just check it.
100(1.04)^12 = $160.10, which is at least $160.

A final note on growth and decay: Sometimes the population is tripling or halving instead of changing by a
certain percent. In that case, the formula changes to

final   amount  =   original    amount  (multiplier)number  of  changes

Two more topics related to percentages may be tested. You may be given a sample of a population that fits
a certain requirement and asked to determine how many members of the general population will also be
expected to fit that requirement. You may also be given the results of a study or poll and told that there is a
margin of error of a certain percentage.

Let’s look at an example that tests both of these advanced ideas.

29.A    summer  beach   volleyball  league  has 750 players in  it. At  the start   of  the season, 150

of  the players are randomly    chosen  and polled  on  whether games   will    be  played  while   it

is  raining,    or  if  the games   should  be  cancelled.  The results of  the poll    show    that    42  of

the polled  players would   prefer  to  play    in  the rain.   The margin  of  error   on  the poll    is

±4%.    What    is  the range   of  players in  the entire  league  that    would   be  expected    to  prefer

to  play    volleyball  in  the rain    rather  than    cancel  the game?

A) 24–32

B) 39–48

C) 150–195

D) 180–240

Here’s How to Crack It

The first step is to determine the percent of polled players that wanted to play in the rain.