PSAT Math: Percentages

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Percentages aren’t just for test grades; you’ll find them frequently throughout life—discount pricing in stores, income tax brackets, and stock price trackers all use percents in some form. It’s critical that you know how to use them correctly, especially on Test Day.

Suppose you have a bag containing 10 blue marbles and 15 pink marbles, and you’re asked what percent of the marbles are pink. You can determine this easily by using the formula Percent = part/whole × 100 % . Plug 15 in for the part and 10 + 15 (= 25) for the whole to get 15/25 × 100 % = 60 % pink marbles.

Another easy way to solve many percent problems is to use the following statement: (blank) percent of (blank) is (blank). Translating from English into math, you obtain (blank)% × (blank) = (blank).

You might also be asked to determine the percent change in a given situation. Fortunately, you can find this easily using a variant of the percent formula:

Percent increase or decrease = amount of increase or decrease/original amount × 100%

Sometimes more than one change will occur. Be especially careful here, as it can be tempting to take a “shortcut” by just adding two percent changes together (which will almost always lead to an incorrect answer). Instead you’ll need to find the total amount of the increase or decrease and calculate accordingly.

An example of a question that tests your percentage expertise follows.

1. A bank normally offers a compound annual interest rate of 0.25% on any savings account with a minimum balance of $5,000. The bank is currently offering college students a higher rate, 0.42%, with a $1,000 minimum balance. Assume the average balances are kept constant at the required minima (e.g., all interest is withdrawn) for the following.

How much more interest does the regular account earn after three years than the student account?

Work through the Kaplan Method for Math Questions step-by-step to solve this question. The following table shows Kaplan’s strategic thinking on the left, along with suggested math scratchwork on the right.

Strategic Thinking Math Scratchwork
Step 1: Read the first question in the set, looking for clues
The intro provides information on two account types.		 regular acct: 0.25%, $5,000 min
student acct: 0.42%, $1,000 min
Step 2: Identify and organize the information you need
You need to find how much more interest the $5,000 account will have after three years.		 difference in interest: ?
Step 3: Based on what you know, plan your steps to navigate the first question
What pieces needed to find the answer are missing? How do you find the difference in interest?You’ll need the amount of interest that each account accrues after three years. Use the three-part percent formula to find annual interest, then find the interest after three years, then take the difference.		 reg. int. = ?
stu. int. = ?

reg. int. x 3 = ?

stu. int. x 3 = ?
reg. – stu. = ?
(blank)% of (blank) is (blank)
Step 4: Solve, step-by-step, checking units as you go
How much interest does each account earn after one year? After three years?Plug in appropriate values. Remember to adjust the decimal point on the percents appropriately. Triple the interest amounts to get the total accrued interest after three years.What’s the difference in interest earned?
Subtract.		 0.0025 x $5,000 = $12.50
0.0042 x $1,000 = $4.20

$12.50 x 3 = $37.50

$4.20 x 3 = $12.60
$37.50 – $12.60 = $24.90
Step 5: Did I answer the right question?
You’ve found how much more interest the regular account makes after three years, so you’re done with the first question.		 24.9

Note

Disregard the 0 in the hundredths place when gridding in your answer.