Percents
Percents
Percents are a specific type of fraction. Percent literally means “of 100” in Latin, so after you ace the SAT, go to college, drop out to become famous, and eventually amass 75% of all the money in the world, you’ll then have 75 /100 of the world’s money. Awesome.
Until then, you don’t have that much money, and you still have to take the SAT (and pay for the privilege). So let’s look at an example question:
4 is what percent of 20?
The first thing you have to know how to do is translate this sort of question into an equation. It’s actually pretty straightforward as long as you see that “is” is the same as saying “equals,” and “what” is the same as saying “x.” So if 4 equals x percent of 20, then
4 = x%(20)
Since a percent is actually a number out of 100, this means
Now just work out the math:
Therefore, 4 is 20% of 20.
Converting Percents into Fractions or Decimals
Converting percents into fractions or decimals is a crucial SAT skill. If you ever want to multiply or divide a number by a percent, you first have to convert it.
  • To convert from a percent to a fraction, take the percentage number and place it as a numerator over the denominator 100. If you have 88 percent of something, then you can quickly convert it into the fraction 88/100.
  • To convert from a percent to a decimal, you must take a decimal point and insert it into the percent number two spaces from the right: 79% equals .79, while 350% equals 3.5.
What Percent of this Word Problem Don’t You Understand, Bucko?
SAT word problems often seem to be phrased as if the person who wrote them doesn’t know how to speak English. The SAT does this purposefully, because it thinks that verbal tricks are a good way to test your math skills. If that makes no sense to you, good. It makes no sense to us either. Here’s an example of the kind of linguistic trickery we’re talking about:
What percent of 2 is 5?
Because the 2 is the smaller number and because it appears first in the question, you’re first instinct may be to calculate what percent 2 is of 5.
But as long as you remember that “is”means “equals” and “what” means “x” you’ll be able to correctly translate the word problem into math:
x%(2) = 5
So 5 is 250% of 2.
Percent Increase and Decrease
One of the most common ways the SAT tests percent is through the concept of percent increase and decrease.
  • Percent increase—If the price of a $10 shirt increases 10%, the new price is the original $10 plus 10% of the $10 original.
  • Percent decrease—If the price of a $10 shirt decreases 10%, the new price is the original $10 minus 10% of the $10 original.
One of the classic blunders students make on these questions is to figure out what the 10% increase or decrease is, but then, lost in a haze of joy and relief, to forget to carry out the necessary addition or subtraction. SAT traps take advantage of this. Be wary.
A vintage bowling league shirt cost $20 in the 1990s. But during the 1970s, when the shirt was first made, it cost 15% less. What was the price of the shirt in the 1970s?
(A) $3
(B) $17
(C) $23
(D) $35
(E) $280
First find the price decrease (remember that 15% = .15):
Now, since the price of the shirt was less back in the 1970s, subtract $3 from the $20 price from the early 1990s:
The answer is B. If you only finished the first part of this question and looked at the answers, you might see the $3 at answer A and forget to finish the calculation.
Double Percents
Some SAT questions ask you to determine a percent of a percent.
The original price of a banana in a store is $2. During a sale, the store reduces the price by 25% and Joe buys the banana. Joe then raises the price of the banana 10% from the price at which he bought it and sells it to Sam. How much does Sam pay for the banana?
This question asks you to determine the effect of two successive percent changes. The key to solving it is realizing that each percentage change is dependent on the last. You have to work out the effect of the first percentage change, come up with a value, and then use that value to determine the effect of the second percentage change.
When you’re working on a percentage problem that involves a series of percentage changes, you should follow the same basic procedure that we explained for one percentage change, except here you should run through the procedure twice. For the first percentage change, figure out what’s the whole, calculate the percentage of the whole, make sure to perform addition or subtraction if necessary, then take the new value and put it through these same steps for the second percentage change.
To answer the example problem, first find 25% of the original price:
Now subtract that $.50 from the original price:
Then increase $1.50 by 10%:
Sam buys the banana for $1.50 + $.15 = $1.65. A total rip-off.
Some students, sensing a shortcut, are tempted to just combine the two percentage changes on double percent problems. This is not a real shortcut. It’s more like a dark alley filled with cruel and nasty people who want you to do badly on the SAT.
If you reasoned on the last example problem that the first percentage change lowered the price 25% and the second raised the price 10%, meaning that the total change was a reduction of 15%, then
Subtract that $.30 from the original price:
We promise you that when the SAT gives you a double-percent problem, it will include this sort of wrong answer as a trap among the choices.
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