Tricky Percentage Questions on the SAT and ACT: Make Sure You’re Not Confidently MISSING Them!
One of the topics that most students assume they’re familiar with but confidently miss is percentages. Percentage questions on the SAT and ACT may look basic, but they’re not as easy as they seem. One misstep and you’ll find yourself missing a question you deserve to get right. In this article, I’ll look at some tricky percentage questions on the SAT and ACT and teach you a foolproof method to solve them. The key is translating words into math, a skill many students struggle with. Are you ready to learn how to tackle some tricky SAT and ACT math percentage questions? Let’s go!
What is a percentage?
A percentage is basically a classic case of part over whole. In this case, 100% represents 1 and can also be represented as 100/100. Percentages are always out of 100. For example, 1/4 of a pizza is 25%, which can also be expressed as 25/100. The word “percent” comes from Latin meaning “out of 100.” Do NOT forget this. To convert a fraction to a percent, just cross multiply. For example, to figure out what 1/20 is as a percent, set up the equation 1/20 = x/100 and solve 1(100) 20x to find that 1/20 is 5%! Easy, right? So how can these questions be difficult? We’ll see!
Tricky SAT Percentage Question
Katarina is a botanist studying the production of two types of pear trees. She noticed that Type A trees produced 20% more pears than Type B trees did. If Type A trees produced 144 pears, how many pears did Type B trees produce?
A) 115
B) 120
C) 112
D) 108
How would you go about solving this question? Most of my students miss it. They multiply 144 by 20% and then subtract the result from 144, getting them approximately 115, which they incorrectly select as the correct answer. If this is how you would approach the problem, you need to rethink your approach. The key to solving the problem is to translate words into math. I’ll show you.
The phrase “Type A trees produced 20% more than Type B trees did” can be translated as follows. “Type A trees” will become “A.” “Produced” will become an equal sign. The phrase “20% more” will become 1.2. And “than Type B trees did” will become B. The result?
A=1.2B
Notice that we’ll be dividing A by 1.2 in order to find B. This is very different than multiplying by .2 and subtracting! How did we get 1.2? The phrase “more than” is the clue. More than WHAT? More than whatever Type B produced. How much did Type B produce? We don’t know yet, but we do know that it produced 100% of whatever it produced. Thus, “20% more than” is “20% more than 100%,” which is 120%, which is 1.2.
The question also mentions that Type A trees produced 144 pears, so we plug in 144 for A, giving us this equation:
144=1.2B
Simple algebra tells us to divide 144 by 1.2, resulting in the correct answer choice, B) 120.
Easy, right? It is, as long as you very carefully translate words into math.
Tricky ACT Percentage Question
Now let’s take a look at a tricky ACT percentage question. This one doesn’t have any numbers at all–just percentages.
In 1991, Sally improved on her long jump distance by 10%. In 1992, she improved on the previous year’s distance by 20%. By how much did Sally improve on her 1990 long jump distance?
A) 30%
B) 32%
C) 33%
D) 25%
E) 35%
Most students simply add 10% and 20% and choose 30%, but this is absolutely WRONG. They key to understanding this question and solving it correctly will once again be to translate words into math. Algebra never fails us if we set things up correctly.
So, let’s begin. We know that in 1991, Sally improved on her jump of 1990 by 10%. What was her jump in 1990, by the way? Do you know? I don’t, so I’m going to call it X. If Sally jumped X in 1990 and improved on that by 10% in 1991, then what was her distance in 1991? 1.1x. And if in 1992 Sally improved on her previous year’s jump distance, what is her jump distance in 1992? It’s NOT 1.3x and it’s NOT 1.2x. It’s 1.2(1.1x). Why? Because in 1992 she jumped 20% farther than she jumped in 1991, not in 1990.
1990 = x
1991 = 1.1x
1992 1.2(1.1x)
So how much did she improve by on her original jump? Multiply 1.2 times 1.1 and you’ll have your answer: 1.32x. Her jump in 1992 was 32% farther than her jump in 1990. The answer, therefore, is B.
Make sense?
Hopefully these tips help you tackle tricky percentage questions on the SAT and ACT!
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