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The SAT Math Question Almost Everyone Misses
The SAT is known for being very tricky, and this question is no exception. In fact, pretty much every student I’ve ever had gets the answer to this question wrong. Why? Usually it’s because they fail to read and understand the question or because they lack an understanding of percentages or algebra. Let’s take a look!
Seems simple enough on the surface, right? A girl’s buying a laptop, gets a discount, pays tax. Normal stuff, yeah? So what do you think the answer is? Here’s a hint. It’s not C. But C is the answer choice everybody puts!
Let’s learn exactly how to solve the question.
First of all, we’ve got to understand exactly what the question wants. And the question wants to know “which of the following represents the original price of the computer in terms of p?”
The key phrase here is original price.
So why do people pick C? They mistakenly assume it’s a basic question about calculating the cost of a laptop at a discount price plus tax. They mistakenly assume that p is the original price. But it doesn’t want the total cost. It wants the original price, and there is no variable for the original price.
So we’ve got to create a variable for the original price. Let’s call the original price x.
If x is the original price, what’s the discount price? The question says that Alma got a 20% discount, which means that she’s only paying 80% of the total cost of the laptop, which means that the discount price is .8x.
But Alma also has to pay an 8% tax. While a discount means subtracting a percentage, a tax means adding a percentage. So whatever the cost of the laptop is for Alma, she’s got to pay 108% of that. The cost of the discounted laptop plus tax is therefore (1.08)(.8x), because Alma is paying 108% of 80% percent of the laptop’s price.
What does p represent, by the way? The problem states that p is the total amount Alma paid to the cashier. Therefore:
p = (1.08)(.8)(x)
And the question wants the original price of the laptop, which means we’re solving for x. Easy algebra now, right? Divide both sides by 1.08 and by .8 to find that the original price of the laptop is:
x = p / (1.08)(.8)
or answer choice D!
Tricky, huh? Do you think YOU could have gotten this right? Or would you simply speed through the question and put C like everyone else?
Hope this problem encourages you to carefully read the questions on the SAT Math test and understand what they truly want. I also hope it encourages you to gain an understanding of percentages, tax, and basic algebra!
Frankly, this is a real-world scenario! Knowing how to calculate discounts and factor in tax will help you when you’re making purchases of your own!
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