2.7 SAT Math - Arithmetic Word Problems

Last but not least, let's talk about the easier word problems.  There are certainly some tough ones on this test, but those will be covered later.

An SAT arithmetic word problem (using only numbers, not variables) might look something like this:

Marie purchased six bags of apples from the store at a price of $3.69 a bag.  When she arrived home, she realized that they were on sale for $3.19 a bag, so she returned to the store to get a refund of the difference.  The cashier gave her the difference in quarters.  How many quarters did Marie receive?

This question uses very simple math concepts, but is intimidating because of its length, and because of the change in information - first they tell you one thing, then they mix it up a little and tell you something else...

The first thing to remember on ANY word problem is

-Break-It-Down Strategy: Start by breaking the word problem down into phrases.  Every time you see a comma, a period, or the word 'and' you should physically draw a line stopping your reading.  So the above question should look like this in your test booklet:

Marie purchased six bags of apples from the store at a price of $3.69 a bag|.  When she arrived home,| she realized that they were on sale for $3.19 a bag,| so she returned to the store to get a refund of the difference.| The cashier gave her the difference in quarters.  | How many quarters did Marie receive?

Every time you see that bar, you need to make sure you've either done work on that phrase, or that you understand what is being communicated there. 

Phrase #1: Marie purchased six bags of apples from the store at a price of $3.69 a bag.  What work needs to be done? $3.69 times 6 to determine how much she spent. 
Phrase #2: When she arrived home, Any work? No.  Move on.
Phrase #3: she realized that they were on sale for $3.19 a bag Any work? Yes! You need to do $3.19 times 6 to determine how much she should have paid.
Phrase #4: so she returned to the store to get a refund of the difference.  The clue word here is "difference".  Subtract the number she should have paid from the number she did pay to see what her refund was.
Phrase #5: The cashier gave her the difference in quarters.  How much is a quarter worth?
Phrase #6: How many quarters did Marie receive? Divide the amount she should have been refunded by the amount a quarter is worth to determine the number of quarters she received.

What answer did you get?

(A) 2
(B) 12
(C) 13
(D) 76
(E) 77

The correct answer is (B) 12.

-Trick to Watch Out For: Especially on SAT word problems, it's important not only that you read carefully, but that you always re-read the question portion before picking your answer.  Yup, you’ve seen that before, in the overall rules, but it’s so important it’s getting repeated.  SAT questions love to point you in a particular direction, and then ask you for something slightly different.  So you'll do all this hard work and confidently pick an answer, only to have made the careless mistake of not answering the exact question asked.  Examples:

Sam is training for a marathon.  She runs 8 miles on Monday, 4 miles on Tuesday, 3.5 miles on Wednesday, 10 miles on Thursday, and 6 miles on Friday.  She plans to take Sunday off.  What is one-half the distance she must run on Saturday if she wants to complete 40 miles for the week?

Did you catch that? They have you do all this adding and subtracting, only to ask you for one-half the distance she must run, not the actual distance.  The actual distance, you can bet, will be one of the answer choices, and if you're not careful, you'll pick it confidently, never knowing you got tricked.

Another example using a little harder math:

The ratio of red marbles to green marbles is 4 to 3.  If there are 28 marbles in the bag, how many marbles will need to be removed to make the ratio of red to green equal?

They're not asking for the number of red marbles or the number of green marbles like in a traditional ratio problem.  They're asking for an extra step of work, an extra step you might miss if you don't re-read exactly what they want from you before selecting your answer.  (If you don't know how to solve this problem, don't worry, we'll come back to it when we cover ratios.)