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# Tip #37 to Get a Top SAT Math Score (page 2)

By McGraw-Hill Professional
Updated on Sep 10, 2011

Remember remainders? Back in 5th grade you had this thing down. You learned it, put it up on the fridge, and ran out into the yard for prisoner dodgeball. But now it's six years later, and you've no idea what I'm talking about.

Remainders are what's left over when you use long division.

The r1 means remainder 1. That's it. So why is this on the SAT? I think that years ago, when the SAT made the decision to allow calculators on the test, they started using remainder questions since they are hard to do with a calculator. But the Buddha said that if a man is shot by an arrow, do not waste time on discovering who shot him, just help him. So here's the help. Remainders are easy, and as usual, the SAT always asks the same concepts.

Let's look at this question:

Solution: This is a great review of our "Use the Answers" strategy. Just try each number to see which answer choice does not give remainder 3, when divided by 4.

Each choice works EXCEPT choice C, 22, which gives a remainder of 2 not 3.

### Medium

1. What is the remainder when 13 is divided by 3 ?
1. 0
2. 1
3. 2
4. 3
5. 4
2. All the following can be the remainders of 24 divided by an even number EXCEPT
1. 12
2. 10
3. 8
4. 6
5. 4
3. All the following numbers have the same remainder when divided by 4 EXCEPT
1. 7
2. 15
3. 19
4.
5. 22
6. 27

### Hard

1. Which of the following could be remainders when five consecutive positive integers are each divided by 4 ?
1. 1, 2, 3, 0, 1
2. 1, 2, 3, 4, 1
3. 1, 2, 0, 1, 2
4. 0, 1, 2, 1, 0
5. 0, 4, 3, 2, 1
2. For all negative integers m and n, let m n be defined as the remainder when n is divided by m. If – 18 n = 3, which of the following can be the value of n ?
1. –18
2. –36
3. –41
4. 36
5. 39
3. For all integers p and q, let p Θ q be defined as the remainder when p is divided by q. How many different values for b make the statement 24 Θ b = 3 true?
1. 0
2. 1
3. 2
4. 3
5. 4

1. B Your calculator tells you that 13 divided by 3 is 4.3333. That does not give us the answer. Instead we need to channel 5th grade: you haven't showered in a week, and you're sure that this next pack of baseball cards will complete your set. Now you remember, remainder is just the left over when you do long division.
2. A Just divide 24 by even numbers and see which answers we can cross off.
3. So the answer is 12, since all the other answer choices can be remainders when 24 is divided by even numbers.

4. D This is a great review of the "Use the Answers" strategy. Just try each answer choice to see which one does not give remainder 3 when divided by 4.
5. Each choice works EXCEPT choice D, 22, which gives a remainder of 2 not 3.

6. A This is a nice vocab review. Remember that "consecutive" means in a row, "positive" means greater than 0, and "integer" means no decimals. So just choose 5 consecutive positive integers and divide each by 4, and see which answer choice is correct. Remember that the correct answer might be a different starting point, but the same pattern as your numbers.
7. E This is a great preview of "Weird Symbol Questions" (Skill 45). This is not some symbol that you missed in algebra class. Nobody knows this symbol. The SAT is making it up and telling us what to do with it. So you just have to stay confident and roll with it. The symbol represents the remainder when the second number is divided by the first. So n divided by –18 should give a remainder of 3. Simply try each answer choice. 39 divided by –18 equals –2 with a remainder of 3.
8. C Another preview of "Weird Symbol Questions." The operation just represents the remainder when the first number is divided by the second number. So 24 divided by b should give a remainder of 3. What can b equal to make that work? Here's the key: if the remainder is 3, then we must multiply to get 24 – 3 = 21. So we can divide by 7 or 21 to get remainder of 3, and there are 2 possibilities. This is a "hard" because most people who do not read this book have absolutely no idea how to do this question.

Go to: Tip #38