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# Tip #37 to Get a Top SAT Math Score

By Brian Leaf
McGraw-Hill Professional

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

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