SAT Math: Sets Terminology (w/ example)

Here are the SAT Math ‘Sets’ terms you should know.

Set questions ask you to compare overlapping groups to determine which members are in each set.

Example:

See comments for answer and explanation.

From my SAT guide SAT Unlocked, which includes a complete list of practice questions in The Official SAT Study Guide that test this SAT Math topic.

SAT Math: When to Plug-in Numbers II (w/ examples)

Previously, we talked about the strategy of plugging in a number whenever an SAT Math question mentions a number or integer. This number plug-in strategy works equally as well for questions with equations in the answer choices – questions that are often among the hardest on the entire SAT Math section.

Whenever you see an SAT Math question with equations in the answer choices, plug in a number.

Pick a number and plug it into the question to get a value. Then plug the number into each answer choice to see which one produces the same value.

Remember:
When plugging in numbers, be sure to pick EASY numbers and ALWAYS plug in for ALL answer choices.

Example 1:

The number plug-in strategy also works great for word problems with equations in the answer choices.

Example 2:

Answers and explanations in the comments.

From my SAT guide SAT Unlocked, which includes a complete list of practice questions in The Official SAT Study Guide for which this number plug-in strategy is effective.

SAT Math: Sum of Consecutive Integers (w/ example)

Consecutive integer questions typically tell you the sum total of a group of consecutive integers and then ask you to find one of these integers.

To handle sum of consecutive integer questions:

1. First divide the sum by the number of integers to get the midpoint of the sequence.
2. Then count up or down from this midpoint to find the integer asked for by the question.

Example:

The sum of five, consecutive odd integers is 195. What is the greatest of these integers?

(A)  33
(B)  36
(C)  39
(D)  43
(E)  71

Answer in the Comments.

SAT Math: When to Plug-in Numbers (w/ example)

Plugging in numbers is a simple and very effective strategy that can help you answer many SAT Math questions, including even some of the hardest ‘Numbers and Operations’ questions.

Any time a question mentions a ‘number’ or ‘integer’, make up your own value that fits the description in the question, and then plug that value into the answer choices to see which one works.

A couple of things to remember:

Use EASY numbers.
1 (sometimes), 2, 3, 4, 5, 10, and 100 are usually best, depending on the question.

Check ALL answers
Occasionally, the number you plug in may be correct for more than one answer choice (especially if you plug in ’1′). Be sure to check all answers to make sure only one is correct. If you get more than one correct answer, plug in a different number for the remaining choices.

Example:

Answer and explanation in the Comments.

From my SAT course book SAT Unlocked, which includes a complete list of questions in The Official SAT Study Guide for which this number plug-in strategy is effective.

SAT Math: Number Lines (w/ example)

Once or twice per test, the SAT will ask you to interpret values on a number line.

When a number line question includes undefined points (labeled by variables), estimate the values of those points before answering the question.

Number Line Example:

See Comments for the answer.

Tip:
Number line questions often include fractions and negative numbers.
Subtracting a negative number moves the value to the right on the number line (positively).
Multiplying a number by a fraction makes the number smaller.

From SAT Unlocked, which includes a complete list of the number line practice questions found in The Official SAT Study Guide.

SAT Math Exercise: Number Properties

Assuming whole numbers (integers), what is the correct answer for each of the following:

1. positive x positive = positive or negative?
2. negative x negative = positive or negative?

3. positive x negative = positive or negative?

4. even + odd = even or odd?

5. odd + odd = even or odd?

6. even + even = even or odd?

7. even x odd = even or odd?

8. odd x odd = even or odd?

9. even x even = even or odd?

10. positive odd x negative even = positive odd or negative even?

11. negative odd x negative odd = positive odd or negative even?

12. negative odd x positive even = positive odd or negative even?

13. Which is greater? -3 or -4?

See Comments for answers.

SAT Math: Sum of Consecutive Integers

Consecutive Integers are those which occur in numerical order. (like 3,4,5,6,…)

One type of consecutive integer question tells you the sum total of a group of consecutive integers and asks you to find one of these integers.

To answer Sum of Consecutive Integer questions:

1. Divide the sum total by the number of integers to find the midpoint of the sequence.

2. Then count up or down from this midpoint to find the integer asked for by the question.

Example:

Answer and explanation below.

From my SAT guide SAT Unlocked, which includes a complete list of practice questions in The Official SAT Study Guide that test this SAT Math topic.

SAT Math: Repeating Sequences (w/ example)

The SAT will occasionally include a sequence where the numbers repeat themselves in a pattern. In repeating sequence questions, you’re usually asked which of the repeating terms lies at a point far down the sequence.

1. Figure out how many terms it takes before the sequence repeats;

2. Divide the number of the term you need by the total number of repeating terms;

3. Use the remainder to find which number in the repeating sequence is the correct term.

Answer and explanation below.

From my SAT guide SAT Unlocked, which includes a complete list of practice questions in The Official SAT Study Guide that test this SAT Math topic.

SAT Math: Geometric Sequences (w/ example)

Sequences which multiply the same number over and over again are known as ‘geometric’ sequences.

Tip:

It is often easier simply to multiply out the geometric sequence until you get to the term you need.

Answer and explanation below.

From my SAT guide SAT Unlocked, which includes a complete list of practice questions in The Official SAT Study Guide that test this SAT Math topic.

SAT Math: Arithmetic Sequences (w/ example)

Sequences which add the same number over and over again are known as ‘arithmetic’ sequences.

Answer and explanation below.

From my SAT guide SAT Unlocked, which includes a complete list of practice questions in The Official SAT Study Guide that test this SAT Math topic.

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