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SAT Math : Integers

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Example Question #8 : How To Find The Next Term In An Arithmetic Sequence

An arithmetic sequence begins as follows:

$\sqrt{5} , \sqrt{10},...$

Give the next term of the sequence in simplest radical form.

Possible Answers:

$3 \sqrt{5}$

$\sqrt{15}$

None of the other choices gives the correct response.

$2 \sqrt{5}$

$2 \sqrt{10}$

Correct answer:

None of the other choices gives the correct response.

Explanation:

Since no perfect square integer greater than 1 divides evenly into 5 or 10, both of the first two terms of the sequence are in simplest form.

The common difference of an arithmetic sequence can be found by subtracting the first term from the second:

$d = a_{2} - a_{1}$

Setting $a_{1}= \sqrt{5}, a_{2}= \sqrt{10}$ :

$d = \sqrt{10} - \sqrt{5}$

Add this to the second term to obtain the desired third term:

$a_{3} = a_{2} +d =\sqrt{10} + ( \sqrt{10} - \sqrt{5}) = \sqrt{10} + \sqrt{10} - \sqrt{5} = 2\sqrt{10}- \sqrt{5}$

This is not among the given choices.

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Example Question #9 : How To Find The Next Term In An Arithmetic Sequence

An arithmetic sequence begins as follows:

$\frac{1}{5} , \frac{1}{3} , ...$

Give the sixth term of the sequence in decimal form.

Possible Answers:

0.8

0.875

$0.9\overline{3}$

$0.8\overline{6}$

$0.\overline{8}$

Correct answer:

$0.8\overline{6}$

Explanation:

The common difference of an arithmetic sequence can be found by subtracting the first term from the second:

$d = a_{2} - a_{1}$

Setting $a_{1}= \frac{1}{5}, a_{2}= \frac{1}{3}$ :

$d = \frac{1}{3} - \frac{1}{5} = \frac{5}{15} - \frac{3}{15} = \frac{2}{15}$

The th term $a_{n}$ of an arithmetic sequence can be derived using the formula

$a_{n} = a_{1} + (n-1)d$

Setting $n = 6 , a_{1} = \frac{1}{5}= \frac{3}{15}, d = \frac{2}{15}$ :

$a_{n} = \frac{3}{15} + (6-1) \cdot \frac{2}{15}$

$= \frac{3}{15} +5 \cdot \frac{2}{15}$

$= \frac{3}{15} + \frac{10}{15}$

$= \frac{13}{15}$

The decimal equivalent of this can be found by dividing 13 by 15 as follows:

Division

The correct choice is $0.8\overline{6}$ .

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Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

An arithmetic sequence begins as follows:

4, 5 i ,...

Give the sixth term of the sequence.

Possible Answers:

-20 + 30 i

25+30i

-20 + 25i

20+25 i

-16+25i

Correct answer:

-16+25i

Explanation:

The common difference of an arithmetic sequence can be found by subtracting the first term from the second:

$d = a_{2} - a_{1}$

Setting $a_{1}= 4, a_{2}= 5i$ :

d = 5i - 4 = -4+5i

The th term $a_{n}$ of an arithmetic sequence can be derived using the formula

$a_{n} = a_{1} + (n-1)d$

Setting $a_{1}= 4, n = 6, d= -4+5i$

$a_{6} =4 + (6-1) ( -4+5i)$

=4 +5( -4+5i)

=4 +( -20+25i)

=(4 -20)+25i

=-16+25i

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Example Question #21 : Nth Term Of An Arithmetic Sequence

Complete the sequence:

1, 8, 27, x, 125

Possible Answers:

150

125

400

335

Correct answer:

Explanation:

The pattern of this sequence is n^3 where represents the place of each number in the order of the sequence.

Here are our givens:

n^3

1^3 = 1 , our first term.

2^3 = 8 , our second term.

3^3 = 27 , our third term.

This means that our fourth term will be:

4^3 = 64 .

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Example Question #1 : How To Find The Missing Number In A Set

Which number completes the following series: 1, 2, 4, 8, 16, 32, 64, _?

Possible Answers:

Not enough information

128

Correct answer:

128

Explanation:

All of the numbers in this series are 2^n-1. The number that we are looking for is the eighth number. So 2^8–1 = 2⁷ = 128.

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Example Question #2 : How To Find The Missing Number In A Set

Alhough Danielle’s favorite flowers are tulips, she wants at least one each of three different kinds of flowers in her bouquet. Roses are twice as expensive as lilies and lilies are 25% of the price of tulips. If a rose costs $20 and Danielle only has $130, how many tulips can she buy?

Possible Answers:

Correct answer:

Explanation:

She can only buy 2 tulips at $80, because if she bought 3 she wouldn’t have enough to afford the other 2 kinds of flowers. She has to spend at least 30 dollars (20 + 10) on 1 rose and 1 lily.

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Example Question #131 : Integers

Which of the following is not a rational number?

Possible Answers:

√2

.001

0.111...

1.75

Correct answer:

√2

Explanation:

A rational number is a number that can be written in the form of a/b, where a and b are integers, aka a real number that can be written as a simple fraction or ratio. 4 of the 5 answer choices can be written as fractions and are thus rational.

5 = 5/1, 1.75 = 7/4, .001 = 1/1000, 0.111... = 1/9

√2 cannot be written as a fraction because it is irrational. The two most famous irrational numbers are √2 and pi.

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Example Question #1 : How To Find The Missing Number In A Set

Which set represents all the single-digits integers (0-9) that are either prime, a perfect square, or found in the number 68?

Possible Answers:

$\dpi{100} \small \left \{1,2,3,4,5,6,7,8,9 \right \}$

$\dpi{100} \small \left \{2,3,4,5,6,7,8,9 \right \}$

$\dpi{100} \small \left \{ 0,1,2,3,4,5,6,7,8,9 \right \}$

$\dpi{100} \small \left \{0,2,3,5,6,7,8 \right \}$

$\dpi{100} \small \left \{1,3,4,5,7,9 \right \}$

Correct answer:

$\dpi{100} \small \left \{ 0,1,2,3,4,5,6,7,8,9 \right \}$

Explanation:

The prime digits are 2, 3, 5, and 7.

The perfect square digits are 0, 1, 4, and 9.

The only digits not represent in these two groups are 6 and 8, which are, coincidentally, found in the number 68.

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Example Question #171 : Integers

If four different integers are selected, one from each of the following sets, what is the greater sum that these four integers could have?

W = {4, 6, 9, 10}

X = {4, 5, 8, 10}

Y = {3, 6, 7, 11}

Z = {5, 8, 10, 11}

Possible Answers:

Correct answer:

Explanation:

By observing each of these sets, we can easily determine the largest number in each; however, the problem is asking for us to find the greatest possible sum if we select four different integers, one from each set. The largest number is 11. We will either select this number from set Y or set Z.

We will select set

Y for the 11

because the next larger number in set

Z is 10, which is greater than the next largest number is set Y, 7.

We can use set Z for 10.

Because the 10 has already been selected, choosing the integer from W and X should be easy because 9 is the next largest integer from set W

and

8 is the next largest integer from set X.

11 + 10 + 9 + 8 = 38

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Example Question #6 : How To Find The Missing Number In A Set

A team has a win-loss ratio of $4:1$ . If the team wins six games in a row, the win-loss ratio will now be $6:1$ . How many losses did the team have initially?

Possible Answers:

$5$

$3$

$2$

$1$

$4$

Correct answer:

$3$

Explanation:

If a team's ratio of wins to losses increases from $4:1$ to $6:1$ by winning six games, they must have 12 wins initially and 3 losses.

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SAT Math : Integers

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #8 : How To Find The Next Term In An Arithmetic Sequence

Example Question #9 : How To Find The Next Term In An Arithmetic Sequence

Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

Example Question #21 : Nth Term Of An Arithmetic Sequence

Example Question #1 : How To Find The Missing Number In A Set

Example Question #2 : How To Find The Missing Number In A Set

Example Question #131 : Integers

Example Question #1 : How To Find The Missing Number In A Set

Example Question #171 : Integers

Example Question #6 : How To Find The Missing Number In A Set

All SAT Math Resources

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