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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

Study concepts, example questions & explanations for SSAT Middle Level Math

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Example Questions

Example Question #151 : Data Analysis

How many of the following four numbers are elements of the set

$\left \{ x \; | \; 0.3 < x < 0.4\right \}$ ?

(A) $\frac{1}{3}$

(B) $\frac{2}{5}$

(D) $\frac{5}{13}$

Possible Answers:

Four

One

Three

Two

None

Correct answer:

Three

Explanation:

By dividing the numerator of each fraction by its denominator, each fraction can be rewritten as its decimal equivalent:

$\frac{1}{3} = 1 \div 3 = 0.333...$

$\frac{2}{5} = 2 \div 5 = 0.4$

$\frac{3}{8} = 0.375$

$\frac{5}{13} = 5 \div 13 = 0.384615...$

All fractions except can be seen to fall between 0.3 and 0.4, exclusive. Three is the correct answer.

Note that $\frac{2}{5}$ is equal to 0.4, so we don't include it. The criterion requires strict inequality.

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Example Question #581 : Ssat Middle Level Quantitative (Math)

Define $K = \left \{ x \; | \; x \textrm{ is a multiple of 5 }\right \}$ .

How many of the four sets listed are subsets of the set ?

(A) $\left \{ 7335, 8934, 1970, 5585, 8625 \right \}$

(B) $\left \{ 8655, 4135, 7472, 9530, 2265\right \}$

(D) $\left \{ 9730, 8390, 6380, 5980, 3975\right \}$

Possible Answers:

Two

One

None

Four

Three

Correct answer:

Two

Explanation:

For a set to be a subset of , all of its elements must also be elements of - that is, all of its elements must be multiples of 5. An integer is a multiple of 5 if and only if its last digit is 5 or 0, so all we have to do is examine the last digit of each number in all four sets.

In the sets $\left \{ 9730, 8390, 6380, 5980, 3975\right \}$ and $\left \{ 5725, 7695, 3640, 9375, 8405\right \}$ , every element ends in a 5 or a 0, so all elements of both sets are in ; both sets are subsets of .

However, $\left \{ 7335, 8934, 1970, 5585, 8625 \right \}$ includes one element that does not end in either 5 or 0, namely 8934, so 8934 is not an element in ; subsequently, this set is not a subset of . Similarly, $\left \{ 8655, 4135, 7472, 9530, 2265\right \}$ is not a subset of , since it includes 7472, which ends in neither 0 nor 5.

The correct answer is therefore two.

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Example Question #582 : Ssat Middle Level Quantitative (Math)

What are the next two numbers of this sequence?

10, 14, 19, 23, 28, 32, 37...

Possible Answers:

41, 46

41, 45

42, 47

41, 47

42, 46

Correct answer:

41, 46

Explanation:

The sequence is formed by alternately adding and adding to each term to get the next term.

$\begin{matrix} 10 + 4 = 14\\ 14 + 5 = 19\\ 19+4= 23\\ 23+5=28\\ 28+4 = 32\\ 32+5=37\\ 37+4=41\\ 41+5=46 \end{matrix}$

and are the next two numbers.

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Example Question #11 : Sets

What is the value of y in the pattern below?

$\frac{2}{3}, \frac{4}{6}, \frac{6}{9}, \frac{y}{12}$

Possible Answers:

Correct answer:

Explanation:

What that the fractions in this pattern have in common is that they are all the equivalent of $\frac{2}{3}$ .

The value of y should be a number that is the equivalent of $\frac{2}{3}$ when divided by 12.

Given that $\frac{1}{3}$ of 12 is 4, $\frac{2}{3}$ of 12 would be equal to 8, the correct answer.

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Example Question #152 : Data Analysis

What is the value of in the sequence below?

108, 36, 12, 4, x

Possible Answers:

$\frac{4}{3}$

$\frac{3}{4}$

$\frac{1}{2}$

Correct answer:

$\frac{4}{3}$

Explanation:

In this sequence, every subsequent number is equal to one third of the preceding number:

108, 36, 12, 3, x

$108\div3=36$

$36\div3=12$

$12\div3=4$

Given that $4\div3 =\frac{4}{3}$ , that is the correct answer.

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Example Question #21 : How To Find The Missing Part Of A List

Find the next number that should appear in the set below:

$\frac{1}{2}, \frac{1}{4},\frac{1}{8}, \frac{1}{16}$

Possible Answers:

$\frac{1}{32}$

$\frac{1}{24}$

$\frac{1}{18}$

$\frac{1}{40}$

Correct answer:

$\frac{1}{32}$

Explanation:

In this set, each subsequent fraction is half the size of the preceding fraction; (the denominator is doubled for each successive fraction, but the numerator stays the same). Given that the last fraction in the set is $\frac{1}{16}$ , it follows that the subsequent fraction will be $\frac{1}{32}$ .

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Example Question #2 : Generate Two Numerical Patterns Using Two Given Rules: Ccss.Math.Content.5.Oa.B.3

Complete the table below using the equation y=3x+6

Screen shot 2015 07 27 at 8.14.00 am

Possible Answers:

Correct answer:

Explanation:

In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding value for x=4 . We can plug into the in our equation to solve for .

y=3(4)+6

y=12+6

y=18

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Example Question #2 : Generate Two Numerical Patterns Using Two Given Rules: Ccss.Math.Content.5.Oa.B.3

Complete the table below using the equation y=4x+2

Screen shot 2015 07 27 at 8.25.13 am

Possible Answers:

Correct answer:

Explanation:

In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding value for x=5 . We can plug into the in our equation to solve for .

y=4(5)+2

y=20+2

y=22

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Example Question #2 : Generate Two Numerical Patterns Using Two Given Rules: Ccss.Math.Content.5.Oa.B.3

Complete the table below using the equation y=5x+7

Screen shot 2015 07 27 at 8.30.35 am

Possible Answers:

Correct answer:

Explanation:

In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding value for x=6 . We can plug into the in our equation to solve for .

y=5(6)+7

y=30+7

y=37

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Example Question #3 : Generate Two Numerical Patterns Using Two Given Rules: Ccss.Math.Content.5.Oa.B.3

Complete the table below using the equation y=6x+11

Screen shot 2015 07 27 at 8.34.12 am

Possible Answers:

Correct answer:

Explanation:

In order to solve this question, we need to use both the equation and the table. We are looking for the corresponding value for x=13 . We can plug into the in our equation to solve for .

y=6(13)+11

y=78+11

y=89

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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #151 : Data Analysis

Example Question #581 : Ssat Middle Level Quantitative (Math)

Example Question #582 : Ssat Middle Level Quantitative (Math)

Example Question #11 : Sets

Example Question #152 : Data Analysis

Example Question #21 : How To Find The Missing Part Of A List

Example Question #2 : Generate Two Numerical Patterns Using Two Given Rules: Ccss.Math.Content.5.Oa.B.3

Example Question #2 : Generate Two Numerical Patterns Using Two Given Rules: Ccss.Math.Content.5.Oa.B.3

Example Question #2 : Generate Two Numerical Patterns Using Two Given Rules: Ccss.Math.Content.5.Oa.B.3

Example Question #3 : Generate Two Numerical Patterns Using Two Given Rules: Ccss.Math.Content.5.Oa.B.3

All SSAT Middle Level Math Resources

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