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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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All SSAT Middle Level Math Resources

10 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #13 : How To Find A Ratio

One dollar is equal to about 116.76 Japanese yen. For how many yen should a tourist to Japan be able to exchange $2,500 at that rate (nearest whole yen)?

Possible Answers:

$291,900 \textrm{ yen}$

$2,141\textrm{ yen}$

$214\textrm{ yen}$

$21\textrm{ yen}$

$29,190 \textrm{ yen}$

Correct answer:

$291,900 \textrm{ yen}$

Explanation:

One dollar is equal to 116.76 yen, so multiply $2,500 by this conversion rate to get

$2,500 \times 116.76 = 291,900$ yen.

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Example Question #14 : Numbers And Operations

Sharon is having a birthday party. So far, she has invited twenty of her friends from school, nine of whom are girls. She wants to make the ratio of boys to girls at the party two to one. If she decides to add her two cousins, both girls, to the guest list, and no other girls, how many more boys does she need to invite?

Possible Answers:

Correct answer:

Explanation:

So far, Sharon has invited twenty friends from school - eleven boys and nine girls. Including Sharon's cousins and Sharon herself, there are eleven boys and twelve girls.

For there to be a two-to-one boy-to-girl ratio, Sharon must have twice as many boys as girls. She will need $12 \times 2 = 24$ boys total, so she will need to invite 24-11 = 13 more boys.

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Example Question #681 : Ssat Middle Level Quantitative (Math)

Phil invites sixty friends from his current school, thirty-five of whom are girls, to his birthday party; he also invites his two female cousins. Phil wants the ratio of girls to boys at the party to be two to one, so he decides to also invite some girls from his old school. How many new girls will he need to invite, assuming he does not invite anyone else?

Possible Answers:

Correct answer:

Explanation:

So far, there are 37 girls - 35 classmates and 2 cousins - and 26 boys - 25 classmates and Mike himself. For the ratio of girls to boys to be 2 to 1, the number of girls must be twice the number of boys, or $26 \times 2 = 52$ girls. Mike will need 52-37 = 15 more girls.

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Example Question #1 : Ratios & Proportional Relationships

Write as a unit rate: 330 revolutions in minutes

Possible Answers:

revolutions per minute

Correct answer:

revolutions per minute

Explanation:

Divide the number of revolutions by the number of minutes to get revolutions per minute:

$330\div 15 = 22$ ,

making revolutions per minute the correct choice.

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Example Question #1 : Ratios & Proportional Relationships

If candidate A receives vote for every votes that candidate B receives. At the end of the election candidate B has 320 votes. How many votes did candidate A get?

Possible Answers:

960

320

$106\tfrac{2}{3}$

Correct answer:

$106\tfrac{2}{3}$

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every vote cast for candidate A, candidate B got votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$1:3\rightarrow \frac{1}{3}$

We know that candidate B received 320 votes. Write a new ratio.

$A:320\rightarrow\frac{A}{320}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{1}{3}=\frac{A}{320}$

Cross multiply and solve for .

3(A)=320(1)

Simplify.

3A=320

Divide both sides of the equation by .

$\frac{3A}{3}=\frac{320}{3}$

Solve.

$A=106\tfrac{2}{3}$

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Example Question #21 : Numbers And Operations

If candidate A receives votes for every votes that candidate B receives. At the end of the election candidate B has 320 votes. How many votes did candidate A get?

Possible Answers:

132

128

282

155

160

Correct answer:

128

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every votes cast for candidate A, candidate B got votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$2:5\rightarrow \frac{2}{5}$

We know that candidate B received 320 votes. Write a new ratio.

$A:320\rightarrow\frac{A}{320}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{2}{5}=\frac{A}{320}$

Cross multiply and solve for .

5(A)=320(2)

Simplify.

5A=640

Divide both sides of the equation by .

$\frac{5A}{5}=\frac{640}{5}$

Solve.

A=128

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Example Question #22 : Numbers And Operations

If candidate A receives vote for every votes that candidate B receives. At the end of the election candidate B has 320 votes. How many votes did candidate A get?

Possible Answers:

335

410

Correct answer:

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every vote cast for candidate A, candidate B got votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$1:5\rightarrow \frac{1}{5}$

We know that candidate B received 320 votes. Write a new ratio.

$A:320\rightarrow\frac{A}{320}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{1}{5}=\frac{A}{320}$

Cross multiply and solve for .

5(A)=320(1)

Simplify.

5A=320

Divide both sides of the equation by .

$\frac{5A}{5}=\frac{320}{5}$

Solve.

A=64

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Example Question #1 : Ratios & Proportional Relationships

If candidate A receives votes for every votes that candidate B receives. At the end of the election candidate B has 300 votes. How many votes did candidate A get?

Possible Answers:

180

100

190

Correct answer:

180

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every votes cast for candidate A, candidate B got votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$3:5\rightarrow \frac{3}{5}$

We know that candidate B received 300 votes. Write a new ratio.

$A:300\rightarrow\frac{A}{300}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{3}{5}=\frac{A}{300}$

Cross multiply and solve for .

5(A)=300(3)

Simplify.

5A=900

Divide both sides of the equation by .

$\frac{5A}{5}=\frac{900}{5}$

Solve.

A=180

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Example Question #2 : Ratios & Proportional Relationships

If candidate A receives votes for every votes that candidate B receives. At the end of the election candidate B has 255 votes. How many votes did candidate A get?

Possible Answers:

$127\tfrac{1}{2}$

237

123

255

Correct answer:

$127\tfrac{1}{2}$

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every votes cast for candidate A, candidate B got votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$3:6\rightarrow \frac{3}{6}$

Reduce.

$\frac{3}{6}=\frac{1}{2}$

We know that candidate B received 255 votes. Write a new ratio.

$A:320\rightarrow\frac{A}{255}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{1}{2}=\frac{A}{255}$

Cross multiply and solve for .

2(A)=255(1)

Simplify.

2A=255

Divide both sides of the equation by .

$\frac{2A}{2}=\frac{255}{2}$

Solve.

$A=127\tfrac{1}{2}$

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Example Question #1 : Ratios & Proportional Relationships

If candidate A receives vote for every votes that candidate B receives. At the end of the election candidate B has 300 votes. How many votes did candidate A get?

Possible Answers:

150

310

160

302

Correct answer:

150

Explanation:

In order to solve this problem we need to create a ratio with the given information. It says that for every vote cast for candidate A, candidate B got votes. We can write the following ratio.

$A:B\rightarrow\frac{A}{B}$

Now substitute in the given numbers.

$1:2\rightarrow \frac{1}{2}$

We know that candidate B received 300 votes. Write a new ratio.

$A:300\rightarrow\frac{A}{300}$

Now, use the original relationship to create a proportion and solve for the number of votes that candidate A received.

$\frac{1}{2}=\frac{A}{300}$

Cross multiply and solve for .

2(A)=300(1)

Simplify.

2A=300

Divide both sides of the equation by .

$\frac{2A}{2}=\frac{300}{2}$

Solve.

A=150

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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 #13 : How To Find A Ratio

Example Question #14 : Numbers And Operations

Example Question #681 : Ssat Middle Level Quantitative (Math)

Example Question #1 : Ratios & Proportional Relationships

Example Question #1 : Ratios & Proportional Relationships

Example Question #21 : Numbers And Operations

Example Question #22 : Numbers And Operations

Example Question #1 : Ratios & Proportional Relationships

Example Question #2 : Ratios & Proportional Relationships

Example Question #1 : Ratios & Proportional Relationships

All SSAT Middle Level Math Resources

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