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SSAT Middle Level Math : Numbers and Operations

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

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

Example Questions

Example Question #111 : Ratio And Proportion

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 3200 cars in the parking lot and $8\%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

182

218

256

188

800

Correct answer:

256

Explanation:

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that $8\%$ of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$8:100\rightarrow\frac{8}{100}$

Reduce.

$\frac{8}{100}\rightarrow \frac{4}{50}\rightarrow \frac{2}{25}$

We know that there are 3200 cars in the parking lot. We can write the following ratio by substituting the variable Red for the number of red cars:

$Red:3200\rightarrow \frac{Red}{3200}$

Now, we can create a proportion using our two ratios.

$\frac{2}{25}=\frac{Red}{3200}$

Cross multiply and solve for Red .

$25 \times Red=2\times3200$

Simplify.

25 Red=6400

Divide both sides of the equation by .

$\frac{25Red}{25}=\frac{6400}{25}$

Solve.

Red=256

There are 256 red cars in the parking lot.

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Example Question #1 : Understand The Concept Of A Unit Rate: Ccss.Math.Content.6.Rp.A.2

A motorcyclist travels $2310\textup{ miles}$ in $55\textup{ hours}$ . What is the motorcyclist’s speed in miles per hour (mph)?

Possible Answers:

$47\textup{ mph}$

$42\textup{ mph}$

$60\textup{ mph}$

$46\textup{ mph}$

$49\textup{ mph}$

Correct answer:

$42\textup{ mph}$

Explanation:

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$2310\ miles: 55\ hours=\frac{2310\ miles}{55\ hours}$

Reduce and solve.

$42\textup{ mph}$

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Example Question #771 : Ssat Middle Level Quantitative (Math)

Candidate A receives votes for every vote that candidate B receives. At the end of the election candidate B has 900 votes. How many votes did candidate A get?

Possible Answers:

2700

900

300

100

1800

Correct answer:

2700

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 vote. We can write the following ratio.

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

Now substitute in the given numbers.

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

We know that candidate B received 900 votes. Write a new ratio.

$A:900\rightarrow\frac{A}{900}$

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

$\frac{3}{1}=\frac{A}{900}$

Cross multiply and solve for .

1(A)=900(3)

Simplify and solve.

A=2700

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Example Question #772 : Ssat Middle Level Quantitative (Math)

Candidate A receives votes for every vote that candidate B receives. At the end of the election candidate B has 134 votes. How many votes did candidate A get?

Possible Answers:

338

389

839

893

938

Correct answer:

938

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 vote. We can write the following ratio.

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

Now substitute in the given numbers.

$7:1\rightarrow \frac{7}{1}$

We know that candidate B received 134 votes. Write a new ratio.

$A:134\rightarrow\frac{A}{134}$

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

$\frac{7}{1}=\frac{A}{134}$

Cross multiply and solve for .

1(A)=134(7)

Simplify and solve.

A=938

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Example Question #2 : Understand The Concept Of A Unit Rate: Ccss.Math.Content.6.Rp.A.2

A motorcycle travels $1445\textup{ miles}$ in $17\textup{ hours}$ . What is the motorcyclist’s speed in miles per hour (mph)?

Possible Answers:

$87\textup{ mph}$

$83\textup{ mph}$

$85\textup{ mph}$

$77\textup{ mph}$

$75\textup{ mph}$

Correct answer:

$85\textup{ mph}$

Explanation:

In order to find the motorcyclist’s speed, we need to create a ratio of the miles travelled in a single hour.

$1445\ miles: 17\ hours=\frac{1445\ miles}{17\ hours}$

Reduce and solve.

85mph

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Example Question #21 : Make Tables Of Equivalent Ratios, Find Missing Values, And Plot Values On A Coordinate Plane: Ccss.Math.Content.6.Rp.A.3a

Traffic from the suburbs into a city typically follows an observable pattern. On any given morning there are cars on the road for every trucks on the road. On Monday morning there are trucks on the road. How many cars are on the road?

Possible Answers:

$56\ \text{cars}$

$51\ \text{cars}$

$59\ \text{cars}$

$49\ \text{cars}$

$28\ \text{cars}$

Correct answer:

$49\ \text{cars}$

Explanation:

In order to solve this problem we must make a table of ratios. In the question we are given the base ratio:

$7\ \text{cars}:3\ \text{trucks}$

We can use this ratio to make a table.

Cars

According to the table, there are $49\ \text{cars}$ .

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Example Question #776 : Ssat Middle Level Quantitative (Math)

The ratio of boys to girls in Ms. Smith’s class is 5:4. If there are 20 girls, how many boys are in the class?

Possible Answers:

Correct answer:

Explanation:

One way to solve this problem is to use cross multiplication. Set the ratio of $\textsl{boys}: \boldsymbol{\textsl{ girls}}=\frac{x}{20}$ to solve for the number of boys in the class.

Therefore, $\frac{5}{4}=\frac{x}{20}$

4x=100

x=25

Therefore, there are 25 boys in the class.

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Example Question #777 : Ssat Middle Level Quantitative (Math)

There are 50 pieces of fruit in a fruit basket. There are 22 apples, the rest are oranges. What is the ratio of oranges to apples?

Possible Answers:

44:6

14:11

6:5

11:14

Correct answer:

14:11

Explanation:

First we need to determine how many pieces of fruit are oranges. To do this, we subtract: $50-22=28 \textsl{ oranges}$

Therefore the ratio of $\textsl{ oranges}:\textsl{ apples}=28:22.$

This ratio can be simplified by dividing each side by 2. The ratio is then $14:11=\textsl{ oranges}:\textsl{ apples}$ .

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Example Question #114 : Ratio And Proportion

There are 50 orange cats and 20 black cats. What is the ratio of black to orange cats?

Possible Answers:

3:2

2:3

5:2

2:5

Correct answer:

2:5

Explanation:

The number of black cats goes before the colon since this question is asking for the ratio of black to orange cats.

Therefore, there are $20:50=\textsl{ black}: \textsl{ orange cats}$ .

This can be simplified if you divide both numbers by 10. This gives a ratio of 2:5 .

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Example Question #111 : How To Find A Ratio

Find .

$\frac{6}{25}=\frac{9}{x}$

Possible Answers:

2.16

37.5

Correct answer:

37.5

Explanation:

If you have to solve a proportion or a ratio, all you have to do is cross-multiply and divide by what is left.

$9\times25=6x$

225=6x

$\frac{225}{6}=x$

x=37.5

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All SSAT Middle Level Math Resources

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SSAT Middle Level Math : Numbers and Operations

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #111 : Ratio And Proportion

Example Question #1 : Understand The Concept Of A Unit Rate: Ccss.Math.Content.6.Rp.A.2

Example Question #771 : Ssat Middle Level Quantitative (Math)

Example Question #772 : Ssat Middle Level Quantitative (Math)

Example Question #2 : Understand The Concept Of A Unit Rate: Ccss.Math.Content.6.Rp.A.2

Example Question #21 : Make Tables Of Equivalent Ratios, Find Missing Values, And Plot Values On A Coordinate Plane: Ccss.Math.Content.6.Rp.A.3a

Example Question #776 : Ssat Middle Level Quantitative (Math)

Example Question #777 : Ssat Middle Level Quantitative (Math)

Example Question #114 : Ratio And Proportion

Example Question #111 : How To Find A Ratio

All SSAT Middle Level Math Resources

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