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ISEE Middle Level Quantitative : ISEE Middle Level (grades 7-8) Quantitative Reasoning

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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All ISEE Middle Level Quantitative Resources

6 Diagnostic Tests 110 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #235 : Numbers And Operations

You are given a bag with 5 red marbles, 3 green marbles and 7 blue marbles. What percent of the bag are red marbles?

Possible Answers:

$33.3\%$

$5\%$

$55\%$

$50\%$

Correct answer:

$33.3\%$

Explanation:

When finding the percent, we must take the part and divide it by the whole.

$Percent=\frac{part}{whole}$

In this case, 5 is the part and we must find the sum of everything to make the whole as shown in the denominator below.

$Percent=\frac{5}{5+7+3}=\frac{5}{15}$

We can now reduce the fraction and convert to percent.

$Percent=\frac{5}{15}=\frac{1}{3}=33.3\%$

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Example Question #16 : Percentage

A store is having a 40% off clearance sale on items of clothing. Rosa bought a new dress from this store. If the dress's original price was $80, how much did Rosa pay?

Possible Answers:

$\$40$

$\$30$

$\$50$

$\$48$

Correct answer:

$\$48$

Explanation:

If the store sells the dress for 40% off, that means it is worth 60% of its original price.

100 - 40 = 60

Therefore, if you multiply 60% times the original price of the dress, you will know what the current price of the dress is.

To do this, first divide your percentage by 100.

$60\div100 = 0.6$

Then, multiply the result of this times the original price of the dress.

$80 \times 0.6 = 48$

The new result is your answer.

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Example Question #61 : Ratios & Proportional Relationships

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 100 cars in the parking lot and $60 \%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

Correct answer:

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 $60\%$ of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$60:100\rightarrow\frac{60}{100}$

Reduce.

$\frac{60}{100}\rightarrow \frac{6}{10}\rightarrow \frac{3}{5}$

We know that there are 100 cars in the parking lot. We can write the following ratio by substituting the variable Red for the number of red cars:

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

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

$\frac{3}{5}=\frac{Red}{100}$

Cross multiply and solve for Red .

$5 \times Red=3\times100$

Simplify.

5 Red=300

Divide both sides of the equation by .

$\frac{5Red}{5}=\frac{300}{5}$

Solve.

Red=60

There are red cars in the parking lot.

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Example Question #1 : Find A Percent Of A Quantity As A Rate Per 100: Ccss.Math.Content.6.Rp.A.3c

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 250 cars in the parking lot and $10 \%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

Correct answer:

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 $10\%$ of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$10:100\rightarrow\frac{10}{100}$

Reduce.

$\frac{10}{100}\rightarrow \frac{1}{10}$

We know that there are 250 cars in the parking lot. We can write the following ratio by substituting the variable Red for the number of red cars:

$Red:250\rightarrow \frac{Red}{250}$

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

$\frac{1}{10}=\frac{Red}{250}$

Cross multiply and solve for Red .

$10 \times Red=1\times 250$

Simplify.

10 Red=250

Divide both sides of the equation by .

$\frac{10Red}{10}=\frac{250}{10}$

Solve.

Red=25

There are red cars in the parking lot.

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Example Question #3 : Find A Percent Of A Quantity As A Rate Per 100: Ccss.Math.Content.6.Rp.A.3c

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 136 cars in the parking lot and $25 \%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

Correct answer:

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 $25\%$ of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$25:100\rightarrow\frac{25}{100}$

Reduce.

$\frac{25}{100}\rightarrow \frac{1}{4}$

We know that there are 136 cars in the parking lot. We can write the following ratio by substituting the variable Red for the number of red cars:

$Red:136\rightarrow \frac{Red}{136}$

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

$\frac{1}{4}=\frac{Red}{136}$

Cross multiply and solve for Red .

$4 \times Red=1\times136$

Simplify.

4 Red=136

Divide both sides of the equation by .

$\frac{4Red}{4}=\frac{136}{4}$

Solve.

Red=34

There are red cars in the parking lot.

Report an Error

Example Question #4 : Find A Percent Of A Quantity As A Rate Per 100: Ccss.Math.Content.6.Rp.A.3c

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 164 cars in the parking lot and $25 \%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

Correct answer:

Explanation:

$25:100\rightarrow\frac{25}{100}$

Reduce.

$\frac{25}{100}\rightarrow \frac{1}{4}$

We know that there are 164 cars in the parking lot. We can write the following ratio by substituting the variable Red for the number of red cars:

$Red:164\rightarrow \frac{Red}{164}$

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

$\frac{1}{4}=\frac{Red}{164}$

Cross multiply and solve for Red .

$4 \times Red=1\times164$

Simplify.

4 Red=164

Divide both sides of the equation by .

$\frac{4Red}{4}=\frac{164}{4}$

Solve.

Red=41

There are red cars in the parking lot.

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Example Question #61 : Grade 6

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 135 cars in the parking lot and $60 \%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

Correct answer:

Explanation:

$60:100\rightarrow\frac{60}{100}$

Reduce.

$\frac{60}{100}\rightarrow \frac{6}{10}\rightarrow \frac{3}{5}$

We know that there are 135 cars in the parking lot. We can write the following ratio by substituting the variable Red for the number of red cars:

$Red:135\rightarrow \frac{Red}{135}$

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

$\frac{3}{5}=\frac{Red}{135}$

Cross multiply and solve for Red .

$5 \times Red=3\times135$

Simplify.

5 Red=405

Divide both sides of the equation by .

$\frac{5Red}{5}=\frac{405}{5}$

Solve.

Red=81

There are red cars in the parking lot.

Report an Error

Example Question #6 : Find A Percent Of A Quantity As A Rate Per 100: Ccss.Math.Content.6.Rp.A.3c

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 400 cars in the parking lot and $40 \%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

164

148

160

116

Correct answer:

160

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 $40\%$ of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$40:100\rightarrow\frac{40}{100}$

Reduce.

$\frac{40}{100}\rightarrow \frac{4}{10}\rightarrow \frac{2}{5}$

We know that there are 400 cars in the parking lot. We can write the following ratio by substituting the variable Red for the number of red cars:

$Red:400\rightarrow \frac{Red}{400}$

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

$\frac{2}{5}=\frac{Red}{400}$

Cross multiply and solve for Red .

$5 \times Red=2\times400$

Simplify.

5 Red=800

Divide both sides of the equation by .

$\frac{5Red}{5}=\frac{800}{5}$

Solve.

Red=160

There are 160 red cars in the parking lot.

Report an Error

Example Question #7 : Find A Percent Of A Quantity As A Rate Per 100: Ccss.Math.Content.6.Rp.A.3c

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 200 cars in the parking lot and $50 \%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

100

120

102

120

210

Correct answer:

100

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 $50\%$ of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$50:100\rightarrow\frac{50}{100}$

Reduce.

$\frac{50}{100}\rightarrow \frac{5}{10}\rightarrow \frac{1}{2}$

We know that there are 200 cars in the parking lot. We can write the following ratio by substituting the variable Red for the number of red cars:

$Red:200\rightarrow \frac{Red}{200}$

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

$\frac{1}{2}=\frac{Red}{200}$

Cross multiply and solve for Red .

$2 \times Red=1\times200$

Simplify.

2 Red=200

Divide both sides of the equation by .

$\frac{2Red}{2}=\frac{200}{2}$

Solve.

Red=100

There are 100 red cars in the parking lot.

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Example Question #62 : Ratios & Proportional Relationships

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are 300 cars in the parking lot and $30 \%$ of them are red. How many red cars are in the parking lot?

Possible Answers:

Correct answer:

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 $30\%$ of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$30:100\rightarrow\frac{30}{100}$

Reduce.

$\frac{30}{100}\rightarrow \frac{3}{10}$

We know that there are 300 cars in the parking lot. We can write the following ratio by substituting the variable Red for the number of red cars:

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

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

$\frac{3}{10}=\frac{Red}{300}$

Cross multiply and solve for Red .

$10 \times Red=3\times300$

Simplify.

10 Red=900

Divide both sides of the equation by .

$\frac{10Red}{10}=\frac{900}{10}$

Solve.

Red=90

There are red cars in the parking lot.

Report an Error

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All ISEE Middle Level Quantitative Resources

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ISEE Middle Level Quantitative : ISEE Middle Level (grades 7-8) Quantitative Reasoning

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

All ISEE Middle Level Quantitative Resources

Example Questions

Example Question #235 : Numbers And Operations

Example Question #16 : Percentage

Example Question #61 : Ratios & Proportional Relationships

Example Question #1 : Find A Percent Of A Quantity As A Rate Per 100: Ccss.Math.Content.6.Rp.A.3c

Example Question #3 : Find A Percent Of A Quantity As A Rate Per 100: Ccss.Math.Content.6.Rp.A.3c

Example Question #4 : Find A Percent Of A Quantity As A Rate Per 100: Ccss.Math.Content.6.Rp.A.3c

Example Question #61 : Grade 6

Example Question #6 : Find A Percent Of A Quantity As A Rate Per 100: Ccss.Math.Content.6.Rp.A.3c

Example Question #7 : Find A Percent Of A Quantity As A Rate Per 100: Ccss.Math.Content.6.Rp.A.3c

Example Question #62 : Ratios & Proportional Relationships

All ISEE Middle Level Quantitative Resources

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