ISEE Middle Level Quantitative : Numbers and Operations

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

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Example Questions

Example Question #901 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

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:

\displaystyle \$30

\displaystyle \$50

\displaystyle \$40

\displaystyle \$48

Correct answer:

\displaystyle \$48

Explanation:

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

\displaystyle 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.

\displaystyle 60\div100 = 0.6

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

\displaystyle 80 \times 0.6 = 48

The new result is your answer.

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 \displaystyle 100 cars in the parking lot and \displaystyle 60 \% of them are red. How many red cars are in the parking lot?

Possible Answers:

\displaystyle 64

\displaystyle 60

\displaystyle 36

\displaystyle 72

\displaystyle 56

Correct answer:

\displaystyle 60

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

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

Reduce.

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

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

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

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

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

Cross multiply and solve for \displaystyle Red.

\displaystyle 5 \times Red=3\times100

Simplify.

\displaystyle 5 Red=300

Divide both sides of the equation by \displaystyle 5.

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

Solve.

\displaystyle Red=60

There are \displaystyle 60 red cars in the parking lot.

 

Example Question #2 : 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 \displaystyle 250 cars in the parking lot and \displaystyle 10 \% of them are red. How many red cars are in the parking lot?

Possible Answers:

\displaystyle 52

\displaystyle 15

\displaystyle 30

\displaystyle 25

\displaystyle 50

Correct answer:

\displaystyle 25

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

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

Reduce.

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

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

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

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

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

Cross multiply and solve for \displaystyle Red.

\displaystyle 10 \times Red=1\times 250

Simplify.

\displaystyle 10 Red=250

Divide both sides of the equation by \displaystyle 10.

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

Solve.

\displaystyle Red=25

There are \displaystyle 25 red cars in the parking lot.

Example Question #901 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

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

Possible Answers:

\displaystyle 54

\displaystyle 34

\displaystyle 45

\displaystyle 38

\displaystyle 43

Correct answer:

\displaystyle 34

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

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

Reduce.

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

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

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

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

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

Cross multiply and solve for \displaystyle Red.

\displaystyle 4 \times Red=1\times136

Simplify.

\displaystyle 4 Red=136

Divide both sides of the equation by \displaystyle 4.

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

Solve.

\displaystyle Red=34

There are \displaystyle 34 red cars in the parking lot.

Example Question #902 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

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

Possible Answers:

\displaystyle 33

\displaystyle 47

\displaystyle 52

\displaystyle 41

\displaystyle 36

Correct answer:

\displaystyle 41

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

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

Reduce.

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

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

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

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

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

Cross multiply and solve for \displaystyle Red.

\displaystyle 4 \times Red=1\times164

Simplify.

\displaystyle 4 Red=164

Divide both sides of the equation by \displaystyle 4.

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

Solve.

\displaystyle Red=41

There are \displaystyle 41 red cars in the parking lot.

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 \displaystyle 135 cars in the parking lot and \displaystyle 60 \% of them are red. How many red cars are in the parking lot?

Possible Answers:

\displaystyle 81

\displaystyle 60

\displaystyle 79

\displaystyle 72

\displaystyle 93

Correct answer:

\displaystyle 81

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

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

Reduce.

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

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

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

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

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

Cross multiply and solve for \displaystyle Red.

\displaystyle 5 \times Red=3\times135

Simplify.

\displaystyle 5 Red=405

Divide both sides of the equation by \displaystyle 5.

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

Solve.

\displaystyle Red=81

There are \displaystyle 81 red cars in the parking lot.

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 \displaystyle 400 cars in the parking lot and \displaystyle 40 \% of them are red. How many red cars are in the parking lot?

Possible Answers:

\displaystyle 160

\displaystyle 148

\displaystyle 116

\displaystyle 61

\displaystyle 164

Correct answer:

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

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

Reduce.

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

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

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

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

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

Cross multiply and solve for \displaystyle Red.

\displaystyle 5 \times Red=2\times400

Simplify.

\displaystyle 5 Red=800

Divide both sides of the equation by \displaystyle 5.

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

Solve.

\displaystyle Red=160

There are \displaystyle 160 red cars in the parking lot.

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 \displaystyle 200 cars in the parking lot and \displaystyle 50 \% of them are red. How many red cars are in the parking lot?

Possible Answers:

\displaystyle 120

\displaystyle 100

\displaystyle 102

\displaystyle 120

\displaystyle 210

Correct answer:

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

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

Reduce.

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

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

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

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

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

Cross multiply and solve for \displaystyle Red.

\displaystyle 2 \times Red=1\times200

Simplify.

\displaystyle 2 Red=200

Divide both sides of the equation by \displaystyle 2.

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

Solve.

\displaystyle Red=100

There are \displaystyle 100 red cars in the parking lot.

Example Question #8 : 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 \displaystyle 300 cars in the parking lot and \displaystyle 30 \% of them are red. How many red cars are in the parking lot?

Possible Answers:

\displaystyle 99

\displaystyle 74

\displaystyle 72

\displaystyle 81

\displaystyle 90

Correct answer:

\displaystyle 90

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

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

Reduce.

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

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

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

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

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

Cross multiply and solve for \displaystyle Red.

\displaystyle 10 \times Red=3\times300

Simplify.

\displaystyle 10 Red=900

Divide both sides of the equation by \displaystyle 10.

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

Solve.

\displaystyle Red=90

There are \displaystyle 90 red cars in the parking lot.

Example Question #62 : 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 \displaystyle 400 cars in the parking lot and \displaystyle 4 \% of them are red. How many red cars are in the parking lot?

Possible Answers:

\displaystyle 8

\displaystyle 16

\displaystyle 24

\displaystyle 36

\displaystyle 18

Correct answer:

\displaystyle 16

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 \displaystyle 4\% of the cars are red. In other words, for every hundred cars \displaystyle 4 of them are red. We can write the following ratio:

\displaystyle 4:100\rightarrow\frac{4}{100}

Reduce.

\displaystyle \frac{4}{100}\rightarrow \frac{2}{50}\rightarrow \frac{1}{25}

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

\displaystyle Red:40\rightarrow \frac{Red}{400}

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

\displaystyle \frac{1}{25}=\frac{Red}{400}

Cross multiply and solve for \displaystyle Red.

\displaystyle 25 \times Red=1\times400

Simplify.

\displaystyle 25 Red=400

Divide both sides of the equation by \displaystyle 25.

\displaystyle \frac{25Red}{25}=\frac{400}{25}

Solve.

\displaystyle Red=16

There are \displaystyle 16 red cars in the parking lot.

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