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ISEE Middle Level Math : Numbers and Operations

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

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All ISEE Middle Level Math Resources

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Example Questions

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Example Question #1 : Numbers And Operations

What is the least common multiple of 5, 12, and 15?

Possible Answers:

$\dpi{100} 60$

$\dpi{100} 100$

$\dpi{100} 120$

$\dpi{100} 24$

Correct answer:

$\dpi{100} 60$

Explanation:

You can write out the multiples of each number, and find the first number that is common to all of them.

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

12: 12, 24, 36, 48, 60

15: 15, 30, 45, 60

The correct answer is 60.

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Example Question #1 : Ratio And Proportion

What is the greatest common factor of 12, 24 and 96?

Possible Answers:

$\dpi{100} 3$

$\dpi{100} 4$

$\dpi{100} 6$

$\dpi{100} 12$

Correct answer:

$\dpi{100} 12$

Explanation:

To find the greatest common factor of three numbers, first factor each number as a product of prime numbers:

$\dpi{100} 96: 2\times 2\times 2\times 2\times 2\times 3$

$\dpi{100} 24: 2\times 2\times 2\times 3$

$\dpi{100} 12: 2\times 2\times 3$

Now take all of the factors that are in common between 12, 24 and 96. In this case, that is 2, 2 and 3.

$\dpi{100} 2\times 2\times 3=12$

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Example Question #1 : How To Find A Ratio

Logan needs to answer 60 questions to finish his test. If he has answered 25% of the questions in 20 minutes, how long will it take him to complete the entire test?

Possible Answers:

$60\ minutes$

$120\ minutes$

$90\ minutes$

$80\ minutes$

$40\ minutes$

Correct answer:

$80\ minutes$

Explanation:

To solve:

First, find the number of answers completed by calculating:

$\small 60\cdot 0.25=15$

Then, find how long it would take him to complete the 60 question test if for every 20 minutes he answer 15 questions:

$\small 60 \div 15=4$ (sets of 15 questions)

$\small \small \small 4\cdot 20 =80$ minutes altogether to finish the test.

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Example Question #1 : How To Find A Ratio

Which ratio is equivalent to $13 \frac{1}{2} : 1 \frac{1}{2}$ ?

Possible Answers:

7:1

25:3

9:1

8:1

17:2

Correct answer:

9:1

Explanation:

A ratio can be rewritten as a quotient; do this, and simplify it.

$13 \frac{1}{2} : 1 \frac{1}{2}$

Rewrite as

$13 \frac{1}{2} \div 1 \frac{1}{2} = \frac{27}{2} \div \frac{3}{2} = \frac{27}{2} \cdot \frac{2}{3} = \frac{9}{1} \cdot \frac{1}{1} = \frac{9}{1}$

or 9:1

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Example Question #1 : How To Find A Ratio

I have 5 white chocolates, 3 milk chocolates, and 9 dark chocolates. What is the ratio of white chocolates to the other types of chocolates?

Possible Answers:

5:3

5:11

12:5

5:9

5:12

Correct answer:

5:12

Explanation:

There are 5 white chocolates. There are a total of 12 milk and dark chocolates. The ratio of white to other chocolates is 5:12.

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Example Question #1 : How To Find A Ratio

In February, there were 12 rainy days, 6 cloudy days and 10 sunny days. What was the ratio of sunny days in February?

Possible Answers: