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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

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find A Proportion

What is the value of x in $\frac{x+4}{x}=\frac{4}{12}?$

Possible Answers:

Correct answer:

Explanation:

Since this is a proportion, you can cross-multiply. Once you do that, the left side is 4x. Your right side is 12x+48 . Set those equal to each other. Then, combine like terms. Subtract 12x from both sides so that the equation is now -8x=48 . Divide both sides by -8. Your answer is -6.

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Example Question #1 : How To Find A Proportion

Michelle is having a party, and she is experimenting with different mixtures of soda, trying to come up with something original. In particular, she likes a drink she made when she mixed together three ounces of cola and five ounces of grape soda. She has two and a half liters of cola and wants to use it all to make some of this drink; how much grape soda does she need to mix it with?

Possible Answers:

$4 \frac{1}{6} \textrm{ L}$

$3 \frac{1}{6} \textrm{ L}$

$6 \textrm{ L}$

None of the other responses gives the correct answer.

$1\frac{1}{2} \textrm{ L}$

Correct answer:

$4 \frac{1}{6} \textrm{ L}$

Explanation:

The ratio of ounces of cola to ounces of grape soda in the initial mixture can be expressed as $\frac{3}{5}$ . It must be equal to that of liters of cola to liters of grape soda in the mixture Michelle will make for the party, which, since the number of liters of grape soda is unknown, is $\frac{2\frac{1}{2}}{N}$ . Set these equal and solve for :

$\frac{2\frac{1}{2}}{N} = \frac{3}{5}$

Set the cross-products equal to each other:

$3 N = 2\frac{1}{2} \cdot 5$

$3 N = \frac{5}{2} \cdot 5$

$3 N = \frac{25}{2}$

$\frac{1}{3} \cdot 3 N =\frac{1}{3} \cdot \frac{25}{2}$

$N = \frac{25}{6} = 4 \frac{1}{6}$

Michelle will use $4 \frac{1}{6}$ liters of grape soda in the final mixture.

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Example Question #7 : How To Find A Proportion

Robert, Jeff, and Paul are sharing a bag of chips that contains 20 chips. The three of them eat all of the chips. If Robert has eaten 8 chips, and Jeff eats twice as many chips as Paul, how many chips has Jeff eaten?

Possible Answers:

Correct answer:

Explanation:

What do we know? We know that there are 20 chips in the bag, and we know that Robert has eaten 8 of them. Thus, we can calculate that there are 20-8=12 chips remaining. Of this remaining, Jeff has eaten 2 parts and Paul has eaten 1 part: that's 3 parts, so let's calculate how many chips constitute each part:

$\frac{12}{3}=4$

So, each part is equal to 4 chips.

Jeff has eaten 2 parts, so 2*4=8 gives us our answer.

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Example Question #5 : How To Find A Proportion

If one cupcake costs 75 cents, how much does a dozen cupcakes cost?

Possible Answers:

$\$7.00$

$\$10.00$

$\$ 9.00$

$\$8.00$

Correct answer:

$\$ 9.00$

Explanation:

You can solve this problem using a proportion.

$\frac{1}{0.75}=\frac{12}{x}$

To solve for x, cross multiply.

$1\times x=12\times.75$

x=9.00

9 dollars

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Example Question #6 : How To Find A Proportion

If you can purchase two pairs of jeans for 50 dollars, how many pairs of jeans can you purchase with 200 dollars?

Possible Answers:

Correct answer:

Explanation:

You can use a proportion to solve this problem.

$\frac{2}{50}=\frac{x}{200}$

Cross multiply to solve for x.

$50\times x=200\times2$

50x =400

$400\div50 = 8$

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Example Question #141 : Ratio And Proportion

Phil earns $\$10.00$ for each hour he works. For every hour he works, he then gives $\$2.00$ to his sister Lola. How much money will Lola have if Phil works 13.5 hours?

Possible Answers:

$\$67.50$

$\$23.50$

$\$135.00$

$\$27.00$

$\$15.50$

Correct answer:

$\$27.00$

Explanation:

To Solve:

Multiply the $\$2.00$ Lola receives by the 13.5 hours Phil worked:

$\small $2.00 \cdot 13.5=27$

Phil will give Lola $\$27.00$ if he works 13.5 hours.

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Example Question #31 : Ratio And Proportion

If the ratio of boys to girls in a classroom is 11:12 , and there are a total of of students in the classroom, how many boys are in the classroom?

Possible Answers:

Correct answer:

Explanation:

If the ratio of boys to girls in a classroom is 11:12 , that means that there are boys for every girls. Thus, when there are students in a classroom, the breakdown will be boys and girls. If there are students in a classroom, the breakdown will be boys and girls, which translates to a ratio of 22:24 , or 11:12 .

Thus, if there are students, will be boys.

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Example Question #32 : Ratio And Proportion

You survey 500 students about the plans for a new practice court for the basketball team and they must give a yes or no answer. 490 students are against the use of funds on this project. What proportion of students said that they agreed with the plan?

Possible Answers:

0.98

0.05

0.5

0.025

0.02

Correct answer:

0.02

Explanation:

If 490 disagreed with the plan, that means the rest agreed.

So to find that value, you must do the total minus the no's

500-490=10 .

To find the proportion you must divide the part by the whole giving us an answer of 0.02

10/500=0.02 .

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Example Question #33 : Ratio And Proportion

If Mike gets two times the amount of work done than Joe, what is a ratio representing the work that each get done?

Possible Answers:

1:3

5:2

6:5

1:1

2:1

Correct answer:

2:1

Explanation:

Since Mike does twice the work that Joe does, his part of the ratio must be double the value of Joe's. The only ratio given that has that is 2:1 .

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Example Question #34 : Numbers And Operations

Which statement does not follow from the statement $\frac{A}{9} = \frac{B }{11}$ ?

Possible Answers:

$\frac{A}{11} = \frac{B }{9}$

$\frac {9}{A}= \frac{11}{B }$

$\frac{A}{B} = \frac{9} {11}$

$\frac{9} {A}= \frac{11}{B }$

Correct answer:

$\frac{A}{11} = \frac{B }{9}$

Explanation:

If $\frac{A}{9} = \frac{B }{11}$ , then:

The ratio of the numerators is equivalent to that of the denominators, in the same order. Hence,

$\frac{A}{B} = \frac{9} {11}$ and $\frac{9} {A}= \frac{11}{B }$ are true.

The reciprocals of the ratios are equivalent, so

$\frac {9}{A}= \frac{11}{B }$

However, it does not hold that

$\frac{A}{11} = \frac{B }{9}$ .

This can be seen as follows:

$\frac{A}{9} = \frac{B }{11}$

$\frac{A}{9} \cdot \frac{9}{11}= \frac{B }{11}\cdot \frac{9}{11}$

$\frac{A}{11}= \frac{9B }{121} \ne \frac{B}{9}$ .

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Numbers and Operations

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #1 : How To Find A Proportion

Example Question #1 : How To Find A Proportion

Example Question #7 : How To Find A Proportion

Example Question #5 : How To Find A Proportion

Example Question #6 : How To Find A Proportion

Example Question #141 : Ratio And Proportion

Example Question #31 : Ratio And Proportion

Example Question #32 : Ratio And Proportion

Example Question #33 : Ratio And Proportion

Example Question #34 : Numbers And Operations

All ISEE Middle Level Math Resources

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