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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Example Questions

Example Question #1 : Percentage

What is 60% of 120?

Possible Answers:

\(\displaystyle 80\)

\(\displaystyle 60\)

\(\displaystyle 6\)

\(\displaystyle 72\)

Correct answer:

\(\displaystyle 72\)

Explanation:

In order to figure out what 60% of 120 is, multiply 60% by 120. To do this, first divide your percentage by 100.

\(\displaystyle 60 \div 100 = 0.6\)

Then, multiply the result times 120.

\(\displaystyle 120 \times0.6 = 72\)

The new result is your answer.

Example Question #231 : Numbers And Operations

What is 75% of 25% of 48?

Possible Answers:

\(\displaystyle 7\)

\(\displaystyle 25\)

\(\displaystyle 20\)

\(\displaystyle 9\)

Correct answer:

\(\displaystyle 9\)

Explanation:

The question asks you to find 75% of a smaller part of 48. In order to figure this out, you must first figure out what the value of the smaller part is. To figure out what 25% of 48 is, multiply 48 by 25%. First, divide the percentage by 100.

\(\displaystyle 25\div100 =0.25\)

Then, multiply 48 by the result.

\(\displaystyle 48 \times0.25 = 12\)

The second part of the question asks you to figure out what 75% of this new number is. Just like before, first divide the percentage by 100.

\(\displaystyle 75\div100=0.75\)

Then, multiply the result times 12.

\(\displaystyle 12 \times0.75 = 9\)

The result is the answer.

Example Question #232 : Numbers And Operations

What is 50% more than 15% of 40?

Possible Answers:

\(\displaystyle 9\)

\(\displaystyle 15\)

\(\displaystyle 30\)

\(\displaystyle 35\)

Correct answer:

\(\displaystyle 9\)

Explanation:

The question asks you to figure out what 50% more than a smaller part of 40 is. To do this, you must first solve what 15% of 40 is. First, divide the percentage by 100.

\(\displaystyle 15\div100=0.15\)

Then, multiply the result times 40.

\(\displaystyle 40 \times0.15 = 6\)

You then must figure out what 50% more than this new number is. 50% more is equal to 150% of the original value. Just like before, divide this percentage by 100.

\(\displaystyle 150\div100 = 1.5\)

Then, multiply the result times 6.

\(\displaystyle 6\times1.5 = 9\)

This result is your answer.

Example Question #233 : Numbers And Operations

What is 20% more than half of 40?

Possible Answers:

\(\displaystyle 20\)

\(\displaystyle 24\)

\(\displaystyle 8\)

\(\displaystyle 30\)

Correct answer:

\(\displaystyle 24\)

Explanation:

The question asks you to figure out what 20% more than a smaller amount of 40 is. To do this, you must first solve for the smaller amount. So, first divide 40 by 2 since it asks for half of 40.

\(\displaystyle 40\div2=20\)

Since 20% than a number is equal to 120% of the original value of that number, multiply 20 by 120%. To do this, first divide the percentage by 100.

\(\displaystyle 120 \div100 = 1.2\)

Then, multiply the result times 20.

\(\displaystyle 20 \times 1.2 = 24\)

This result is your answer.

 

Example Question #891 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

What is 300% of 12?

Possible Answers:

\(\displaystyle 300\)

\(\displaystyle 360\)

\(\displaystyle 36\)

\(\displaystyle 3600\)

Correct answer:

\(\displaystyle 36\)

Explanation:

To figure out what a percentage of a particular number is, first divide that percentage by 100.

\(\displaystyle 300 \div 100 = 3\)

Then, multiply the result times the original number.

\(\displaystyle 12 \times 3 = 36\)

This result is your answer.

Example Question #235 : Numbers And Operations

A clothing store discounted a shirt by 25% one week. The following week, they discounted that new price by another 20% What is currently the price of the shirt if it originally cost $20?

Possible Answers:

\(\displaystyle \$9\)

\(\displaystyle \$10\)

\(\displaystyle \$12\)

\(\displaystyle \$15\)

Correct answer:

\(\displaystyle \$12\)

Explanation:

If the clothing store discounts an already discounted price, it means that we are trying to find a percentage of an already smaller part of the original number. First, if the original discount was 25%, that means that the shirt was sold for 75% the original price the first week.

\(\displaystyle 100 - 25 = 75\)

So, we must first figure out what the shirt was worth at 75% the original price. To do this, divide the percentage by 100.

\(\displaystyle 75 \div100=0.75\)

Multiply the result times the original price of the shirt.

\(\displaystyle 20 \times0.75 = 15\)

This is the price of the shirt after the first discount. This new price is then discounted by another 20%. So, the newest price will be 80% of the value of the first discount.

\(\displaystyle 100 - 20 = 80\)

To find out what the price is after this is done, multiply the percentage by the new price. So, first divide the percentage by 100.

\(\displaystyle 80\div100=0.8\)

Multiply this result by the discounted price.

\(\displaystyle 15 \times 0.8 = 12\)

The result is your answer.

Example Question #892 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Jamal, Sophia, Jake, and Eric went to a restaurant for a special occasion. Their bill totalled $96.22. If they left an 18% tip, how much was the tip?

Possible Answers:

\(\displaystyle \$20.21\)

\(\displaystyle \$18.25\)

\(\displaystyle \$19.24\)

\(\displaystyle \$17.32\)

Correct answer:

\(\displaystyle \$17.32\)

Explanation:

To figure out what 18% of any number is, first divide the percentage by 100.

\(\displaystyle 18\div100 = 0.18\)

Then, multiply this result times the original number.

\(\displaystyle 96.22 \times 0.18 = 17.32\)

The result is your answer.

Example Question #13 : Percentage

Jamal, Sophia, Jake, and Eric went to a restaurant for a special occasion. Their bill totalled $96.22. If they left an 18% tip, how much did they pay in all (tip included)?

Possible Answers:

\(\displaystyle \$114.47\)

\(\displaystyle \$115.46\)

\(\displaystyle \$116.43\)

\(\displaystyle \$113.54\)

Correct answer:

\(\displaystyle \$113.54\)

Explanation:

To figure out what 18% of any number is, first divide the percentage by 100.

\(\displaystyle 18\div100 = 0.18\)

Then, multiply this result times the original number.

\(\displaystyle 96.22 \times 0.18 = 17.32\)

The result is the tip. To figure out the total amount paid, add the tip to the original price of the bill.

\(\displaystyle 96.22 +17.32 = 113.54\)

Example Question #238 : Numbers And Operations

\(\displaystyle A\) and \(\displaystyle B\) are positive integers; \(\displaystyle A < B\). Which is the greater quantity?

(a) \(\displaystyle A \%\) of \(\displaystyle 4B\)

(b) \(\displaystyle B \%\) of \(\displaystyle 4A\)

Possible Answers:

(a) and (b) are equal

(a) is the greater quantity

(b) is the greater quantity

It is impossible to determine which is greater from the information given

Correct answer:

(a) and (b) are equal

Explanation:

\(\displaystyle A \%\) of \(\displaystyle 4B\) is equal to 

\(\displaystyle 4B \cdot \frac{A}{100} = \frac{4AB}{100}\)

 

\(\displaystyle B \%\) of \(\displaystyle 4A\) is equal to 

\(\displaystyle 4A \cdot \frac{B}{100} = \frac{4AB}{100}\)

 

The two are equal regardless of the value or relation of \(\displaystyle A\) and \(\displaystyle B\).

Example Question #239 : Numbers And Operations

\(\displaystyle A\) and \(\displaystyle B\) are positive integers; \(\displaystyle A < B\). Which is the greater quantity?

(a) \(\displaystyle \frac{1}{2} \%\) of \(\displaystyle A\)

(b) 0.5 % of \(\displaystyle B\)

Possible Answers:

(a) and (b) are equal

(a) is the greater quantity

It is impossible to determine which is greater from the information given

(b) is the greater quantity

Correct answer:

(b) is the greater quantity

Explanation:

\(\displaystyle 0.5 = \frac{5}{10} = \frac{5 \div 5}{10 \div 5 } = \frac{1}{2}\), so 0.5% of a number is the same as \(\displaystyle \frac{1}{2} \%\) of the number. Therefore, in each choice, we are taking the same percent of a number. Since \(\displaystyle A < B\), 0.5%, or \(\displaystyle \frac{1}{2} \%\), of \(\displaystyle A\) is less than 0.5% of \(\displaystyle B\).

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