ISEE Middle Level Quantitative : Percentage

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

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Example Questions

Example Question #1 : Percentage

Using the information given in each question, compare the quantity in Column A to the quantity in Column B.

Column A                       Column B

120% of 80% of 100       130% of 70% of 105

Possible Answers:

The quantity in Column A is greater.

The quantity in Column B is greater.

The relationship cannot be determined from the information given.

The two quantities are equal.

Correct answer:

The quantity in Column A is greater.

Explanation:

Remember that "percent" means "per 100" and "of" means to multiply.

So 120% of 80% of 100 =

\(\displaystyle 1.2 (.8)(100)=96\)

and 130% of 70% of 105 =

\(\displaystyle 1.3(.7)(105)=(.91)105=95.55\)

Column A is greater.

Example Question #2 : Percentage

Which is the greater quantity?

(a) \(\displaystyle \frac{1}{2} \% \textrm{ of }1,000\)

(b) \(\displaystyle 0.5\)

Possible Answers:

(a) is greater

(b) is greater

It is impossible to tell from the information given

(a) and (b) are equal

Correct answer:

(a) is greater

Explanation:

\(\displaystyle \frac{1}{2} \% \textrm{ of }1,000\) can be rewritten as \(\displaystyle 0.5 \% \textrm{ of }1,000\), and restated as \(\displaystyle 0.005 \times 1,000\)

\(\displaystyle 0.005 \times 1,000 = 5 > 0.5\)

Example Question #3 : Percentage

What is 60% of 60% of 25,000?

Possible Answers:

\(\displaystyle 9,000\)

\(\displaystyle 15,000\)

\(\displaystyle 8,000\)

\(\displaystyle 6,000\)

\(\displaystyle 12,000\)

Correct answer:

\(\displaystyle 9,000\)

Explanation:

60% of 25,000 is equal to \(\displaystyle 0.60 \times 25,000 = 15,000\)

60% of that is \(\displaystyle 0.60 \times 15,000 = 9,000\)

Example Question #885 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

\(\displaystyle N\) is a positive number. Which of the following is the greater quantity?

(A) 50% of \(\displaystyle N\)

(B) 20% of  \(\displaystyle 3N\)

Possible Answers:

(A) is greater

(B) is greater

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

(A) and (B) are equal

Correct answer:

(B) is greater

Explanation:

50% of \(\displaystyle N\) is equal to \(\displaystyle 0.5N\).

20% of \(\displaystyle 3N\) is equal to \(\displaystyle 0.2 \cdot 3N = 0.6 N\)

Since \(\displaystyle N\) is positive and \(\displaystyle 0.5 < 0.6\)

\(\displaystyle 0.5N < 0.6N\),

and (B) is greater.

 

Example Question #4 : Percentage

What is 42 percent of 5?

Possible Answers:

\(\displaystyle 21\)

\(\displaystyle .42\)

\(\displaystyle 4.2\)

\(\displaystyle 2.1\)

Correct answer:

\(\displaystyle 2.1\)

Explanation:

The easiest way to find 42 percent of 5 is to first find 42 percent of 10. 

42 percent of 10 can be calculated by multiplying .42 by 10. This results in 4.2. 

Given that 5 is half of 10, it follows that 42 percent of 5 is equal to half of 4.2. 

Half of 4.2 is equal to 2.1, which is the correct answer. 

Example Question #886 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Katie collects trading cards. 15% of her collection are rare cards. If there are a total of 500 cards in Katie's collection, how many of them are rare?

Possible Answers:

\(\displaystyle 150\)

\(\displaystyle 75\)

\(\displaystyle 15\)

\(\displaystyle 50\)

\(\displaystyle 125\)

Correct answer:

\(\displaystyle 75\)

Explanation:

To begin, you can set up a proportion:

\(\displaystyle \frac{15}{100}=\frac{x}{500}\)

When trying to find a percent of a number, convert the percent into a decimal. To do this, divide the percent by 100.

\(\displaystyle 15 \div 100 = 0.15\)

\(\displaystyle 0.15=\frac{x}{500}\)

You then multiply 500 by 0.15. Since 500 represents 100% of Katie's cards, multiplying by 0.15 will give you how many cards equal 15% of the total.

\(\displaystyle x=500 \times 0.15 = 75\)

The result is your answer.

Example Question #5 : Percentage

What is 10% of 30% of 100?

Possible Answers:

\(\displaystyle 20\)

\(\displaystyle 30\)

\(\displaystyle 3\)

\(\displaystyle 10\)

Correct answer:

\(\displaystyle 3\)

Explanation:

This question asks you to find a percentage of a smaller part of 100. You must first figure out what the smaller part of 100 equals. Since percents are based off of 100, 30% of 100 is the number 30. You must then find 10% of this number.

To do this, multiply 30 times 10%. First, divide the percentage by 100.

\(\displaystyle 10\div100 = 0.1\)

Multiply the result times 30.

\(\displaystyle 30 \times 0.1 = 3\)

The new result is your answer.

Example Question #887 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Amir will be selling 20% of his stamp collection. If he has 60 stamps now, how many will he have after he sells some of his stamps?

Possible Answers:

\(\displaystyle 48\)

\(\displaystyle 12\)

\(\displaystyle 20\)

\(\displaystyle 40\)

Correct answer:

\(\displaystyle 48\)

Explanation:

If Amir gets rid of 20% of his cards, he will only have 80% of his cards remaining afterwards.

\(\displaystyle 100 - 20 = 80\)

Therefore, we can figure out how many cards Amir will have after selling 20% of his cards by multiplying times 80% since that will be the amount of cards he will have left, compared to the original number.

To do this, first divide the percentage by 100.

\(\displaystyle 80 \div100 = 0.8\)

Then, multiply the result of this times 60.

\(\displaystyle 60 \times 0.8 = 48\)

The result is your answer.

Example Question #6 : Percentage

What is 60% of 120?

Possible Answers:

\(\displaystyle 60\)

\(\displaystyle 72\)

\(\displaystyle 6\)

\(\displaystyle 80\)

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 #1 : Percentage

What is 75% of 25% of 48?

Possible Answers:

\(\displaystyle 7\)

\(\displaystyle 20\)

\(\displaystyle 25\)

\(\displaystyle 9\)

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.

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