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ACT Math : Whole and Part

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Example Questions

Example Question #1 : How To Find The Whole From The Part With Percentage

Ed eats 3 cookies every day. If he increases the total amount of cookies he has to begin with by 50%, it would take 21 days to finish all of his cookies. How many cookies does he have to begin with?

Possible Answers:

63 cookies

21 cookies

42 cookies

12 cookies

Correct answer:

42 cookies

Explanation:

We let T be the total amount of cookies and D be the number of days it takes to eat all of the cookies before increasing by 50%, and A be the number of days after increasing by 50%. With the information given, we can write the expressions, T=3D and 1.5T=3A. For the second equation, we know A=21. We plug in and get T=42.

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Example Question #4 : How To Find The Whole From The Part With Percentage

There are 8 blue balls in a bag. 40% of all the balls in the bag are blue. How many total balls are in the bag?

Possible Answers:

Correct answer:

Explanation:

You evaluate 8/0.4 = 20.

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Example Question #1 : How To Find The Whole From The Part With Percentage

95 is 20% of what number?

Possible Answers:

400

475

550

500

Correct answer:

475

Explanation:

multiply the part times 100 then divide by the percent.

(95 x 100) / 20 = 475

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Example Question #1 : How To Find The Whole From The Part With Percentage

If $\dpi{100} \small 80\%$ of a number is $\dpi{100} \small 240$ , what is $\dpi{100} \small 125\%$ of the number?

Possible Answers:

$\dpi{100} \small 250$

$\dpi{100} \small 375$

$\dpi{100} \small 200$

$\dpi{100} \small 325$

$\dpi{100} \small 300$

Correct answer:

$\dpi{100} \small 375$

Explanation:

Since $\dpi{100} \small 80\%$ of the number is $\dpi{100} \small 240$ , the number is $\dpi{100} \small \frac{240}{.80}$ which equals $\dpi{100} \small 300$ . Then calculate $\dpi{100} \small 125\%$ of $\dpi{100} \small 300$ :

$\dpi{100} \small 1.25\times 300=375$ .

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Example Question #1 : How To Find The Whole From The Part With Percentage

Gwen has a collection of 1,000 books. The average thickness of each book is 1.25” thick. She wants to buy enough bookshelves that all of her books will fit on it.

What is the shortest length of bookshelf she should buy, in whole feet, to fit all her books?

Possible Answers:

125 feet

110 feet

120 feet

105 feet

115 feet

Correct answer:

105 feet

Explanation:

Length of books = 1,000 books x 1.25” per book = 1,250”

Translate to feet

1” = 12’

1250” / 12 = 104.16 feet

Round up to 105 feet to be able to fit all the books.

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Example Question #2 : How To Find The Whole From The Part With Percentage

Nathan spends $20\%$ of his total homework time on Math. He spends one hour on Biology homework, which is twice the amount of time that he spends on Math. What is the total amount of time, in minutes, that Nathan spends on homework?

Possible Answers:

180

120

150

230

200

Correct answer:

150

Explanation:

If minutes of Biology () is twice as much time as that which is spent on Math (), then Math must equal 30 minutes.

60 = 2M , so M = 30 .

minutes is equivalent to $20\%$ of the total time (): 30 = 0.2t

Solve for by dividing both sides of the equation by 0.2 .

$t=150\ minutes$

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Example Question #2 : How To Find The Whole From The Part With Percentage

A bowl contains marbles that are either red or green. The probability of selecting a red marble at random from the bowl is $25\%$

Which of the following expressions represents the total number of red marbles in the bowl?

Possible Answers:

$\frac{x}{25}$

25x

50x

$\frac{2.5x}{10}$

$\frac{25x}{10}$

Correct answer:

$\frac{2.5x}{10}$

Explanation:

It’s best to start with a fraction that is a part over 100. For this problem, we are looking for a fraction that shows $\frac{25}{100}$ . If you go through the choices available, $\frac{2.5}{10}=\frac{25}{100}$ . Therefore, if you plug in any value for “X” in this fraction, you will know the total number of marbles in the bowl. Here is an example:

If there are 4 marbles in the bowl, you’d expect 1 to be red. If we use this equation, we get

$\frac{(2.5)(4)}{10}=\frac{10}{10}=1$

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ACT Math : Whole and Part

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find The Whole From The Part With Percentage

Example Question #4 : How To Find The Whole From The Part With Percentage

Example Question #1 : How To Find The Whole From The Part With Percentage

Example Question #1 : How To Find The Whole From The Part With Percentage

Example Question #1 : How To Find The Whole From The Part With Percentage

Example Question #2 : How To Find The Whole From The Part With Percentage

Example Question #2 : How To Find The Whole From The Part With Percentage

All ACT Math Resources

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