ACT Math : Arithmetic

Study concepts, example questions & explanations for ACT Math

varsity tutors app store varsity tutors android store varsity tutors ibooks store

Example Questions

Example Question #57 : Percentage

In 2014, a basketball team won \(\displaystyle 35\) games. In 2013, the team won \(\displaystyle 20\%\) fewer games than it did in 2014. How many games did the team win in 2013?

Possible Answers:

\(\displaystyle 27\)

\(\displaystyle 31\)

\(\displaystyle 28\)

\(\displaystyle 30\)

\(\displaystyle 29\)

Correct answer:

\(\displaystyle 28\)

Explanation:

If the team won \(\displaystyle 20\%\) fewer games, subtract \(\displaystyle 20\%\) of \(\displaystyle 35\) from \(\displaystyle 35\):

Step 1: Find \(\displaystyle 20\)% of \(\displaystyle 35\)

\(\displaystyle 35 \cdot 0.2 = 7\)

Step 2: Subtract from \(\displaystyle 35\)

\(\displaystyle 35-7=28\)

Example Question #6 : How To Find The Percent Of Decrease

If a new television cost \(\displaystyle \$300\) for a store to purchase and was originally on sale for \(\displaystyle \$600\), by what percentage must it be marked down in order for the store to make a \(\displaystyle 15\%\) profit?

Possible Answers:

\(\displaystyle 21.4\%\)

\(\displaystyle 73.91\%\)

\(\displaystyle 42.5\%\)

\(\displaystyle 45\%\)

\(\displaystyle 7.5\%\)

Correct answer:

\(\displaystyle 42.5\%\)

Explanation:

First, calculate the amount of profit that will need to be made to earn a \(\displaystyle 15\%\) profit. This is done by converting \(\displaystyle 15\%\) to \(\displaystyle 0.15\) and multiplying it by \(\displaystyle 300\) to get \(\displaystyle 45\). This means that the store can mark down the television to \(\displaystyle 345\) dollars. Thus, we are asking for the percent change from \(\displaystyle 600\) to \(\displaystyle 345\).  This is calculated:

\(\displaystyle \frac{345-600}{600}=-0.425\)

This means that it is a \(\displaystyle 42.5\%\) markdown.

Example Question #1 : How To Find The Percent Of Decrease

A person who was originally \(\displaystyle \small 130\) pounds lost \(\displaystyle \small 12\) pounds. By what percentage did his or her body weight decrease? Round to the nearest hundredth of a percent.

Possible Answers:

\(\displaystyle \small 10.17\%\)

\(\displaystyle \small 7.83\%\)

\(\displaystyle \small 4.83\%\)

\(\displaystyle \small 9.23\%\)

\(\displaystyle \small \small 90.77\%\)

Correct answer:

\(\displaystyle \small 9.23\%\)

Explanation:

The formula for percentage change is represented as:

\(\displaystyle \frac{\textup{end - start}}{\textup{start}}\)

Since the person has lost \(\displaystyle \small 12\) pounds, he or she will weigh \(\displaystyle \small 118\). Thus, we know that our formula could be written:

\(\displaystyle \small \frac{118-130}{130} = \frac{-12}{130}=-0.09230769230769....\)

Since we are looking for the percentage of decrease, we can represent this as a positive number. (To decrease by a positive amount is to have a negative percentage change, absolutely speaking.) Thus, our answer is \(\displaystyle \small 9.23\%\).

Example Question #1 : How To Find Percentage

Jack and Jill have saved up $3500 for a vacation to Bermuda. Package Deal A costs $2500 plus an additional 30% tax. Package Deal B costs $2400 with an additional 3/9 of the price added for airfare. Package deal C costs $3225 with an included 10% tax. Package deal D costs $1800 per person. Which package deal will save them the most money?

 

Possible Answers:

B

D

C

A

Correct answer:

B

Explanation:

Calculate the price of each Package Deal. A = $2500(1.3) = $3250, B = $2400 (1+3/9) = $3200. C = $3225, D = $3600. Remember that 1 = 9/9 for fraction addition. Package deal C’s wording is tricky, the tax is already included. Package Deal B is the best deal.

 

 

Example Question #2 : How To Find Percentage

Tim Duncan made 14 out of 16 free throws.  Tony Parker made 9 out of 10 free throws.   Danny Green made 7 out of 8 free throws.   Whose shooting percentage was the best? 

 

Possible Answers:

All three players were equally the best

Tony Parker

Tim and Danny were both equally the best

Tim Duncan

Danny Green

Correct answer:

Tony Parker

Explanation:

For Tim, his percentage was .875 or 87.5%.   For Tony, his percentage was .90 or 90%.  For Danny, his percentage was also .875 or 87.5%.  Thus Tony was the best. 

 

 

 

 

 

Example Question #151 : Arithmetic

Johnny earned 5 % commission on a car he sold for $25,000.  How much money did he make?

Possible Answers:

$2,000

$2,500

None of the answers are correct

$1,250

$1,500

Correct answer:

$1,250

Explanation:

$ sales x % Commission = $ Commission

25000 x 0.05 = 1250

Example Question #4 : Other Percentage

Joey buys a sweatshirt for $35 that was originally sold for $50.  What is the percent discount?

Possible Answers:

30 %

15 %

70 %

50 %

20 %

Correct answer:

30 %

Explanation:

Amount of discount = original price – new price

% discount = amount of discount ÷ original price

% discount = 15/50 = 0.3 or 30%    

Example Question #5 : Other Percentage

Bryan has white socks and blue socks in his drawer, in a ratio of 4 : 7. What percent of his socks are white?

Possible Answers:

57%

75%

36%

64%

30%

Correct answer:

36%

Explanation:

You divide the number of blue socks, 4, by the number of total socks, 11, giving you 36%.

Example Question #6 : Other Percentage

There are 9 marbles in a box, and 4 of them are red. 

What percentage of the marbles in the box are NOT red?

Possible Answers:

50%

44%

99%

45%

55%

Correct answer:

55%

Explanation:

There are 5 non-red marbles and 9 total marbles.

5/9 = 0.555, which is about 55%

Example Question #4 : How To Find Percentage

What number is 130% of 50?

Possible Answers:

\(\displaystyle 75\)

\(\displaystyle 90\)

\(\displaystyle 105\)

\(\displaystyle 120\)

\(\displaystyle 65\)

Correct answer:

\(\displaystyle 65\)

Explanation:

Verbal cues are "is" and "of." Is means equals and of means multiplication.

So the equation to solve becomes \(\displaystyle x = 1.30(50)\) which equals 65.

Learning Tools by Varsity Tutors