HSPT Math : How to work with percentages

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #21 : How To Find The Solution To An Equation

A class has 25 students. If 60% of them are boys, how many students are girls?

Possible Answers:

9

8

20

15

10

Correct answer:

10

Explanation:

We know that 40% of the class are girls because 60% are boys. To express 40% as a fraction of the 25 total students, we set up a proportion to find the number of girls in the class. 

When solving for , we find that there are 10 girls in the class. 

Example Question #31 : How To Work With Percentages

Fifteen percent of the students in the classroom brought their lunch from home. If 9 students brought their lunch from home, how many students are in the classroom total?

Possible Answers:

135

60

6

50

Correct answer:

60

Explanation:

You can think of the total number of students in the classroom as an unknown variable, .

You can set up an equation that includes  and the information given. Normally in a percent problem, you would start with the total amount of something and multiply it by the percent to get the part of that total amount. You can set this up the same way, but the total amount is the missing information:

Total Amount x Percent = Part of Total Amount

  

You use  to numerically represent 15 percent. 

Now you can algebraically solve for , which will give you the total number of students in the class. You do this by dividing each side by .

Therefore there are 60 total students.

Example Question #2 : How To Solve Arithmetic Word Problems

Candidate A gets  of the votes in an election.

Candidate B gets 35% of the votes.

If 2.8 million people votes, how many more votes than Candidate A did Candidate B receive?

Possible Answers:

Correct answer:

Explanation:

First we need to get  and 35% in the same terms so that we can subtract one from the other. Since 7ths are repeating decimals, it will be easiest to use fractions.

.

Now we multiply this fraction by 2.8 million, which reduces nicely to , which equals 180,000.

Example Question #1 : Coordinate Geometry

In a poll, Camille learned that  of her classmates spoke English at home,  spoke Spanish, and  spoke other languages. If she were to graph this data on a pie chart, what would be the degree measurement for the part representing students who speak Spanish at home?

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, you must first solve for what percentage of the entire group comprise of Spanish-speaking students. To do this, divide the total amount of Spanish-speaking students by the total number of students.

Multiply this number by 100 and round up in order to get your percentage.

Then, multiply this number times the total degrees in a circle to find out the measurement of the piece representing Spanish-speaking students on the pie chart.

Round up:

Example Question #31 : How To Work With Percentages

What is  as a fraction?

Possible Answers:

Correct answer:

Explanation:

The meaning of a percent is the number over 100 parts.

Example Question #42 : Percentage

If  out of  students have contact lenses, what percentage of students have contact lenses?

Possible Answers:

 percent

 percent

 percent

 percent

 percent

Correct answer:

 percent

Explanation:

When dividing  by , the reduced form is:

 is the equivalent of  percent, which is therefore the correct answer.

Example Question #43 : Percentage

A class with  students went on a field trip, but one of the students was absent.  What percentage of students in the class went on the field trip?

Possible Answers:

Correct answer:

Explanation:

The percentage of students who attended the field trip can be found by dividing the number present by the total number of students.  Here this is  divided by .  You then multiply by  to get the percentage.

Example Question #101 : Problem Solving

To get on the ballot for Student Body President, Annie needs the signatures of 5% of the sophomores, 5% of the juniors, and 5% of the seniors. 

Annie currently has a petition with the signatures of 22 seniors out of a total of 412, 23 juniors out of a total of 436, and 26 sophomores out of a total of 536. Does Annie have the signatures she needs to get on the ballot?

Possible Answers:

No; she does not have the signatures of enough sophomores

No; she does not have the signatures of enough seniors

Yes

No; she does not have the signatures of enough juniors

Correct answer:

No; she does not have the signatures of enough sophomores

Explanation:

Annie needs the signatures of 5% of the 412 seniors; this is

,

which means she needs the signatures of at least 21 seniors. She has 22.

She needs the signatures of 5% of the 436 juniors; this is

,

which means she needs the signatures of at least 22 juniors. She has 23.

She needs the signatures of 5% of the 536 sophomores; this is

.

which means she needs the signatures of at least 27 sophomores. She has 26.

She has enough signatures from seniors and juniors, but not sophomores.

Example Question #34 : Percentages

Four students ran for student body president - Carolyn, Dick, Mike, and Rhonda.

According to the rules, a candidate must win at least 60% of the vote in order to claim an outright victory; otherwise, a runoff must be held between the top two vote-getters. It is known that Carolyn, Dick, and Mike won 87 votes, 56 votes, and 73 votes. It is also known that Rhonda won the election outright. How many votes did Rhonda win at the very least?

Possible Answers:

Correct answer:

Explanation:

At the very least, Rhonda won 60% of the votes cast, so the total number of votes won by her opponents can be at most 40% of the votes cast. Suppose this is the case. If we let be the number of votes Rhonda won, then we can set up the ratio

At minimum, Rhonda won 324 votes.

Example Question #101 : Hspt Mathematics

Four students ran for student body president - Benjy, Carla, Hy, and Lisa.

According to the rules, a candidate must win more than 50% of the vote in order to claim an outright victory; otherwise, a runoff must be held between the top two vote-getters.

It is known that Benjy got 56 votes, Carla got 72 votes, and Lisa got 66 votes. It is also known that a runoff must be held between Carla and Lisa. What is the greatest possible percent of the vote that Hy could have gotten?

(Nearest whole percent)

Possible Answers:

Correct answer:

Explanation:

Carla and Lisa won the highest and second-highest number of votes, respectively, so Hy must  have won fewer votes than Lisa. He won at most 65 votes. This would have been

The closest answer is 25%.

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