HSPT Math : Problem Solving
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Example Questions
Example Question #31 : How To Work With Percentages
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?
No; she does not have the signatures of enough seniors
No; she does not have the signatures of enough sophomores
Yes
No; she does not have the signatures of enough juniors
No; she does not have the signatures of enough sophomores
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 #101 : Hspt Mathematics
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?
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 
At minimum, Rhonda won 324 votes.
Example Question #31 : Percentages
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)
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%.
Example Question #101 : Arithmetic
To get on the ballot for senior class president, a student must have the signatures of 15% of the senior class. Out of 341 seniors, 52 have signed Clinton's petition. How many more signatures does Clinton need to get on the ballot?
Clinton has enough signatures to get on the ballot.
Clinton has enough signatures to get on the ballot.
15 % of the 341 members of the senior class is
Since Clinton has 52, he has enough signatures.
Example Question #101 : Hspt Mathematics
Bill decides to donate 15% of his $4000 and Ted decides to donate 25% of his $8000. What percentage of their combined fortunes do Bill and Ted donate?
21.7%
19.2%
22.3%
23.1%
20%
21.7%
This is a simple problem, so long as you don't forget that Bill and Ted have different amounts of money, so you can't simply average 15% and 25% to get 20%.
Calculate how much each donates:
4000(.15)= 600
8000(.25)= 2000
Now divide the total donation by their total wealth:
Now multiply this answer by 100, and then round to the nearest tenth to get 21.7%.
Example Question #43 : How To Work With Percentages
If you have a garden in which you planted 120 seeds, what percentage sprouted if you have 90 plants?
To find the percent you must put the part over the whole,
Whole is represented by the number of seeds planted and the part represents the number of plants in the garden.
Substitute the values into the percent formula
Now multiply by 100 to make it a percent which is 
Example Question #102 : Arithmetic
What percent of 96 is 24?
Translate the sentence into an equation
Isolate 
Remember that the question is asking for a percentage, so convert 
Example Question #1 : Algebra
Solve for 
Example Question #1 : How To Solve One Step Equations
In a math contest, the team from Lincoln High comprised five students - Melanie, Ned, Olivia, Phyllis, and Quinn. Melanie outscored Ned by 12 points; Ned outscored Quinn by 19 points; Phyllis outscored Ned by 45 points and Olivia by 20 points. Who came in third among the five?
Olivia
Ned
Phyllis
Quinn
Melanie
Melanie
Since this reasoning is valid regardless of the actual scores, suppose Quinn scored 100. Then Ned scored 19 more than Quinn, or 119, and Melanie scored 12 more than Ned, or 131. Phyllis scored 45 more than Ned, or 164, and Olivia scored 20 points fewer than Phyllis, or 144. This makes the order, from greatest to least:
Phyllis, Olivia, Melanie, Ned, Quinn
Melanie scored third among the five.
Example Question #1 : How To Solve One Step Equations
Jasmine is participating in a swimming race. If the race is 3000 yards, what percentage of the race has she completed at the 2400 yardline?
Divide 
Answer: Jasmine has completed 80% of the race.
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