PSAT Math : PSAT Mathematics
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Example Questions
Example Question #1 : How To Find Percentage From A Fraction
What is 
Convert the improper fraction 
Example Question #2 : How To Find Percentage From A Fraction
A family with 6 children, aged 4, 4, 5, 7, 12, and 13 are moving to a new home. They all want the same bedroom, so the parents have a lottery. Each child places their name in once for every year of age (the four year olds each put their name in 4 times, the seven year old puts his name in 7 times, etc.) What is the probability of the chosen child being 4 years old?
It is most likely that the chosen child will be the oldest child.
None of the available answers
First, we will determine the total number of ballots:
Since there are two four year olds, and this question is asking the probability of the chosen child being four, the probability is:
Example Question #3 : How To Find Percentage From A Fraction
Three hens each lay 20 eggs for a farmer. Two-fifths of the first hen's eggs are brown. One-fourth of the second hen's eggs are brown. Seven-tenths of the third hen's eggs are white. What percentage of all the eggs are brown?
The first hen lays 8 brown eggs: 2/5 * 20 = 8
The second lays 5 brown eggs: 1/4 * 20 = 5
The third lays 6 brown eggs: 3/10 * 20 = 6
Add up the brown eggs and divide by 60, the total number of eggs:
19/60 = 0.31666667 = 31.67%, or 32%.
Example Question #71 : Percentage
There is a sale in a store and every item is discounted 23%. If a shirt is normally $18.59, what is the price of it after the discount?
We can right 23% as a fraction and set that equal to 
From here we cross multiply and divide.
We round this number to $4.28. This is the amount of discoount we need to apply to the original price. To do this we subtract 4.28 from 18.59.
Example Question #3 : Fractions And Percentage
Louisa and Caroline are trying to save up to start a small business together. Louisa has saved 
45%
56%
18%
78%
64%
78%
The goal of this problem is to solve for how much Louisa and Caroline have saved, together, towards their goal money for starting a small business. In order to do that, you must add what Louisa has saved to what Caroline has saved, then convert the fraction into a percentage.
Add Louisa and Caroline:
Find the lowest common multiple for the denominator:
Add:
Simplify:
To convert a fraction into a percentage, simply multiply the numerator by 100 and divide by the denominator. There are other methods, but this is the easiest.
Equals
78% is your answer.
Example Question #2024 : Psat Mathematics
Refer to the above bar graph.
What percent of the students achieved a score 500 or below?
6 students achieved a score of 201-300; 18 achieved a score of 301-400; 30 achieved a score of 401-500. Add these:
The number of students who took the test is the sum of the students who finished in the six ranges:
The question is now to find out what percent 54 is of 120, which can be calculated as follows:
Example Question #1 : How To Find The Whole From The Part With Percentage
David's trip expenses are pictured in the above pie chart (numbers = % of his total expenses). If he spent $75 on taxis, how much did he spend on hotel and souvenirs combined?
$200
$250
$225
$40
$175
$200
David spent $75 on taxis, which were 15% of his total expenses on the trip. He therefore spent 75(100/15) = $500 on the trip altogether. The hotel and souvenirs make up 35% + 5% = 40% of his total expenses. 40% of 500 is $200.
Example Question #2 : How To Find The Whole From The Part With Percentage
30% of what number is 20?
Solve to the nearest hundredth.
None of the other answers
66.67
1.5
150%
0.67
66.67
This is a very basic form percentage question. This can be rewritten:
0.3 * x = 20
(Remember, the word "of" in a word problem indicates multiplication, while the word "is" indicates an equals sign).
Solve for x: x = 20 / 0.3 = 66.67
Example Question #3 : How To Find The Whole From The Part With Percentage
A toy is on sale for 43% off. Its sale price is $21.37. What is the full price?
None of the available answers
An algebraic expression for this item is:
Example Question #1 : How To Find The Whole From The Part With Percentage
Twenty-six students planned to contribute an equal amount to purchase a gift for their teacher. After 18 students had paid, they had collected $76.50. What is the total price of the gift?
If $76.50 had been collected after 18 students had paid, we can determine how much each student contributed:
$76.50/18 = $4.25 per student
Now we can multiply this by the total number of students (26) to get the full price of the gift:
26 x $4.25 = $110.50
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