PSAT Math : Percentage

Study concepts, example questions & explanations for PSAT Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #2031 : Psat Mathematics

What is  as a percentage?

Possible Answers:

Correct answer:

Explanation:

Convert the improper fraction  to the mixed numeral  or as the decimal .   as a percentage is

Example Question #11 : Fractions And Percentage

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?

Possible Answers:

17.\overline{7}\%

8.\overline{8}\%

None of the available answers

20\%

It is most likely that the chosen child will be the oldest child.

Correct answer:

17.\overline{7}\%

Explanation:

First, we will determine the total number of ballots:

4+4+5+7+12+13=45\hspace{1 mm}ballots

Since there are two four year olds, and this question is asking the probability of the chosen child being four, the probability is:

\frac{4+4}{45}=\frac{8}{45}=0.1\overline{7}=17.\overline{7}\%

Example Question #1 : 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?

Possible Answers:

Correct answer:

Explanation:

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 #2 : Fractions And 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?

Possible Answers:

Correct answer:

Explanation:

We can right 23% as a fraction and set that equal to  over the original price. 

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 #2 : Fractions And Percentage

Louisa and Caroline are trying to save up to start a small business together. Louisa has saved  of their goal money, and Carolina has saved  of their goal money. About how much of their goal money have they saved up together?

Possible Answers:

18%

78%

56%

64%

45%

Correct answer:

78%

Explanation:

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 #71 : Percentage

Histogram

Refer to the above bar graph.

What percent of the students achieved a score 500 or below?

Possible Answers:

Correct answer:

Explanation:

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

Sat_math_131_01

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?

Possible Answers:

$225

$40

$200

$175

$250

Correct answer:

$200

Explanation:

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.

Possible Answers:

None of the other answers

66.67

1.5

150%

0.67

Correct answer:

66.67

Explanation:

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 #1 : 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?

Possible Answers:

\$ 37.49

\$ 49.70

\$ 30.56

\$ 33.55

None of the available answers

Correct answer:

\$ 37.49

Explanation:

An algebraic expression for this item is:

(1-0.43)x=21.37

x=\frac{21.37}{1-0.43}=\$ 37.49

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?

Possible Answers:

Correct answer:

Explanation:

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

Learning Tools by Varsity Tutors