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GED Math : Proportions and Percentages

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Example Question #1 : Proportions And Percentages

At a party, there are 7 women with blonde hair, 9 women with brown hair, and 5 women with red hair. What is the proportion of women with blonde hair?

Possible Answers:

$\small \frac{1}{2}$

$\small \frac{1}{3}$

$\small \frac{7}{9}$

$\small \frac{7}{5}$

Correct answer:

$\small \frac{1}{3}$

Explanation:

A proprotion is the number of a specific event (blonde women) divided by the total number of events (total number of women).

$\small \frac{7}{7+9+5}=\frac{7}{21}=\frac{1}{3}$

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Example Question #1 : Proportions And Percentages

Solve:

$14\%\ of\ 52=$

Possible Answers:

59.28

371.43

45.61

7.28

Correct answer:

7.28

Explanation:

$\small 14\%\ of \ 52=0.14\times 52=7.28$

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Example Question #1 : Proportions And Percentages

Solve:

$\small 23\%\ of\ 73=$

Possible Answers:

$\small 317.4$

$\small 59.3$

$\small 96$

$\small 16.8$

Correct answer:

$\small 16.8$

Explanation:

$\small 23\%\ of\ 73=0.23\times73=16.8$

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Example Question #1 : Proportions And Percentages

A bag contains $\small 7$ green marbles, $\small 2$ red marbles, and $\small 5$ blue marbles. What is the proportion of red marbles?

Possible Answers:

$\small \frac{1}{7}$

$\small \frac{2}{7}$

$\small \frac{2}{5}$

$\small \frac{1}{6}$

Correct answer:

$\small \frac{1}{7}$

Explanation:

The proportion is equal to the number of specific events (red marbles) divided by the total number of events (sum of all colors).

$\small P=\frac{2}{7+2+5}=\frac{2}{14}=\frac{1}{7}$

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Example Question #1 : Proportions And Percentages

What is $17\%$ of ?

Possible Answers:

199.6

170.6

4.9

33.9

Correct answer:

4.9

Explanation:

$17\%\ of\ 29=0.17\times 29=4.9$

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Example Question #1 : Proportions And Percentages

Sherry deposits $3,000 at 6% simple interest per year. How much will she have in this account after three years, assuming she does not make any withdrawals or deposits?

Possible Answers:

$\$3,054$

$\$3,540$

$\$3,180$

$\$3,018$

Correct answer:

$\$3,540$

Explanation:

Use the simple interest formula

I = Prt

with P = 3,000, r = 0.06, t = 3 :

$I = \$ 3,000 \cdot 0.06 \cdot 3 = \$540$

This is the simple interest earned. Add it to the original principal:

$\$ 3,000+\$540 = \$3,540$

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Example Question #7 : Proportions And Percentages

The ratio of students to instructors at a prestigious law school is 15:4. If the school employs 120 instructors, then how many students total must it limit itself to enrolling in order to maintain this student-instructor ratio?

Possible Answers:

630

540

450

720

Correct answer:

450

Explanation:

Let be the maximum number of students admitted.

For the school to maintain a 15:4 student-teacher ratio with 120 instructors, the ratios $\frac{N}{120}$ and $\frac{15}{4}$ must be equal. Therefore, we solve the proportion statement for :

$\frac{N}{120} = \frac{15}{4}$

$\frac{N}{120} \cdot 120= \frac{15}{4} \cdot 120$

$N = \frac{1,800}{4} = 450$

The maximum number of students it can admit is 450.

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Example Question #8 : Proportions And Percentages

The ratio of students to instructors at a prestigious medical school is 25:6. The school employs 90 instructors, and there will be 240 students returning. How many new students must it limit itself to admitting in order to continue to maintain this student-instructor ratio?

Possible Answers:

135

255

325

375

Correct answer:

135

Explanation:

Let be the maximum number of students admitted overall.

For the school to maintain a 25:6 student-teacher ratio with 90 instructors, the ratios $\frac{N}{90}$ and $\frac{25}{6}$ must be equal. Therefore, we solve the proportion statement for :

$\frac{N}{90} = \frac{25}{6}$

$\frac{N}{90} \cdot 90= \frac{25}{6} \cdot 90$

$N= \frac{2,250}{6} = 375$

Since 240 spots are already filled by returning students, the medical school can admit up to 375 - 240 = 135 new students.

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Example Question #9 : Proportions And Percentages

Which of the following statements follows from the statement 8A = 9B ?

Possible Answers:

$\frac{8}{B} = \frac{A}{9}$

$\frac{8}{B} = \frac{9}{A}$

$\frac{8}{A} = \frac{B}{9}$

$\frac{8}{A} = \frac{9}{B}$

Correct answer:

$\frac{8}{B} = \frac{9}{A}$

Explanation:

Two ratios are equivalent if and only if their cross-products are equal. We look for the proportion statement whose cross-products are and . Of the four choices, only $\frac{8}{B} = \frac{9}{A}$ fits this criterion, so it is the correct choice.

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Example Question #10 : Proportions And Percentages

Which of the following statements does not follow from the statement $\frac{X}{5} = \frac{Y }{7}$ ?

Possible Answers:

$\frac{5}{X} = \frac{7}{Y }$

$\frac{X+5}{5} = \frac{Y+7 }{7}$

$\frac{7}{5} = \frac{X }{Y}$

5Y = 7X

Correct answer:

$\frac{7}{5} = \frac{X }{Y}$

Explanation:

From $\frac{X}{5} = \frac{Y }{7}$ we can conclude the following:

5Y = 7X is true, because the cross-products of a proportion statement are true.

$\frac{5}{X} = \frac{7}{Y }$ is true, because if two ratios are equivalent, their reciprocals are equivalent.

$\frac{X+5}{5} = \frac{Y+7 }{7}$ can be demonstrated to be true as follows:

$\frac{X}{5} = \frac{Y }{7}$

$\frac{X}{5} + 1= \frac{Y }{7} + 1$

$\frac{X}{5} +\frac{5}{5} = \frac{Y }{7} + \frac{7}{7}$

$\frac{X+5}{5} = \frac{Y+7 }{7}$

The fourth statement is false:

$\frac{X}{5} = \frac{Y }{7}$

$\frac{X}{5} \cdot \frac{5}{Y} = \frac{Y }{7}\cdot \frac{5}{Y}$

$\frac{X }{Y} = \frac{5} {7}$ , which contradicts the statement that $\frac{7}{5} = \frac{X }{Y}$ .

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GED Math : Proportions and Percentages

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1 : Proportions And Percentages

Example Question #1 : Proportions And Percentages

Example Question #1 : Proportions And Percentages

Example Question #1 : Proportions And Percentages

Example Question #1 : Proportions And Percentages

Example Question #1 : Proportions And Percentages

Example Question #7 : Proportions And Percentages

Example Question #8 : Proportions And Percentages

Example Question #9 : Proportions And Percentages

Example Question #10 : Proportions And Percentages

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