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SAT II Math I : Ratios and Proportions

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

Example Question #1 : Ratios And Proportions

Convert $\small \frac{3}{8}$ into a percentage.

Possible Answers:

None of the other answers are correct.

Correct answer:

Explanation:

Set up a proportion:

$\frac{3}{8}=\frac{x}{100}$

Cross-multiply:

8x=300

Isolate by dividing by 8:

$x=\frac{300}{8}$

Finally, simplify:

$\frac{300}{8}=\frac{75}{2}=37\frac{1}{2}=37.5$

The fraction is therefore equivalent to .

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Example Question #2 : Ratios And Proportions

Convert the following fraction into a percent.

$\small \frac{7}{12}$

Possible Answers:

$\small 171.43$ %

.63 %

63.26 %

$\small .58$ %

$\small \small \small 58.33$ %

Correct answer:

$\small \small \small 58.33$ %

Explanation:

Set up a proportion:

$\small \frac{7}{12}=\frac{x}{100}$

Cross multiply:

$\small 12x=700$

Isolate $\small x$ by dividing both sides by 12:

$\small x = \frac{700}{12}$

Simplify:

$\small \frac{700}{12} = \frac{350}{6} = \frac{175}{3} = 58.33$

(Hint: If you are unable to use long division to solve the fraction $\small \frac{175}{3}$ , take a look at your answer choices and see if you can narrow down your choices. You know that value is going to be greater than one, since 175 is greater than 3. You also know that dividing any number by 3 is going to result in a decimal of .33, .66, or no decimal at all. With these two pieces of information, you should be able to isolate the correct answer without actually solving for it like I did in the last step.)

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Example Question #3 : Ratios And Proportions

Solve for :

$\frac{8}{11} = \frac{11x}{8}$

Possible Answers:

$\frac{121}{64}$

$\frac{1}{x}$

$\frac{64}{121}$

Correct answer:

$\frac{64}{121}$

Explanation:

To solve this proportion, cross multiply.

$\frac{8}{11} = \frac{11x}{8}$

64=121x

From here to solve, divide both sides by 121.

$x=\frac{64}{121}$

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Example Question #4 : Ratios And Proportions

If for every $\frac{1}{2}$ inch on a map it represents miles, how many inches will be needed for a distance of 275 miles?

Possible Answers:

5.5

6.5

4.5

Correct answer:

5.5

Explanation:

The ratio of inches to miles is

$\frac{0.5}{25}$

so you can set up a proportion of $\frac{0.5}{25}=\frac{x}{275}$ .

You then cross multiply to get

25x= 137.5 .

Then you solve for the variable by dividing by which gives us

137.5/25=5.5 .

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Example Question #37 : Mathematical Relationships

In a geometric sequence the ratio of the first term to the third term is 9:1. What is the ratio of the second term to the fifth term?

Possible Answers:

5:2

3:1

27:1

9:1

81:1

Correct answer:

27:1

Explanation:

Recall that in a geometric sequence there is a constant ratio between any pair of consecutive terms:

$r \cdot a_{n} =a_{n+1}$

If the ratio of the first term to the third term is 9:1 then the ratio of two consecutive terms is a number that when multiplied by itself is 9:

r^2 = 9

r=3

Therefore the common ratio for this sequence is 3.

There are three terms between term 2 and 5 so the common ratio will be applied to the second term three times to get the fifth term:

$r^3 \cdot a_{2} = a_{5}$

Since for this sequence

$3^{3} = 27$

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SAT II Math I : Ratios and Proportions

Study concepts, example questions & explanations for SAT II Math I

All SAT II Math I Resources

Example Questions

Example Question #1 : Ratios And Proportions

Example Question #2 : Ratios And Proportions

Example Question #3 : Ratios And Proportions

Example Question #4 : Ratios And Proportions

Example Question #37 : Mathematical Relationships

All SAT II Math I Resources

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