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 #35 : Mathematical Relationships

Convert into a percentage.

Possible Answers:

None of the other answers are correct.

Correct answer:

Explanation:

Set up a proportion:

Cross-multiply:

Isolate by dividing by 8:

Finally, simplify:

The fraction is therefore equivalent to .

Example Question #36 : Mathematical Relationships

Convert the following fraction into a percent.

Possible Answers:

%

.63 %

%

63.26 %

%

Correct answer:

%

Explanation:

Set up a proportion:

Cross multiply:

Isolate by dividing both sides by 12:

Simplify:

(Hint: If you are unable to use long division to solve the fraction , 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.)

Example Question #1 : Ratios And Proportions

Solve for :  

Possible Answers:

Correct answer:

Explanation:

To solve this proportion, cross multiply.

From here to solve, divide both sides by 121.

Example Question #38 : Mathematical Relationships

If for every  inch on a map it represents  miles, how many inches will be needed for a distance of  miles?

Possible Answers:

Correct answer:

Explanation:

The ratio of inches to miles is 

 

so you can set up a proportion of .  

You then cross multiply to get 

.  

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

.

Example Question #39 : 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:

Correct answer:

Explanation:

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

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:

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: 

Since  for this sequence

 

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