SAT Math : Arithmetic

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #53 : Proportion / Ratio / Rate

If  and , what is the ratio of  to ?

Possible Answers:

Correct answer:

Explanation:

To find a ratio like this, you simply need to make the fraction that represents the division of the two values by each other. Therefore, we have:

Recall that division of fractions requires you to multiply by the reciprocal:

which is the same as:

This is the same as the ratio:

Example Question #72 : Fractions

express 7/8 as a ratio

Possible Answers:

7:8

0.875

not possible to express as a ratio

1.15

8:7

Correct answer:

7:8

Explanation:

a ratio that comes from a fraction is the numerator: denominator

7/8 = 7:8

Example Question #71 : Fractions

1 meter contains 100 centimeters.

Find the ratio of 1 meter and 40 centimeters to 1 meter:

Possible Answers:

7:5

12:5

2:3

9:6

3:2

Correct answer:

7:5

Explanation:

1m 40cm = 140cm. 1m = 100cm. So the ratio is 140cm:100cm. This can be put as a fraction 140/100 and then reduced to 14/10 and further to 7/5. This, in turn, can be rewritten as a ratio as 7:5.

Example Question #72 : Fractions

When television remotes are shipped from a certain factory, 1 out of every 200 is defective. What is the ratio of defective to nondefective remotes?

Possible Answers:

199:1

200:1

1:199

1:200

Correct answer:

1:199

Explanation:

One remote is defective for every 199 non-defective remotes.

Example Question #1 : How To Express A Fraction As A Ratio

On a desk, there are  papers for every  paper clips and  papers for every  greeting card. What is the ratio of paper clips to total items on the desk?

Possible Answers:

Correct answer:

Explanation:

Begin by making your life easier: presume that there are  papers on the desk. Immediately, we know that there are  paper clips. Now, if there are  papers, you know that there also must be  greeting cards. Technically you figure this out by using the ratio:

By cross-multiplying you get:

Solving for , you clearly get .

(Many students will likely see this fact without doing the algebra, however. The numbers are rather simple.)

Now, this means that our desk has on it:

 papers

 paper clips

 greeting cards

Therefore, you have  total items.  Based on this, your ratio of paper clips to total items is:

, which is the same as .

Example Question #31 : Fractions

In a classroom of  students, each student takes a language class (and only one—nobody studies two languages).  take Latin,  take Greek,  take Anglo-Saxon, and the rest take Old Norse. What is the ratio of students taking Old Norse to students taking Greek?

Possible Answers:

Correct answer:

Explanation:

To begin, you need to calculate how many students are taking Old Norse. This is:

Now, the ratio of students taking Old Norse to students taking Greek is the same thing as the fraction of students taking Old Norse to students taking Greek, or:

Next, just reduce this fraction to its lowest terms by dividing the numerator and denominator by their common factor of :

This is the same as .

Example Question #81 : Fractions

In a garden, there are  pansies,  lilies,  roses, and  petunias. What is the ratio of petunias to the total number of flowers in the garden?

Possible Answers:

Correct answer:

Explanation:

To begin, you need to do a simple addition to find the total number of flowers in the garden:

Now, the ratio of petunias to the total number of flowers in the garden can be represented by a simple division of the number of petunias by . This is:

Next, reduce the fraction by dividing out the common  from the numerator and the denominator:

This is the same as .

Example Question #81 : Fractions

The price of 10 yards of fabric is c cents, and each yard makes q quilts. In terms of q and c, what is the cost, in cents, of the fabric required to make 1 quilt?

Possible Answers:

(c )/(10q )

(10c )/(q )

(cq )/(10 )

10cq

Correct answer:

(c )/(10q )

Explanation:

We create a conversion ratio that causes yards to cancel out, leaving only cents in the numerator and quilts in the denominator. This ratio is ((c cent )/(10 yard))((1 yard)/(q quilt))=(c )/(10q ) cent⁄quilt . Since the ratio has cents in the numerator and quilts in the denominator, it represents the price in cents per quilt.

Example Question #2 : How To Find Proportion

Susan is doing a bake sale for her sorority. One third of the money she made is from blueberry cupcakes, which cost 50 cents each. A quarter of her sales is from cinnamon cream pies, which cost $1 each. And the rest are from her chocolate brownies, which cost 25 cents each. She made a total of $60 at the end of her bake sale, how many brownies did she sell?

Possible Answers:

130

140

100

150

120

Correct answer:

100

Explanation:

1/3 of sales from cupcakes = $20, ¼ of sales from cream pies = $15 and the rest are from brownies = $60-$20-$15 = $25. Since each brownie costs 25 cents, Susan will have sold 100 of them.

Example Question #91 : Fractions

In 7 years Bill will be twice Amy’s age. Amy was 1.5 times Molly’s age 2 years ago. If Bill is 29 how old is Molly? 

Possible Answers:

5

12

6

8

9

Correct answer:

8

Explanation:

Consider

(Bill + 7) = 2 x (Amy + 7)

(Amy – 2) = 1.5 x (Molly – 2)

Solve for Molly using the two equations by finding Amy’s age in terms of Molly’s age.

Amy = 2 + 1.5 Molly – 3 = 1.5 x Molly – 1

Substitute this into the first equation:

(Bill + 7) = 2 x (Amy + 7) = 2 x (1.5 x Molly – 1 + 7) = 2 x (1.5 x Molly + 6) = 3 x Molly + 12

Solve for Molly:

Bill + 7 – 12 = 3 x Molly

Molly = (Bill – 5) ¸ 3

Substitute Bill = 29

Molly = (Bill – 5) ¸ 3 = 8

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