### All SAT Math Resources

## Example Questions

### Example Question #61 : Fractions

In a mixture of flour and sugar, the ratio of flour to sugar is 5 to 1. How many kilograms of flour will there be in 12 kilograms of this mixture?

**Possible Answers:**

3

4

5

1

2

**Correct answer:**

2

The question says that the mixture has 5 units of flour for every 1 unit of sugar, which adds up to a total of 5 + 1 = 6 units of the mixture; therefore in 6 kilograms of the mixture, 1 kilogram will be sugar.

To find how much sugar will be in 12 kilograms of the mixture, we multiply the amount of sugar in 6 kilograms of the mixture by 2, giving us 1 kilogram of sugar * 2 = 2 kilograms of sugar.

### Example Question #62 : Fractions

A survey of studio offices in a city with 14,000 employees reveals that there are, on average, 12.5 employees per office. If there have been a cumulative total of 3,400 printers sold to the offices of the city, what is the best estimate of the average number of printers per office?

**Possible Answers:**

0.33

0.77

4.1

3.0

1.2

**Correct answer:**

3.0

The best estimate would be to simply divide the number of printers by the number of offices. However, they only gave us the average number of employees per office, thus to find the number of offices we divide:

14,000 (people)/12.5 (per office) = 14,000/12.5 = 1,120 offices

We already know the number of printers available total, thus again divide

3,400 (printers)/1,120 (offices) = 3.04, or** 3.0** printers per office as the best estimate.

### Example Question #71 : Fractions

A factory makes six widgets in a batch that takes 24 minutes to complete. How long does it take to make 57 widgets?

**Possible Answers:**

3 hours

3 hours, 5 minutes

4 hours

3 hours, 45 minutes

3 hours, 30 minutes

**Correct answer:**

4 hours

We have here a basic ratio:

6/24 = 57/x

Solving for x, we get: 6x = 24 * 57; 6x = 1368; x = 228

Now, we must be very careful here, however. Is 228 an even multiple of 24? 228/24 = 9.5. That means that we would have to do 9.5 batches. The question indicates that these are batched in groups of 6; therefore, we have to run 10 batches to get our amount. That would be 240 minutes or 4 hours.

### Example Question #71 : Proportion / Ratio / Rate

Kendall can run 26 miles in 4 hours and 20 minutes. At this rate how long would it take him to run 100 miles?

**Possible Answers:**

18 hours and 35 minutes

15 hours and 50 minutes

12 hours and 20 minutes

16 hours and 40 minutes

10 hours and 55 minutes

**Correct answer:**

16 hours and 40 minutes

Set up a proportion and conver 4 hours and 20 minutes into just minutes for now,

so 26/260 = 100/X

Solve for X = 1000 minutes

1000/60 = 16 hours and 40 minutes

### Example Question #81 : Proportion / Ratio / Rate

A recipe calls for a ratio of for wheat, barley, and flour. If we have 12 pounds of barley, how much wheat do we need to use all of it?

**Possible Answers:**

**Correct answer:**

We can set up a ratio of and then solve for .

### Example Question #82 : Proportion / Ratio / Rate

To ship a package, the postal service charges for the first 150 grams and for each additional 50 grams or part thereof. What is one possible weight in grams for a package that costs to ship?

**Possible Answers:**

**Correct answer:**

The weight will be 150 grams + (1.15 – 0.55)/0.05 * 50g.

You need to subtract first 150 grams cost from the total cost and divide by the price per unit to determine how many units. Next, multiply units by weight per unit and add to the original first 150 grams.

150 + 600 = 750 grams

This is the maximum weight that can be sent at that price; the minimum weight that could be charged this price would be 701 grams. Hence a package weighing 750 grams will be charged $1.15.

### Example Question #83 : Proportion / Ratio / Rate

Six is to thirteen-and-a-half as seventeen is to what?

**Possible Answers:**

None of the other answers are correct.

**Correct answer:**

Let us express this as an algebraic expression:

We can cross multiply:

### Example Question #84 : Proportion / Ratio / Rate

Solve the proportion:

**Possible Answers:**

**Correct answer:**

Cross multiply the proportion and simplify.

### Example Question #81 : Proportion / Ratio / Rate

Toilet used gallons of water in the last hour and uses gallon of water per flush. If Toilet was flushed the same amount, but uses gallons per flush, how much water did Toilet use?

**Possible Answers:**

gallons

gallons

gallons

gallons

gallons

**Correct answer:**

gallons

First you must figure out the proportion . You then cross multiple to get meaning that Toilet uses gallons.

### Example Question #86 : Proportion / Ratio / Rate

In a ceratain class, of the students are boys and of the boys are freshman. If all of the freshmen boys failed the first test, which could be the total number of students in the class?

**Possible Answers:**

**Correct answer:**

In order the split the boys equally in half to have them be freshmen, a third of the class must be an even number. The only choice that when cut in thirds can then be split in half is . and .

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