### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #71 : Number Concepts And Operations

John and Michela are business partners who agreed to split profits at a ratio of , with Michela taking the larger share. If their business made in the first year, how much money did Michela make?

**Possible Answers:**

**Correct answer:**

Let be the amount John takes home and be the amount Michela takes home.

Since their business made ,

We want to know how much Michela made so we need to find the value of .

### Example Question #11 : How To Find A Ratio

The angles in a triangle have a ratio of . What is the measurement of the smallest angle?

**Possible Answers:**

**Correct answer:**

Let be the values of the angles.

Since there are degrees in a triangle,

Since we want the value of the smallest angle, find the value of .

### Example Question #12 : How To Find A Ratio

In a factory, there are glass bottles. If the ratio of red bottles to blue bottles is , how many more blue bottles than red bottles are there?

**Possible Answers:**

**Correct answer:**

First, find the number of red bottles and blue bottles.

Let be the number of red bottles and be the number of blue bottles. Since there is a total of bottles at the factory,

There are red bottles. Find the value of to find the number of blue bottles.

Now, because the question wants to find how many more blue bottles than red bottles there are, subtract the number of red bottles from the number of blue bottles.

### Example Question #13 : How To Find A Ratio

The ratio of offensive players to defensive players on a football team is . If there are players on the team, how many offensive players are there?

**Possible Answers:**

**Correct answer:**

Let be the number of offensive players and be the number of defensive players.

Since there is a total of players on the team,

We need to find the number of offensive players, so we will need to find the value of .

### Example Question #11 : Fractions

A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.

If the tiles marked with an "E" are removed, and the rest are placed in a box, then what is the ratio of consonant tiles to vowel tiles in the box?

Note: for purposes of this problem, "Y" is considered a consonant.

**Possible Answers:**

**Correct answer:**

Out of the 100 tiles, there are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles.

If the "E" tiles are removed, there will be

vowel tiles.

The number of consonant tiles can most easily be found by adding the number of vowel tiles and blanks:

.

The rest of the tiles are consonant tiles; subtract from 100 to get

of them.

Therefore, the ratio of consonant tiles to vowel tiles in the box after removing the "E's" is

- that is, a 28 to 15 ratio.

### Example Question #1 : Ratios & Proportional Relationships

A factory can make tents in minutes. At this rate, how long, in minutes, would it take the factory to make tents?

**Possible Answers:**

**Correct answer:**

First, find out how long it takes the factory to produce tent.

Since it takes the factory minutes to make tent, multiply this number by to find how long it takes to make tents.

It will take the factory minutes to make tents.

### Example Question #3 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

If Billy can drink cans of soda in days, how many cans of soda can he drink in days?

**Possible Answers:**

**Correct answer:**

First, find how many cans of soda Billy can drink in 1 day.

Since, he can drink cans in day, then the following equation will tell us how many cans he drinks in days.

### Example Question #4 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

It costs to buy markers. How much would it cost to buy markers?

**Possible Answers:**

**Correct answer:**

First, find the cost per marker.

Now, multiply this cost per marker by , the number of markers we want.

### Example Question #5 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

A gallon tank of water is leaking gallons every minutes. After how many hours will the tank be empty?

**Possible Answers:**

**Correct answer:**

Set up the following proportion:

,

where is the number of hours it'll take to empty gallons.

Now solve for .

### Example Question #6 : Compute Unit Rates Associated With Ratios Of Fractions: Ccss.Math.Content.7.Rp.A.1

Julie can read pages in minutes. How long, in minutes, would it take Julie to read a book that had pages?

**Possible Answers:**

**Correct answer:**

First, figure out how long it takes Julie to read 1 page.

It takes Julie minutes to read one page. Now, multiply this by the number of pages she needs to read to find out how long it will take her.

It will take Julie minutes to read pages.

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