SSAT Upper Level Math : Number Concepts and Operations

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

Example Question #2 : Decide If Two Quantiies Are In A Proportional Relationship: Ccss.Math.Content.7.Rp.A.2a

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:

Explanation:

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 #1 : Decide If Two Quantiies Are In A Proportional Relationship: Ccss.Math.Content.7.Rp.A.2a

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

Possible Answers:

Correct answer:

Explanation:

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 #13 : 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:

Explanation:

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 #14 : 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:

Explanation:

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 : How To Find A Ratio

Scrabble

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:

Explanation:

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 : How To Find Rate

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:

Explanation:

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 #2 : How To Find Rate

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

Possible Answers:

Correct answer:

Explanation:

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 #3 : How To Find Rate

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

Possible Answers:

Correct answer:

Explanation:

First, find the cost per marker.

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

Example Question #1 : Grade 7

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

Possible Answers:

Correct answer:

Explanation:

Set up the following proportion:

,

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

Now solve for .

Example Question #1 : 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:

Explanation:

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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