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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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

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Example Questions

Example Question #92 : Grade 7

The ratio of offensive players to defensive players on a football team is $2\text{ to }5$ . 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,

2x+5x=42

7x=42

x=6

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

$2x=6\times2=12$

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Example Question #1141 : Ssat Upper Level Quantitative (Math)

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:

29:14

29:15

2: 1

28:15

Correct answer:

28:15

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

9 + 9 + 8 +4 = 30 vowel tiles.

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

9 + 12 + 9 + 8 + 4 + 2= 44 .

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

100 - 44 = 56 of them.

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

$\frac{56}{30} = \frac{56 \div 2 }{30 \div 2 } = \frac{28}{15 }$ - that is, a 28 to 15 ratio.

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Example Question #1 : 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 2:3, with Michela taking the larger share. If their business made $\$36\textup{,}000$ in the first year, how much money did Michela make?

Possible Answers:

$\$21\textup{,}600$

$\$14\textup{,}400$

$\$22\textup{,}200$

$\$18\textup{,}600$

Correct answer:

$\$21\textup{,}600$

Explanation:

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

Since their business made $\$36,000$ ,

2x+3x=36000

5x=36000

x=7200

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

$3x=7200\times3=21600$

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Example Question #1 : Ratios & Proportional Relationships

A factory can make 300 tents in minutes. At this rate, how long, in minutes, would it take the factory to make 9000 tents?

Possible Answers:

450

300

550

500

Correct answer:

450

Explanation:

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

$\frac{15}{300}=0.05$

Since it takes the factory 0.05 minutes to make tent, multiply this number by 9000 to find how long it takes to make 9000 tents.

$0.05\times9000=450$

It will take the factory 450 minutes to make 9000 tents.

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Example Question #2 : Ratios & Proportional Relationships

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.

$\frac{12}{4}=3$

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

$3\times2=6$

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Example Question #1 : Ratios & Proportional Relationships

It costs $\$45$ to buy markers. How much would it cost to buy markers?

Possible Answers:

$\$50$

$\$60$

$\$65$

$\$75$

Correct answer:

$\$75$

Explanation:

First, find the cost per marker.

$45\div15=3$

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

$25\times3=75$

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Example Question #3 : Ratios & Proportional Relationships

A 200 gallon tank of water is leaking gallons every minutes. After how many hours will the tank be empty?

Possible Answers:

3000

Correct answer:

Explanation:

Set up the following proportion:

$\frac{2}{0.5}=\frac{200}{x}$ ,

where is the number of hours it'll take to empty 200 gallons.

Now solve for .

2x=100

x=50

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Example Question #4 : Ratios & Proportional Relationships

Julie can read pages in minutes. How long, in minutes, would it take Julie to read a book that had 120 pages?

Possible Answers:

Correct answer:

Explanation:

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

$2\div5=0.4$

It takes Julie 0.4 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.

$0.4\times120=48$

It will take Julie minutes to read 120 pages.

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Example Question #5 : Ratios & Proportional Relationships

If it takes Dennis 120 minutes to paint walls, how many minutes does it take him to paint wall?

Possible Answers:

Correct answer:

Explanation:

Divide the time it take Dennis to paint walls by the number of walls he painted to find how long it will take him to paint one wall.

$120\div8=15$

It will take Dennis minutes to paint one wall.

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Example Question #6 : Ratios & Proportional Relationships

An arcade charges players $\$1.25$ to play on the machine for minutes. How much money would it cost a player if she wanted to play for an hour?

Possible Answers:

$\$35$

$\$20$

$\$30$

$\$25$

Correct answer:

$\$25$

Explanation:

First, find out how much money it costs to play for one minute.

$1.25\div3=0.41667$

Now, multiply this amount by the number of minutes in an hour to find how much it will cost for the player to play for one hour.

$0.41667\times60=25$

It will cost her $\$25$ to play for one hour.

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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #92 : Grade 7

Example Question #1141 : Ssat Upper Level Quantitative (Math)

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

Example Question #1 : Ratios & Proportional Relationships

Example Question #2 : Ratios & Proportional Relationships

Example Question #1 : Ratios & Proportional Relationships

Example Question #3 : Ratios & Proportional Relationships

Example Question #4 : Ratios & Proportional Relationships

Example Question #5 : Ratios & Proportional Relationships

Example Question #6 : Ratios & Proportional Relationships

All SSAT Upper Level Math Resources

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