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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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

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All SSAT Middle Level Math Resources

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Example Questions

Example Question #115 : How To Find A Ratio

There are 50 orange cats and 20 black cats. What is the ratio of black to orange cats?

Possible Answers:

5:2

2:3

3:2

2:5

Correct answer:

2:5

Explanation:

The number of black cats goes before the colon since this question is asking for the ratio of black to orange cats.

Therefore, there are $20:50=\textsl{ black}: \textsl{ orange cats}$ .

This can be simplified if you divide both numbers by 10. This gives a ratio of 2:5 .

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Example Question #111 : How To Find A Ratio

Find .

$\frac{6}{25}=\frac{9}{x}$

Possible Answers:

2.16

37.5

Correct answer:

37.5

Explanation:

If you have to solve a proportion or a ratio, all you have to do is cross-multiply and divide by what is left.

$9\times25=6x$

225=6x

$\frac{225}{6}=x$

x=37.5

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Example Question #781 : Ssat Middle Level Quantitative (Math)

What is the simplest form of the following ratio: 325:50?

Possible Answers:

1:13

26:1

1:26

13:2

Correct answer:

13:2

Explanation:

In order to determine the simplest form of a ratio, divide both sides of the ratio by a common factor. If we divide each side of this ratio by 5, we get 65:10.

This can still be simplified by dividing by 5 again.

Therefore, the simplest form of the ratio is 13:2.

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Example Question #6 : Use Ratio Reasoning To Convert Measurement Units: Ccss.Math.Content.6.Rp.A.3d

A carpenter is making a model house and he buys $8\textup{ feet}$ of crown molding to use as accent pieces. He needs $18\textup{ inches}$ of the molding for the house. How many feet of the material does he need to finish the model?

Possible Answers:

$2 \tfrac{1}{2} \textup{ feet}$

$3 \tfrac{1}{2} \textup{ feet}$

$1 \tfrac{2}{3} \textup{ feet}$

$1 \tfrac{1}{2} \textup{ feet}$

$2 \tfrac{3}{4} \textup{ feet}$

Correct answer:

$1 \tfrac{1}{2} \textup{ feet}$

Explanation:

We can solve this problem using ratios. There are $12\ inches$ in $1\ foot$ . We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $18\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$18\ inches:x\ feet\rightarrow \frac{18\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{18\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=18\ inches \times (1\ foot)$

Simplify.

12x=18

Divide both sides by .

$\frac{12x}{12}=\frac{18}{12}$

Solve.

$x=1 \tfrac{1}{2} \ feet$

The carpenter needs $1 \tfrac{1}{2} \ feet$ of material.

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Example Question #2101 : Psat Mathematics

A carpenter is making a model house and he buys $8\ feet$ of crown moulding to use as accent pieces. He needs $144\ inches$ of the moulding for the house. How many additional feet of the material will he need to purchase to finish the model?

Possible Answers:

Correct answer:

Explanation:

We can solve this problem using ratios. There are $12\ inches$ in $1\ foot$ . We can write this relationship as the following ratio:

$12\ inches:1\ foot\rightarrow \frac{12\ inches}{1\ foot}$

We know that the carpenter needs $144\ inches$ of material to finish the house. We can write this as a ratio using the variable to substitute the amount of feet.

$144\ inches:x\ feet\rightarrow \frac{144\ inches}{x\ feet}$

Now, we can solve for by creating a proportion using our two ratios.

$\frac{12\ inches}{1\ foot}=\frac{144\ inches}{x\ feet}$

Cross multiply and solve for .

$12\ inches \times (x\ feet)=144\ inches \times (1\ foot)$

Simplify.

12x=144

Divide both sides by .

$\frac{12x}{12}=\frac{144}{12}$

Solve.

$x=12 \ feet$

The carpenter needs $12 \ feet$ of material. Since he already has 8 feet he will need to purchase more to finish the project.

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Example Question #1 : How To Find A Proportion

Give the value of that makes this proportion statement correct:

$\frac{100}{N} = \frac{70}{30}$

Possible Answers:

$N = 33 \frac{1}{3}$

$N = 23 \frac{1}{3}$

$N = 42 \frac{6}{7}$

$N = 233 \frac{1}{3}$

N = 21

Correct answer:

$N = 42 \frac{6}{7}$

Explanation:

Cross-multiply, then solve for :

$\frac{100}{N} = \frac{70}{30}$

$70 N = 100 \cdot 30$

70 N = 3,000

$70 N \div 70= 3,000\div 70$

$N = 42 \frac{6}{7}$

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Example Question #1 : How To Find A Proportion

Give the value of that makes this proportion statement correct:

$\frac{100}{N} = \frac{40}{30}$

Possible Answers:

$N = 83 \frac{1}{3}$

N = 75

N = 12

$N = 133 \frac{1}{3}$

$N = 66 \frac{2}{3}$

Correct answer:

N = 75

Explanation:

Cross-multiply, then solve for :

$\frac{100}{N} = \frac{40}{30}$

$40 N = 100 \cdot 30$

40 N = 3,000

$40 N \div 40= 3,000\div 40$

N = 75

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Example Question #3 : How To Find A Proportion

Give the value of that makes this proportion statement correct:

$\frac{N}{80} = \frac{40}{30}$

Possible Answers:

N = 60

$N = 106 \frac{2}{3}$

$N = 133 \frac{1}{3}$

N = 150

N = 120

Correct answer:

$N = 106 \frac{2}{3}$

Explanation:

Multiply both sides by 80 and solve for :

$\frac{N}{80} = \frac{40}{30}$

$\frac{N}{80} \cdot80 = \frac{40}{30} \cdot80$

$N = \frac{40 \cdot 80}{30} = 106 \frac{2}{3}$

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Example Question #2 : How To Find A Proportion

Give the value of that makes this proportion statement correct:

$\frac{N}{75} = \frac{40}{30}$

Possible Answers:

N = 100

$N = 83 \frac{1}{3}$

$N = 56 \frac{1}{4}$

N = 80

N = 120

Correct answer:

N = 100

Explanation:

Multiply both sides by 75 and solve for :

$\frac{N}{75} = \frac{40}{30}$

$\frac{N}{75} \cdot 75 = \frac{40}{30} \cdot 75$

$N = \frac{40 \cdot 75}{30} = 100$

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Example Question #3 : How To Find A Proportion

Read this problem, but do not solve it.

4 out of every 5 dentists surveyed recommend Triton sugarless gum to patients who chew gum. If 2,100 dentists were surveyed, how many dentists recommended Triton?

If we let be the number of dentists who recommended Triton, what proportion statement could be used to solve this problem?

Possible Answers:

$\frac{N}{2,100} = \frac{4}{5}$

$\frac{N}{2,100} = \frac{5}{4}$

$\frac{N}{4} = \frac{5}{2,100}$

$\frac{N}{2,100} = \frac{1}{5}$

$\frac{2,100}{N} = \frac{4}{5}$

Correct answer:

$\frac{N}{2,100} = \frac{4}{5}$

Explanation:

The ratios that are set equal to each other in a proportion statement must compare the same quantities in the same order.

In each ratio, we can put number of dentists who recommended Triton in the numerator, and number of dentists who were surveyed in the denominator.

One ratio is 4 dentists recommending Triton to 5 dentists surveyed (the general ratio): this is $\frac{4}{5}$ .

The other ratio is dentists recommending Triton to 2,100 dentists surveyed (the actual number); this is $\frac{N}{2,100}$ .

The proportion statement sets these equal:

$\frac{N}{2,100} = \frac{4}{5}$

which is the correct choice.

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SSAT Middle Level Math : SSAT Middle Level Quantitative (Math)

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #115 : How To Find A Ratio

Example Question #111 : How To Find A Ratio

Example Question #781 : Ssat Middle Level Quantitative (Math)

Example Question #6 : Use Ratio Reasoning To Convert Measurement Units: Ccss.Math.Content.6.Rp.A.3d

Example Question #2101 : Psat Mathematics

Example Question #1 : How To Find A Proportion

Example Question #1 : How To Find A Proportion

Example Question #3 : How To Find A Proportion

Example Question #2 : How To Find A Proportion

Example Question #3 : How To Find A Proportion

All SSAT Middle Level Math Resources

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