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SSAT Middle Level Math : Numbers and Operations

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

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Example Questions

Example Question #121 : Ratio And Proportion

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

Possible Answers:

26:1

1:26

13:2

1:13

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 #1 : Solving Word Problems With One Unit Conversion

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:

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

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

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

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

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

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 #2103 : 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 #122 : Ratio And Proportion

Give the value of that makes this proportion statement correct:

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

Possible Answers:

N = 21

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

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

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

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

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 #123 : Ratio And Proportion

Give the value of that makes this proportion statement correct:

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

Possible Answers:

N = 12

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

N = 75

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

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

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 #124 : Ratio And Proportion

Give the value of that makes this proportion statement correct:

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

Possible Answers:

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

N = 150

N = 60

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

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 #125 : Ratio And 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 = 120

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

N = 80

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 #126 : Ratio And 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:

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

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

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

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

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

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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Example Question #127 : Ratio And Proportion

If Jason eats one-third of half a dozen donuts, how many donuts has he eaten?

Possible Answers:

donuts

Correct answer:

donuts

Explanation:

Half a dozen donuts is equal to 6 donuts, given that there are 12 items per dozen.

One-third of 6 is 2. Therefore, 2 donuts is the correct answer.

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Example Question #128 : Ratio And Proportion

Kenny is having a party, and he is experimenting with different mixtures of soda to come up with something original. He particularly likes a mixture of four ounces of lemon lime soda and three ounces of cream soda. He has two and a half liters of lemon lime soda and wants to use it all; how much cream soda does he need?

Possible Answers:

None of the other responses gives the correct answer.

$4 \frac{4}{5} \textrm{ L}$

$3 \frac{1}{3} \textrm{ L}$

$2 \frac{3}{8} \textrm{ L}$

$1 \frac{7}{8} \textrm{ L}$

Correct answer:

$1 \frac{7}{8} \textrm{ L}$

Explanation:

The ratio of ounces of lemon lime soda to ounces of cream soda in the initial mixture can be expressed as $\frac{4}{3}$ . This ratio must remain the same for the mixture Ken will make for the party. Let be the number of liters of cream soda. Then the ratio is $\frac{2\frac{1}{2}}{N}$ . Set the two ratios equal to each other and solve for :

$\frac{2\frac{1}{2}}{N} = \frac{4}{3}$

Set the cross-products equal to each other:

$4 N = 2\frac{1}{2} \cdot 3$

$4 N = 7\frac{1}{2}$

$4 N \div 4= 7\frac{1}{2} \div 4$

$N= 7\frac{1}{2} \div 4 = \frac{15}{2} \times \frac{1}{4} = \frac{15}{8} = 1 \frac{7}{8}$

Ken will use $1 \frac{7}{8}$ liters of cream soda in the final mixture.

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SSAT Middle Level Math : Numbers and Operations

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #121 : Ratio And Proportion

Example Question #1 : Solving Word Problems With One Unit Conversion

Example Question #2103 : Psat Mathematics

Example Question #122 : Ratio And Proportion

Example Question #123 : Ratio And Proportion

Example Question #124 : Ratio And Proportion

Example Question #125 : Ratio And Proportion

Example Question #126 : Ratio And Proportion

Example Question #127 : Ratio And Proportion

Example Question #128 : Ratio And Proportion

All SSAT Middle Level Math Resources

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