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SSAT Upper Level Math : Number Concepts and Operations

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

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #161 : Number Concepts And Operations

$\frac{\frac{3}{5}}{\frac{1}{4}}=?$

Possible Answers:

$\frac{5}{12}$

$\frac{12}{5}$

$\frac{3}{5}$

$\frac{8}{7}$

Correct answer:

$\frac{12}{5}$

Explanation:

The main line in a fraction means "divide." Rewrite the complex fraction like this:

$\frac{\frac{3}{5}}{\frac{1}{4}}=\frac{3}{5}\div\frac{1}{4}$

Now, divide these two fractions.

$\frac{3}{5}\div\frac{1}{4}=\frac{3}{5}\times\frac{4}{1}=\frac{12}{5}$

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Example Question #162 : Number Concepts And Operations

$\frac{\frac{10}{3}}{\frac{5}{3}}=?$

Possible Answers:

$\frac{2}{5}$

$\frac{7}{2}$

$\frac{5}{3}$

Correct answer:

Explanation:

The main fraction line means "divide." Rewrite the complex fraction like this:

$\frac{\frac{10}{3}}{\frac{5}{3}}=\frac{10}{3}\div\frac{5}{3}$

$\frac{10}{3}\div\frac{5}{3}=\frac{10}{3}\times\frac{3}{5}=\frac{30}{15}=2$

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Example Question #53 : Complex Fractions

Simplify: $\frac{\frac{1}{2}}{2}+\frac{2}{\frac{1}{2}}$

Possible Answers:

$\frac{5}{4}$

$\frac{17}{4}$

Correct answer:

$\frac{17}{4}$

Explanation:

Rewrite the expression using a division sign.

$\frac{\frac{1}{2}}{2}+\frac{2}{\frac{1}{2}}=\frac{1}{2}\div2+2 \div \frac{1}{2}$

Take the reciprocal of the term after the division signs and convert the division sign to a multiplication sign.

$\frac{1}{2}\times\frac{1}{2}+2 \times2=\frac{1}{4}+4=4\frac{1}{4}=\frac{17}{4}$

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Example Question #1 : How To Find The Whole From The Part

After a $25\%$ discount, a car costs $\$6,000$ . How much did the car cost before the discount?

Possible Answers:

$\$7,000$

$\$8,000$

$\$4,500$

$\$6,000$

Correct answer:

$\$8,000$

Explanation:

Let be the cost of the car before the discount. Since we know that the car at a discount costs $\$6,000$ , we can write the following equation:

x-0.25x=6000

Now, solve for to find the cost of the car before the discount.

0.75x=6000

$x=\frac{6000}{0.75}$

x=8000

The car originally cost $\$8,000$ before the $25\%$ discount was applied.

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Example Question #1 : How To Find The Whole From The Part

There are yellow marbles in a bag. If $12.5\%$ of the marbles in the bag are yellow, how many total marbles are in the bag?

Possible Answers:

Correct answer:

Explanation:

Let be the total number of marbles in the bag. Since we know that $12.5\%$ of the marbles are yellow, we can set up the following equation and solve for :

0.125x=10

$x=\frac{10}{0.125}$

x=80

There are total marbles in the bag.

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Example Question #3 : Whole And Part

Byron eats 600 calories for lunch. If he eats $25\%$ of his calories at lunch, what is the total number of calories he eats for the day?

Possible Answers:

2600

2400

2000

2200

Correct answer:

2400

Explanation:

Let be the total number of calories Byron eats in a day. With the information given in the question, we can write the following equation and solve for .

0.25x=600

$x=\frac{600}{0.25}$

x=2400

Byron eats 2400 calories for the day described in the question.

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Example Question #2 : How To Find The Whole From The Part

Max bought a t-shirt that was on sale at the store for $15\%$ . If he paid $\$15.00$ for the shirt, how much would the shirt have costed before the sale?

Possible Answers:

$\$18.15$

$\$16.75$

$\$17.65$

$\$20.12$

Correct answer:

$\$17.65$

Explanation:

Let be the cost of the t-shirt before it went on sale. With the information given in the question, we can write the following equation and solve for .

x-0.15x=15

This can be rewritten as:

1x-0.15x=15

0.85x=15

$x=\frac{15}{0.85}$

x=17.65

The shirt cost $\$17.65$ before the sale.

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Example Question #2 : How To Find The Whole From The Part

Roselyn spent $\$20.25$ when she bought a vacuum that was $18\%$ off. How much did the vacuum cost before the sale?

Possible Answers:

$\$24.10$

$\$26.50$

$\$25.00$

$\$24.70$

Correct answer:

$\$24.70$

Explanation:

Let be the cost of the vacuum before the sale. With the information given in the question, we can write the following equation and solve for .

x-0.18x=20.25

This can be rewritten as:

1x-0.18x=20.25

0.82x=20.25

$x=\frac{20.25}{0.82}$

x=24.70

The vacuum cost $\$24.70$ before it went on sale.

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Example Question #5 : Whole And Part

When Teresa saw that plane tickets to Hong Kong were $35\%$ off, she immediately bought a discounted ticket for $\$850$ . How much would the ticket have cost if tickets to Hong Kong were not on sale?

Possible Answers:

$\$1307.69$

$\$1102.29$

$\$1402.17$

$\$1207.69$

Correct answer:

$\$1307.69$

Explanation:

Let be the price of the non-discounted ticket. With the information given in the question, we can write the following equation and solve for .

x-0.35x=850

0.65x=850

$x=\frac{850}{0.65}$

x=1307.69

The plane ticket that Teresa bought would have cost $\$1307.69$ if it were not on sale.

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Example Question #7 : Whole And Part

There are red marbles in a bag. If $75\%$ of the marbles in the bag are red marbles, how many total marbles are in the bag?

Possible Answers:

Correct answer:

Explanation:

Let be the total number of marbles in the bag. With the information given in the question, we can write the following equation and solve for .

0.75x=12

$x=\frac{12}{0.75}$

x=16

There are total marbles in the bag.

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Number Concepts and Operations

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #161 : Number Concepts And Operations

Example Question #162 : Number Concepts And Operations

Example Question #53 : Complex Fractions

Example Question #1 : How To Find The Whole From The Part

Example Question #1 : How To Find The Whole From The Part

Example Question #3 : Whole And Part

Example Question #2 : How To Find The Whole From The Part

Example Question #2 : How To Find The Whole From The Part

Example Question #5 : Whole And Part

Example Question #7 : Whole And Part

All SSAT Upper Level Math Resources

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