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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 #4 : How To Find The Part From The Whole

Jeremy bought $\$10.21$ $\displaystyle \$10.21$ worth of toothpaste. At the checkout, he found that he had a coupon that would take $20\%$ $\displaystyle 20\%$ off the cost of the toothpaste. How much will Jeremy pay for the toothpaste if he uses the coupon?

Possible Answers:

$\$8.17$ $\displaystyle \$8.17$

$\$2.81$ $\displaystyle \$2.81$

$\$2.04$ $\displaystyle \$2.04$

$\$9.13$ $\displaystyle \$9.13$

Correct answer:

$\$8.17$ $\displaystyle \$8.17$

Explanation:

Subtract the amount the coupon would take off from the total amount the toothpaste would cost.

$\$10.21-(0.2\times\$10.21)=\$8.17$ $\displaystyle \$10.21-(0.2\times\$10.21)=\$8.17$

If Jeremy uses the coupon, the toothpaste will cost $\$8.17$ $\displaystyle \$8.17$ .

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Example Question #17 : Whole And Part

The tax on the sale of a house worth $\$150,560$ $\displaystyle \$150,560$ was $\$22,584$ $\displaystyle \$22,584$ . What was the tax rate?

Possible Answers:

$9\%$ $\displaystyle 9\%$

$15\%$ $\displaystyle 15\%$

$5\%$ $\displaystyle 5\%$

$11\%$ $\displaystyle 11\%$

Correct answer:

$15\%$ $\displaystyle 15\%$

Explanation:

To find the tax rate, divide the tax amount by the total worth of the house.

$22584\div150560=0.15$ $\displaystyle 22584\div150560=0.15$

Now, convert this decimal into a percentage.

$0.15\cdot\frac{100}{100}=\frac{15}{100}=15\%$ $\displaystyle 0.15\cdot\frac{100}{100}=\frac{15}{100}=15\%$

The tax rate on this house sale is $15\%$ $\displaystyle 15\%$ .

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Example Question #18 : Whole And Part

If Hannah needs to pay a $12\%$ $\displaystyle 12\%$ tax on her yearly income of $\$36,000$ $\displaystyle \$36,000$ , how much does she need to pay for the tax?

Possible Answers:

$\$3,240$ $\displaystyle \$3,240$

$\$4,221$ $\displaystyle \$4,221$

$\$4,320$ $\displaystyle \$4,320$

$\$5,600$ $\displaystyle \$5,600$

Correct answer:

$\$4,320$ $\displaystyle \$4,320$

Explanation:

Multiply $\$36,000$ $\displaystyle \$36,000$ by 0.12 $\displaystyle 0.12$ to find the amount Hannah needs to pay in taxes.

$\$36,000\times0.12=\$4,320$ $\displaystyle \$36,000\times0.12=\$4,320$

Hannah needs to pay $\$4,320$ $\displaystyle \$4,320$ in taxes.

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Example Question #1251 : Ssat Upper Level Quantitative (Math)

A dress goes on sale for $32\%$ $\displaystyle 32\%$ off. If the dress originally cost $\$34$ $\displaystyle \$34$ , how much does it cost while it is on sale?

Possible Answers:

$\$24.12$ $\displaystyle \$24.12$

$\$22.00$ $\displaystyle \$22.00$

$\$23.12$ $\displaystyle \$23.12$

$\$19.52$ $\displaystyle \$19.52$

Correct answer:

$\$23.12$ $\displaystyle \$23.12$

Explanation:

Subtract the amount discounted from the original cost of the dress to find its sale price.

$34-(0.32\times34)=23.12$ $\displaystyle 34-(0.32\times34)=23.12$

The dress cost $\$23.12$ $\displaystyle \$23.12$ on sale.

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Example Question #6 : How To Find The Part From The Whole

Initially, $\displaystyle m$ number of students were going to chip in to buy their teacher a present that cost $\displaystyle d$ dollars. If $\displaystyle y$ students decide not to pay, which of the following expressions represent how much each remaining student must now pay?

Possible Answers:

$\frac{m-y}{d}$ $\displaystyle \frac{m-y}{d}$

$\frac{d}{y-m}$ $\displaystyle \frac{d}{y-m}$

$\frac{d}{m-y}$ $\displaystyle \frac{d}{m-y}$

$\frac{m}{d}$ $\displaystyle \frac{m}{d}$

Correct answer:

$\frac{d}{m-y}$ $\displaystyle \frac{d}{m-y}$

Explanation:

To determine how much each person must pay, we will need to divide the total dollar amount by the number of people paying.

Before some students decided not to pay, the amount each person would have to pay is represented by the following expression:

$\frac{d}{m}$ $\displaystyle \frac{d}{m}$

Now, since $\displaystyle y$ students dropped out, we need to subtract that from the number of people who will be paying.

$\text{Cost per student}=\frac{d}{m-y}$ $\displaystyle \text{Cost per student}=\frac{d}{m-y}$

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Example Question #11 : How To Find The Part From The Whole

Pauline has $\displaystyle 20$ pieces of candy. If she eats $25\%$ $\displaystyle 25\%$ of the candy then accidentally drops $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of the remaining amount on the ground, how many pieces of candy does she have left?

Possible Answers:

$\displaystyle 15$

$\displaystyle 5$

$\displaystyle 10$

$\displaystyle 12$

Correct answer:

$\displaystyle 10$

Explanation:

First, find out how many pieces of candy Pauline has after eating $25\%$ $\displaystyle 25\%$ of them.

$20-(0.25\times20)=15$ $\displaystyle 20-(0.25\times20)=15$

Now, she loses $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of this remaining amount. Since $\frac{1}{3}$ $\displaystyle \frac{1}{3}$ of $\displaystyle 15$ is $\displaystyle 5$ , that means that her new total is 15 - 5 = 10 pieces of candy.

Pauline is left with 10 pieces of candy.

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Example Question #1252 : Ssat Upper Level Quantitative (Math)

Janice had $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ of a cup of milk. If she used $\frac{1}{12}$ $\displaystyle \frac{1}{12}$ cup to make some scrambled eggs, how much of a cup of milk does she have left?

Possible Answers:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

Correct answer:

$\frac{2}{3}$ $\displaystyle \frac{2}{3}$

Explanation:

Subtract the two fractions. To subtract them, they must have a common denominator. Multiply the numerator and denominator of $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ by $\displaystyle 3$ to create a common denominator of $\displaystyle 12$ , then subtract the numerators and reduce the resulting fraction.

$\frac{3}{4}-\frac{1}{12}=\frac{9}{12}-\frac{1}{12}=\frac{8}{12}=\frac{2}{3}$ $\displaystyle \frac{3}{4}-\frac{1}{12}=\frac{9}{12}-\frac{1}{12}=\frac{8}{12}=\frac{2}{3}$

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Example Question #1 : Operations With Fractions

What is the result of this operation?

$\frac{3}{4}-\frac{1}{4}=?$ $\displaystyle \frac{3}{4}-\frac{1}{4}=?$

Possible Answers:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\displaystyle 1$

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

$\frac{2}{7}$ $\displaystyle \frac{2}{7}$

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

Correct answer:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Explanation:

Since the denominators are exactly the same, we can just subtract the tops.

$\frac{3}{4}-\frac{1}{4}=\frac{2}{4}$ $\displaystyle \frac{3}{4}-\frac{1}{4}=\frac{2}{4}$

By reducing we get

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

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Example Question #2 : Operations With Fractions

What is the result of this operation?

$\frac{2}{7}-\frac{1}{7}=?$ $\displaystyle \frac{2}{7}-\frac{1}{7}=?$

Possible Answers:

$\displaystyle 0$

$\frac{2}{7}$ $\displaystyle \frac{2}{7}$

$\frac{4}{7}$ $\displaystyle \frac{4}{7}$

$\frac{1}{7}$ $\displaystyle \frac{1}{7}$

$\frac{3}{7}$ $\displaystyle \frac{3}{7}$

Correct answer:

$\frac{1}{7}$ $\displaystyle \frac{1}{7}$

Explanation:

Since the denominators are the same, we can just subtract the numerators.

$\frac{2}{7}-\frac{1}{7}=\frac{1}{7}$ $\displaystyle \frac{2}{7}-\frac{1}{7}=\frac{1}{7}$

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Example Question #3 : Operations With Fractions

What is the result of this operation?

$\frac{4}{9}-\frac{1}{9}=?$ $\displaystyle \frac{4}{9}-\frac{1}{9}=?$

Possible Answers:

$\displaystyle 3$

$\frac{4}{9}$ $\displaystyle \frac{4}{9}$

$\frac{1}{9}$ $\displaystyle \frac{1}{9}$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\frac{2}{9}$ $\displaystyle \frac{2}{9}$

Correct answer:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Explanation:

Since the denominators are the same, we can just subtract the numerators.

$\frac{4}{9}-\frac{1}{9}=\frac{3}{9}$ $\displaystyle \frac{4}{9}-\frac{1}{9}=\frac{3}{9}$

By reducing our result, we get

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

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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 #4 : How To Find The Part From The Whole

Example Question #17 : Whole And Part

Example Question #18 : Whole And Part

Example Question #1251 : Ssat Upper Level Quantitative (Math)

Example Question #6 : How To Find The Part From The Whole

Example Question #11 : How To Find The Part From The Whole

Example Question #1252 : Ssat Upper Level Quantitative (Math)

Example Question #1 : Operations With Fractions

Example Question #2 : Operations With Fractions

Example Question #3 : Operations With Fractions

All SSAT Upper Level Math Resources

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