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 #22 : How To Find The Part From The Whole With Percentage

The sales tax for a given city is 8.5%. How much will someone shopping there pay for $139.34 worth of groceries, after tax is figured in?

Possible Answers:

\(\displaystyle \$ 127.50\)

\(\displaystyle \$257.78\)

\(\displaystyle \$147.84\)

\(\displaystyle \$ 151.18\)

\(\displaystyle \$140.52\)

Correct answer:

\(\displaystyle \$ 151.18\)

Explanation:

To calculate the tax, multiply 8.5%. or, equivalently, 0.085, by $139.34, rounding to the nearest cent:

\(\displaystyle 139.34 \cdot 0.085 \approx 11.84\)

Add the tax to the price before tax:

\(\displaystyle 139.34 +11.84 = 151.18\)

The amount paid will be $151.18.

Example Question #2 : How To Work With Percentages

Exactly \(\displaystyle \frac{1}{3}\) of the plants in a garden are tomato plants.  Which of the following could be the total number of plants in the garden?

Possible Answers:

\(\displaystyle 22\)

\(\displaystyle 14\)

\(\displaystyle 20\)

\(\displaystyle 18\)

\(\displaystyle 16\)

Correct answer:

\(\displaystyle 18\)

Explanation:

The total number of plants has to be divisible by 3.  Of the answer choices, the only one that is divisible by 3 is 18.  You can check this because numbers that are divisible have the sum of their digits also divisible by 3. For example,

\(\displaystyle 1 + 8 = 9\) 

which is divisible by 3, so 18 is divisible by 3.

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

330 is 75% of what number?

Possible Answers:

\(\displaystyle 440\)

\(\displaystyle 420\)

\(\displaystyle 220\)

\(\displaystyle 400\)

\(\displaystyle 247 \frac{1}{2}\)

Correct answer:

\(\displaystyle 440\)

Explanation:

330 is 75% of a number we will call \(\displaystyle N\); alternatively, 0.75 multiplied by \(\displaystyle N\) is equal to 330. Set up this equation and solve for \(\displaystyle N\):

\(\displaystyle 0.75 N = 330\)

\(\displaystyle 0.75 N \div 0.75 = 330\div 0.75\)

\(\displaystyle N = 440\)

Example Question #1361 : Numbers And Operations

88 is \(\displaystyle 12 \frac{1}{2}\) % of what number? 

Possible Answers:

\(\displaystyle 74\)

\(\displaystyle 576\)

\(\displaystyle 22\)

\(\displaystyle 704\)

\(\displaystyle 11\)

Correct answer:

\(\displaystyle 704\)

Explanation:

We can rewrite \(\displaystyle 12 \frac{1}{2}\) % as 12.5%. 88 is 12.5% of a number \(\displaystyle N\), or, equivalently, 0.125 multiplied by a number \(\displaystyle N\) is equal to 88. We can write this as an equation and solve for \(\displaystyle N\):

\(\displaystyle 0.125 N = 88\)

\(\displaystyle 0.125 N \div 0.125 = 88 \div 0.125\)

\(\displaystyle N =704\)

Example Question #1362 : Numbers And Operations

32 is \(\displaystyle 2 \frac{1}{2}\) % of what number?

Possible Answers:

\(\displaystyle 800\)

\(\displaystyle \frac{4}{5}\)

\(\displaystyle 7\frac{7}{8}\)

\(\displaystyle 128\)

\(\displaystyle 1,280\)

Correct answer:

\(\displaystyle 1,280\)

Explanation:

We can rewrite \(\displaystyle 2 \frac{1}{2}\) % as 2.5%. 32 is 2.5% of a number \(\displaystyle N\), or, equivalently, 0.025 multiplied by a number \(\displaystyle N\) is equal to 32. We can write this as an equation and solve for \(\displaystyle N\):

\(\displaystyle 0.025 N = 32\)

\(\displaystyle 0.025 N \div 0.025 = 32 \div 0.025\)

\(\displaystyle N = 1,280\)

 

Example Question #2 : Percentages

To get on the ballot for student body president, a student must turn in a petition with the signatures of 3% of the students. If there are 5,319 students, how many signatures must a student get to be on that ballot? (Nearest whole person)

Possible Answers:

\(\displaystyle 1,596\)

\(\displaystyle 106\)

\(\displaystyle 1,064\)

\(\displaystyle 160\)

\(\displaystyle 220\)

Correct answer:

\(\displaystyle 160\)

Explanation:

3% of 5,319 can be calculated by multiplying 5,319 by 0.03, the decimal equivalent of 3%:

\(\displaystyle 5,319 \times 0.03 = ?\)

Multiply 5,319 by 3, then move the decimal point so that two digits are to the right:

\(\displaystyle 5,319 \times 3 =15,957\),

so

\(\displaystyle 5,319 \times 0.03 = 159.57\)

Rounded to the nearest whole number, this is 160 signatures.

Example Question #3 : How To Find The Whole From The Part With Percentage

3,200 is 160% of what number?

Possible Answers:

\(\displaystyle 2,000\)

\(\displaystyle 2,133\frac{1}{3}\)

\(\displaystyle 2,400\)

\(\displaystyle 5,120\)

\(\displaystyle 3,040\)

Correct answer:

\(\displaystyle 2,000\)

Explanation:

Set up the proportion statement and solve for \(\displaystyle N\) by cross-multiplying:

\(\displaystyle \frac{3,200}{N}= \frac{160}{100}\)

\(\displaystyle N \cdot 160 = 3,200 \cdot 100 = 320,000\)

\(\displaystyle N \cdot 160 \div 160 = 320,000\div 160\)

\(\displaystyle N = 2,000\)

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

12 is \(\displaystyle \frac{3}{4} \%\) of what number?

Possible Answers:

\(\displaystyle 1,600\)

\(\displaystyle 900\)

\(\displaystyle \frac{9}{100}\)

\(\displaystyle 9\)

\(\displaystyle 16\)

Correct answer:

\(\displaystyle 1,600\)

Explanation:

Set up the proportion statement and solve for \(\displaystyle N\) by cross-multiplying:

\(\displaystyle \frac{12}{N } = \frac{\frac{3}{4}}{100}\)

\(\displaystyle \frac{3}{4} \cdot N = 12 \cdot 100 = 1,200\)

\(\displaystyle \frac{4}{3} \cdot \frac{3}{4} \cdot N = \frac{4}{3} \cdot 1,200\)

\(\displaystyle N = \frac{4,800}{3} =1,600\)

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

If 40 percent of a number is 44, what is 60 percent of the same number?

Possible Answers:

\(\displaystyle 26.4\)

\(\displaystyle 60\)

\(\displaystyle 66\)

\(\displaystyle 67\)

\(\displaystyle 10.6\)

Correct answer:

\(\displaystyle 66\)

Explanation:

To determine what 60 percent of the number is, one must first determine what the number is. To find the number, set up a proportion relating the original percentage and the value of the percentage where the top number is the fractional value and the bottom number is the total.

  • \(\displaystyle \frac{Portion}{Total}=\frac{40 percent}{100 percent}=\frac{44}{number}\)

Use cross multiplication to solve for the number.

  • \(\displaystyle 4400=40*x\)
  • \(\displaystyle 110=x\) 

Once the number is found, the new percentage can be found. There are two ways to do this: multiplication or a proportion.

  • Multiplication: \(\displaystyle 110*0.60 = 66\)
  • Proportion: \(\displaystyle \frac{60percent}{100percent}=\frac{x}{110}\)

 This means that 60 percent of the number is 66.

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

\(\displaystyle 128\) is \(\displaystyle 40\%\) of what number?

Possible Answers:

\(\displaystyle 320\)

\(\displaystyle 360\)

\(\displaystyle 300\)

\(\displaystyle 31\frac{1}{4}\)

\(\displaystyle 51 \frac{1}{5}\)

Correct answer:

\(\displaystyle 320\)

Explanation:

\(\displaystyle 128\) is \(\displaystyle 40\%\) of a number we will call \(\displaystyle N\); alternatively, \(\displaystyle 0.40\) multiplied by \(\displaystyle N\) is equal to \(\displaystyle 128\). Set up this equation and solve for \(\displaystyle N\):

\(\displaystyle 0.4 N = 128\)

\(\displaystyle 0.4 N \div 0.4 = 128\div 0.4\)

\(\displaystyle N= 320\)

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