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PSAT Math : Arithmetic

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Example Questions

Example Question #151 : Arithmetic

Simplify x/2 – x/5

Possible Answers:

3x/10

5x/3

3x/7

7x/10

2x/7

Correct answer:

3x/10

Explanation:

Simplifying this expression is similar to 1/2 – 1/5. The denominators are relatively prime (have no common factors) so the least common denominator (LCD) is 2 * 5 = 10. So the problem becomes 1/2 – 1/5 = 5/10 – 2/10 = 3/10.

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Example Question #1 : How To Simplify A Fraction

If $\dpi{100} \small \frac{p}{6}$ is an integer, which of the following is a possible value of $\dpi{100} \small p$ ?

Possible Answers:

$\dpi{100} \small 0$

$\dpi{100} \small 2$

$\dpi{100} \small 3$

$\dpi{100} \small 4$

$\dpi{100} \small 16$

Correct answer:

$\dpi{100} \small 0$

Explanation:

$\dpi{100} \small \frac{0}{6}=0$ , which is an integer (a number with no fraction or decimal part). All the other choices reduce to non-integers.

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Example Question #632 : Arithmetic

Simplify: $\frac{4x^{5}y^{3}z}{12x^{3}y^{6}z^{2}}$

Possible Answers:

$\frac{x^{2}}{3y^{3}z}$

$\frac{1}{3x^{2}y^{3}z}$

$\frac{3x^{2}y^{3}}{z}$

$\frac{x^{2}}{8y^{3}z}$

Correct answer:

$\frac{x^{2}}{3y^{3}z}$

Explanation:

$\frac{4x^{5}y^{3}z}{12x^{3}y^{6}z^{2}}=\frac{x^{2}}{3y^{3}z}$

First, let's simplify $\frac{4}{12}$ . The greatest common factor of 4 and 12 is 4. 4 divided by 4 is 1 and 12 divided by 4 is 3. Therefore $\frac{4}{12}=\frac{1}{3}$ .

To simply fractions with exponents, subtract the exponent in the numerator from the exponent in the denominator. That leaves us with $\frac{1}{3}x^{2}y^{-3}z^{-1}$ or $\frac{x^{2}}{3y^{3}z}$

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Example Question #1 : How To Simplify A Fraction

Which of the following is not equal to 32/24?

Possible Answers:

160/96

224/168

16/12

96/72

4/3

Correct answer:

160/96

Explanation:

24/32 = 1.33

16/12 =1.33

224/168 =1.33

4/3 = 1.33

96/72 = 1.33

160/96 = 1.67

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Example Question #1 : Simplifying Fractions

Find the root of

$y=\frac{x^2-\sqrt3x+\sqrt5x-\sqrt{15}}{x-\sqrt3}$

Possible Answers:

$\sqrt3$

$-\sqrt{5 }$

$\sqrt5$

Can not be determined

$-\sqrt3$

Correct answer:

$-\sqrt{5 }$

Explanation:

$y=\frac{x^2-\sqrt3x+\sqrt5x-\sqrt{15}}{x-\sqrt3}=\frac{(x-\sqrt3)(x+\sqrt5)}{x-\sqrt3}=x+\sqrt5$

The root occurs where y=0 . So we substitute 0 for .

$y=x+\sqrt{5}$

$0=x+\sqrt{5}$

This means that the root is at $x=-\sqrt5$ .

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Example Question #22 : General Fractions

Which of the following fractions is not equivalent to $\frac{6}{45}$ ?

Possible Answers:

$\frac{4}{30}$

$\frac{3}{22.5}$

$\frac{2}{15}$

$\frac{12}{89}$

Correct answer:

$\frac{12}{89}$

Explanation:

Let us simplify $\frac{6}{45}$ :

$\frac{6}{45}=\frac{3\times 2}{3\times 15}=\frac{2}{15}$

We can get alternate forms of the same fraction by multiplying the denominator and the numerator by the same number:

$\frac{2\times 2}{15\times 2}=\frac{4}{30}$

$\frac{2\times 1.5}{15\times 1.5}=\frac{3}{22.5}$

Now let's look at $\frac{12}{89}$ :

$6 \times 2 = 12$ , but $45 \times 2 = 90$ .

Therefore, $\frac{12}{89}$ is the correct answer, as it is not equivalent to $\frac{6}{45}$ .

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Example Question #152 : Fractions

Marker Colors	Students
Blue	13
Pink	10
Orange	5
Brown	5
Green	7

The above chart shows the number of students in a class who chose each of the five marker colors available.

What fraction of the class selected a pink marker OR a brown marker?

Possible Answers:

$\frac{1}{2}$

$\frac{2}{8}$

$\frac{1}{3}$

$\frac{1}{4}$

$\frac{3}{8}$

Correct answer:

$\frac{3}{8}$

Explanation:

To solve this problem, you must do three things: find out how many students selected a pink OR brown marker, make that a fraction with the total number of students in the class as the denominator, then simplify that fraction. Shown below:

Students who chose pink OR brown:

Pink: , Brown:

Total students:

10+5=15

Total students in the class:

13+10+5+5+7 = 40

Make it a fraction:

$\frac{15}{40}$

Simplify. To simplify a fraction, you must find the greatest common factor (GCF), then divide both the numerator and the denominator by the GCF. For and , the GCF is , because it is the largest number that goes into both numbers.

$\frac{15}{40}\div \frac{5}{5} = \frac{3}{8}$

The answer is $\frac{3}{8}$ .

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Example Question #1 : Ordering Fractions

Which of the following is greater than 1/2 ?

Possible Answers:

2/5

4/9

9/19

8/17

6/11

Correct answer:

6/11

Explanation:

There are two ways to deal with fractions. One way is to convert them all to decimals. (By using your calculator, divide the numerator by the denominator). Using this method all you would need to do is to see which is greater than 0.5. Otherwise to see which is greater than 1/2, double the numerator and see if the result is greater than the denominator. In B, the correct answer, doubling the numerator gives us 12, which is bigger than 11.

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Example Question #1 : Fractions

Which of the following has the greatest value?

Possible Answers:

65%

52%

4/7

5/8

Correct answer:

65%

Explanation:

If all are converted to decimals, 0.65 is the biggest.

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Example Question #2 : Fractions

Which fraction falls between ½ and 3/4?

Possible Answers:

4/5

1/3

3/6

6/8

5/8

Correct answer:

5/8

Explanation:

The easiest method is to put each of these fractions into a calculator, and then place them in order on a number line to see which value falls in between 1/2 = 0.5 and ¾ = 0.75. Without a calculator you must do long division to find the value of the numerator (top number) divided by the denominator (bottom number) for each fraction. You can actually eliminate answers b. and d. because they are equal to 1/2 and ¾ respectively. 4/5= 0.80, 3/6 = 0.5, 5/8= 0.625, 6/8 = 0.75.

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PSAT Math : Arithmetic

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #151 : Arithmetic

Example Question #1 : How To Simplify A Fraction

Example Question #632 : Arithmetic

Example Question #1 : How To Simplify A Fraction

Example Question #1 : Simplifying Fractions

Example Question #22 : General Fractions

Example Question #152 : Fractions

Example Question #1 : Ordering Fractions

Example Question #1 : Fractions

Example Question #2 : Fractions

All PSAT Math Resources

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