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PSAT Math : PSAT Mathematics

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Example Questions

Example Question #1711 : Psat Mathematics

Find the root of

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

Possible Answers:

$-\sqrt{5 }$

Can not be determined

$\sqrt5$

$-\sqrt3$

$\sqrt3$

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 #152 : Arithmetic

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

Possible Answers:

$\frac{4}{30}$

$\frac{2}{15}$

$\frac{12}{89}$

$\frac{3}{22.5}$

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 : Fractions

Which of the following is greater than 1/2 ?

Possible Answers:

2/5

4/9

9/19

6/11

8/17

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:

4/7

5/8

52%

65%

Correct answer:

65%

Explanation:

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

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Example Question #3 : Fractions

Which fraction falls between ½ and 3/4?

Possible Answers:

1/3

3/6

6/8

5/8

4/5

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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Example Question #1 : How To Order Fractions From Least To Greatest Or From Greatest To Least

If Ben is taller than Jaime, Mary is taller than Ben, and Chris is taller than Mary. Who is the second tallest?

Possible Answers:

Mary

Jaime

Ben

Chris

Not possible to tell

Correct answer:

Mary

Explanation:

Using math symbols to dictate height we find that Ben>Jaime, Mary>Ben, Chris>Mary. Putting these in order we have Chris>Mary, Mary>Ben, Ben>Jaime. This shows that Mary is the second tallest.

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Example Question #1 : Ordering Fractions

Order the following fractions in descending order.

¹/₂, ²/₃, ²/₅, ³/₄, ⁴/₇

Possible Answers:

³/₄, ²/₃, ⁴/₇, ¹/₂, ²/₅

²/₃, ⁴/₇, ³/₄, ¹/₂, ²/₅

¹/₂, ²/₃, ²/₅, ³/₄, ⁴/₇

²/₅, ¹/₂, ⁴/₇, ²/₃, ³/₄

²/₅, ¹/₂, ³/₄, ⁴/₇, ²/₃

Correct answer:

³/₄, ²/₃, ⁴/₇, ¹/₂, ²/₅

Explanation:

Method 1:

Find the common denominator (420) and convert each fraction to this denominator:

¹/₂ = 210/420

²/₃ = 280/420

²/₅ = 168/420

³/₄ = 315/420

⁴/₇ = 240/420

Now sort by numerator, largest to smallest.

Method 2:

Divide each fraction to obtain a decimal. Sort the decimals, largest to smallest.

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Example Question #1 : Fractions

Increasing_n1

Possible Answers:

I and II only

II and III only

II only

I only

I and III only

Correct answer:

I and III only

Explanation:

Increasing_n2

Increasing_n4

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Example Question #2 : Ordering Fractions

Which of the following fractions is between 0.2 and 0.3?

Possible Answers:

$\dpi{100} \small \frac{1}{4}$

$\dpi{100} \small \frac{1}{3}$

$\dpi{100} \small \frac{1}{2}$

$\dpi{100} \small \frac{1}{6}$

$\dpi{100} \small \frac{2}{3}$

Correct answer:

$\dpi{100} \small \frac{1}{4}$

Explanation:

$\dpi{100} \small \frac{1}{4}=0.25$

$\dpi{100} \small 0.2<0.25<0.3$

$\dpi{100} \small \frac{1}{6}\approx 0.167<0.2$

The other three choices are larger than 0.3.

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PSAT Math : PSAT Mathematics

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1711 : Psat Mathematics

Example Question #152 : Arithmetic

Example Question #152 : Fractions

Example Question #1 : Fractions

Example Question #1 : Fractions

Example Question #3 : Fractions

Example Question #1 : How To Order Fractions From Least To Greatest Or From Greatest To Least

Example Question #1 : Ordering Fractions

Example Question #1 : Fractions

Example Question #2 : Ordering Fractions

All PSAT Math Resources

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