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PSAT Math : PSAT Mathematics

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Example Questions

Example Question #2 : Operations With Fractions

If a car travels at 30 mph, how many feet per second does travel?

Possible Answers:

440 ft/s

2,640 ft/s

44 ft/s

264 ft/s

4,400 ft/s

Correct answer:

44 ft/s

Explanation:

30 miles / 1 hour * 5280 ft / 1 mile * 3600 seconds / 1 hour = 44 ft/sec

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Example Question #1 : How To Multiply Fractions

In a group of 20 children, 25% are girls. How many boys are there?

Possible Answers:

Correct answer:

Explanation:

Since $\dpi{100} \small \frac{1}{4}$ of the children are girls, this totals to $\dpi{100} \small 20 \times \frac{1}{4} = 5$ girls in the group.

$\dpi{100} \small 20-5=15$ boys.

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Example Question #121 : Fractions

$\frac{5}{7}*\frac{6}{4}*\frac{12}{2}$

Possible Answers:

$\frac{45}{7}$

$\frac{18}{7}$

$\frac{104}{28}$

$\frac{15}{4}$

$\frac{33}{13}$

Correct answer:

$\frac{45}{7}$

Explanation:

Remember, when you multiply fractions, you can directly multiply their denominators and their numerators; therefore, you can begin this problem by making it into one large fraction:

$\frac{5}{7}*\frac{6}{4}*\frac{12}{2} = \frac{5*6*12}{7*4*2}$

Now, you could multiply all of this out and then divide. However, you can cancel things immediately. The goes into the and the into the . Thus, you have:

$\frac{5*6*12}{7*4*2} = \frac{5*3*3}{7}=\frac{9*5}{7}=\frac{45}{7}$

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Example Question #122 : Fractions

Simplify:

$\frac{15}{8}*\frac{12}{5}*\frac{1}{3}*14$

Possible Answers:

$\frac{21}{14}$

$\frac{14}{21}$

$\frac{41}{21}$

Correct answer:

Explanation:

First, begin by remembering that is the same as $\frac{14}{1}$ :

$\frac{15}{8}*\frac{12}{5}*\frac{1}{3}*\frac{14}{1}$

Next, recall that you multiply fractions by multiplying the numerators and denominators by each other. It is very simple. This would give you:

$\frac{15}{8}*\frac{12}{5}*\frac{1}{3}*\frac{14}{1}=\frac{15*12*1*14}{8*5*3}$

Now, you can cancel the and the 5*3 :

$\frac{15*12*1*14}{8*5*3} = \frac{12*14}{8}$

Next, you can reduce the and the :

$\frac{3*14}{2}$

You can also reduce the resulting and the :

$\frac{3*7}{1}=21$

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Example Question #1 : How To Add Fractions

Jesse has a large movie collection containing X movies. 1/3 of his movies are action movies, 3/5 of the remainder are comedies, and the rest are historical movies. How many historical movies does Jesse own?

Possible Answers:

(4/15)*X

(3/9)*X

(7/12)*X

(2/5)*X

(11/15)*X

Correct answer:

(4/15)*X

Explanation:

1/3 of the movies are action movies. 3/5 of 2/3 of the movies are comedies, or (3/5)*(2/3), or 6/15. Combining the comedies and the action movies (1/3 or 5/15), we get 11/15 of the movies being either action or comedy. Thus, 4/15 of the movies remain and all of them have to be historical.

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Example Question #12 : Operations With Fractions

If x = 1/3 and y = 1/2, find the value of 2x + 3y.

Possible Answers:

5/6

6/5

13/6

Correct answer:

13/6

Explanation:

Substitute the values of x and y into the given expression:

2(1/3) + 3(1/2)

= 2/3 + 3/2

= 4/6 + 9/6

= 13/6

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Example Question #131 : Arithmetic

Alternating1

Possible Answers:

$\dpi{100} -\frac{47}{60}$

$\dpi{100} -\frac{43}{60}$

$\dpi{100} \frac{47}{60}$

$\dpi{100} \frac{17}{60}$

$\dpi{100} \frac{43}{60}$

Correct answer:

$\dpi{100} \frac{47}{60}$

Explanation:

Alternating2

Alternating3

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Example Question #131 : Arithmetic

Solve $\frac{3}{7}+\frac{5}{8}-\frac{1}{2}$ .

Possible Answers:

$\frac{31}{56}$

$\frac{7}{8}$

$\frac{33}{56}$

$\frac{5}{7}$

Correct answer:

$\frac{31}{56}$

Explanation:

Finding the common denominator yields $\frac{24}{56}+\frac{35}{56}-\frac{28}{56}$ . We can then evaluate leaving $\frac{31}{56}$ .

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Example Question #612 : Arithmetic

What is the solution, reduced to its simplest form, for $x = \frac{7}{9}+\frac{3}{5}+\frac{2}{15}+\frac{7}{45}}$ ?

Possible Answers:

$x = \frac{75}{45}$

$x = \frac{7}{15}$

$x = \frac{115}{45}$

$x = \frac{5}{3}$

$x =2$

Correct answer:

$x = \frac{5}{3}$

Explanation:

$x=\frac{7}{9}+\frac{3}{5}+\frac{2}{15}+\frac{7}{45}=\frac{35}{45}+\frac{27}{45}+\frac{6}{45}+\frac{7}{45}=\frac{75}{45}=\frac{5}{3}$

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Example Question #3 : How To Add Fractions

What is the sum of $\small \frac{4}{5}$ and $\small 2 \frac{5}{6}$ ?

Possible Answers:

$\small \frac{49}{12}$

$\small \frac{49}{109}$

$\small \frac{79}{30}$

$\small \frac{30}{109}$

$\small \frac{109}{30}$

Correct answer:

$\small \frac{109}{30}$

Explanation:

We can begin by eliminating the obviously wrong answers. We know that the sum of the two fractions will be more than 1, so the answer choices $\tiny \tiny \frac{49}{109}$ and $\small \frac{30}{109}$ are out. Now, let's add the two fractions:

Begin by converting $\small 2 \frac{5}{6}$ to $\tiny \frac{17}{6}$ .

Now find the common denominator of $\small \frac{4}{5}$ and $\tiny \frac{17}{6}$ . The least common multiple of 5 and 6 is 30, so 30 is the common denominator. Now alter both fractions so that they use the common denominator:

$\tiny \small \frac{4}{5}= \frac{4*6}{5*6}=\frac{24}{30}$

$\tiny \small \frac{17}{6}=\frac{17*5}{6*5}=\frac{85}{30}$

Now we can easily add the two fractions together:

$\small \frac{24}{30}+\frac{85}{30}=\frac{109}{30}$

The answer is $\small \frac{109}{30}$ .

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PSAT Math : PSAT Mathematics

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #2 : Operations With Fractions

Example Question #1 : How To Multiply Fractions

Example Question #121 : Fractions

Example Question #122 : Fractions

Example Question #1 : How To Add Fractions

Example Question #12 : Operations With Fractions

Example Question #131 : Arithmetic

Example Question #131 : Arithmetic

Example Question #612 : Arithmetic

Example Question #3 : How To Add Fractions

All PSAT Math Resources

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