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HSPT Math : Word Problems

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Example Questions

Example Question #31 : Word Problems

Worker graphs

Six friends work for a company as maintenance staff.

Above are six graphs. Each graph shows the distance that one of the six is from his home from 8 AM to 9 AM on a particular day, relative to the time. The time of day is represented by the horizontal axis, and the distance from home is represented by the vertical axis. The name of the person represented by each graph is under the graph.

Of the six, who got halfway there, got sick, and returned home?

Possible Answers:

Mr. Cleese

Mr. Palin

Mr. Chapman

Mr. Gilliam

Correct answer:

Mr. Gilliam

Explanation:

The person's distance increased as he drove to work, but decreased as he returned home. This describes the graph for Mr. Gilliam.

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Example Question #32 : Word Problems

Worker graphs

Six friends work for a company as maintenance staff.

Of the six, who took the express train directly to work?

Possible Answers:

Mr. Palin

Mr. Cleese

Mr. Jones

Mr. Chapman

Correct answer:

Mr. Cleese

Explanation:

The distance from home of the worker in question would have increased steadily without any interruption. The graph with the constantly increasing line is the one to choose; this graph belongs to Mr. Cleese.

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Example Question #33 : Word Problems

Worker graphs

Six friends work for a company as maintenance staff.

Of the six, which one called in sick at 7:30 AM and stayed in bed?

Possible Answers:

Mr. Palin

Mr. Jones

Mr. Cleese

Mr. Gilliam

Correct answer:

Mr. Jones

Explanation:

Someone who called in sick would remain at constant zero distance from his home during the entire time. This would be represented by a horizontal line along the zero axis; this describes the graph for Mr. Jones.

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Example Question #34 : Word Problems

On a map, one half of an inch represents forty miles of real distance.

It takes John 90 minutes to get from Kingsbury to Willoughby driving an average of miles per hour. How many inches apart, in terms of , are the two cities on the map?

Possible Answers:

$\frac{3}{160}R$

$\frac{1}{60}R$

$\frac{1}{120}R$

$\frac{3}{80}R$

Correct answer:

$\frac{3}{160}R$

Explanation:

The distance in real miles between Kingsbury in Willoughby can be found by multiplying rate miles per hour by time 90 minutes, or one and a half hours:

$R \cdot 1 \frac{1}{2} = \frac{3}{2}R$

Let represent map distance between the cities, One half of an inch represents forty miles of real distance, so one inch represents twice this, ir eighty miles. The ratio that compares map distance and real distance is

$\frac{d}{ \frac{3}{2}R} = \frac{ 1}{80}$

$\frac{d}{ \frac{3}{2}R} \cdot \frac{3}{2}R = \frac{1}{80} \cdot \frac{3}{2}R$

$d = \frac{3}{160}R$

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Example Question #474 : Problem Solving

On a map, one half of an inch represents thirty miles of real distance.

The towns of Waterbury and Nashua are three and one half inches apart on this map. How long, in hours, would it take for someone to drive from Waterbury to Nashua if his speed averaged miles per hour?

Possible Answers:

$\frac{7N}{30}$

$\frac{30}{7N}$

$\frac{210}{N}$

$\frac{N}{210}$

Correct answer:

$\frac{210}{N}$

Explanation:

On a map, one half of an inch represents thirty miles of real distance, so one inch represents twice this, or sixty miles. The actual distance from Waterbury to Nashua, which is three and a half inches on the map, is

$60 \cdot 3 \frac{1}{2}=60 \cdot \frac{7}{2} = \frac{420}{2} = 210$

Therefore, the two cities are 210 miles apart. Divide the distance by the rate to get the time:

$210 \div N$ , or $\frac{210}{N}$ .

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Example Question #474 : Hspt Mathematics

John is driving to his parents house on the highway going 45 mph. If he travels for 6 hours, how long was the trip?

Possible Answers:

$300\textup{ miles}$

$325\textup{ miles}$

$275\textup{ miles}$

$270 \textup{ miles}$

$250\textup{ miles}$

Correct answer:

$270 \textup{ miles}$

Explanation:

You will use the distance formula of,

$\textup{rate}\times \textup{time = distance}$ .

Identify the rate and time that is given.

$\\ \textup{rate}=45 \textup{ mph} \\ \textup{time}=6\textup{ hours}$

From here, substitute the known information into the formula to calculate distance.

$\\ \textup{rate}\times \textup{time = distance} \\45\times 6=$

First to find the ones digit multiply the ones digits together.

$5\times 6=30$

Carry the three to the tens digit. Now, to find the tens and hundreds digit, multiply six by four and then add in the three that was carried.

$4\times6=24$

24+3=27

Placing these numbers in their appropriate places results in the following solution.

$270 \textup{ miles}$

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Example Question #34 : Word Problems

What is the prime factorization of 48?

Possible Answers:

$\dpi{100} 2\cdot 2\cdot 2\cdot 2\cdot 3$

$\dpi{100} 2\cdot 24$

$\dpi{100} 4\cdot 12$

$\dpi{100} 2\cdot 2\cdot 12$

Correct answer:

$\dpi{100} 2\cdot 2\cdot 2\cdot 2\cdot 3$

Explanation:

We can find the prime factorization of a number by dividing 48 into smaller numbers.

$\dpi{100} 48=2\times 24$

2 is prime

$\dpi{100} 24=2\times 12$

2 is prime

$\dpi{100} 12=2\times 6$

2 is prime

$\dpi{100} 6=2\times 3$

Both 2 and 3 are prime.

So we have four 2's and one 3. Multiply these numbers to get 48.

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Example Question #2 : How To Do Other Word Problems

What is the least common multiple of 6 and 8?

Possible Answers:

$\dpi{100} 48$

$\dpi{100} 16$

$\dpi{100} 12$

$\dpi{100} 24$

Correct answer:

$\dpi{100} 24$

Explanation:

One easy way to find the least common multiple is to take the largest of the numbers given to you, and find its multiples.

8: 8, 16, 24, 32, 40, 48...

Now start with 8, and see if any of these numbers is divisible by 6. The first number that is divisible by 6 is the least common multiple of 6 and 8.

8: No

16: No

24: Yes

24 is the least common multiple of 6 and 8.

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Example Question #35 : Word Problems

How many whole numbers are between $\dpi{100} \frac{16}{5}$ and $\dpi{100} \frac{50}{7}$ ?

Possible Answers:

$\dpi{100} 4$

$\dpi{100} 6$

$\dpi{100} 3$

$\dpi{100} 2$

Correct answer:

$\dpi{100} 4$

Explanation:

Convert each fraction to a mixed number.

$\dpi{100} \frac{16}{5}=3\frac{1}{5}$

$\dpi{100} \frac{50}{7}=7\frac{1}{7}$

So how many whole numbers are between $\dpi{100} 3\frac{1}{5}$ and $\dpi{100} 7\frac{1}{7}$ ?

4, 5, 6, and 7 would fall between these two numbers. 3 would not. So there are 4 total whole numbers between them.

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Example Question #36 : Word Problems

What is the next number in this progression?

18, 10, 2, -6

Possible Answers:

Correct answer:

Explanation:

This is an arithmetic progression. Therefore you must add or subtract a number to the number before it to arrive at the next number. We must find the difference between each number and apply it to the final number to find the next number in the series.

To start, take the second number and subtract the first number.

In this case it yields 10-18=-8

Then take the third number and subtract the second number which results in 2-10=-8

If the resulting number is the same you now know the difference between each number in the sequence and can apply the difference to each resulting number.

In this case the difference is

So we take the final number and add the difference to it to result with -6+-8=-14

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HSPT Math : Word Problems

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #31 : Word Problems

Example Question #32 : Word Problems

Example Question #33 : Word Problems

Example Question #34 : Word Problems

Example Question #474 : Problem Solving

Example Question #474 : Hspt Mathematics

Example Question #34 : Word Problems

Example Question #2 : How To Do Other Word Problems

Example Question #35 : Word Problems

Example Question #36 : Word Problems

All HSPT Math Resources

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