HSPT Math : How to do other word problems

Study concepts, example questions & explanations for HSPT Math

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Example Questions

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Example Question #1 : How To Do Other Word Problems

What is the prime factorization of 48?

Possible Answers:

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

\dpi{100} 4\cdot 12

\dpi{100} 2\cdot 24

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

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.

Example Question #2 : How To Do Other Word Problems

What is the least common multiple of 6 and 8?

Possible Answers:

\dpi{100} 12

\dpi{100} 48

\dpi{100} 16

\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.

Example Question #3 : How To Do Other Word Problems

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

Possible Answers:

\dpi{100} 3

\dpi{100} 6

\dpi{100} 4

\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.

Example Question #4 : How To Do Other 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 

Then take the third number and subtract the second number which results in 

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 

Example Question #5 : How To Do Other Word Problems

How many inches are in a foot?

Possible Answers:

Correct answer:

Explanation:

This is a conversion question.

There are 12 inches in a foot.

Example Question #6 : How To Do Other Word Problems

What is 

Possible Answers:

Correct answer:

Explanation:

When multiplying monomials with the same base, you add the powers of each monomial together.

So in this case 

Yielding an answer of 

Example Question #7 : How To Do Other Word Problems

Possible Answers:

Correct answer:

Explanation:

This tests your knowledge of scientific notation.

To solve you must move the decimal places to the right to the power of the ten.

In this case you must move the decimal place to the right 7 spaces from its original spot.

The solution is 



Example Question #8 : How To Do Other Word Problems

You have 5 types of meat, 3 different types of vegetables, and 8 different types of bread. How many different sandwiches can you make using only one of each ingredient?

Possible Answers:

Correct answer:

Explanation:

This is a combination question.

To find the total number of sandwiches using only one ingredient we create three spaces for each ingredient and place each number of possible ingredients into each space. 

We then multiply each number in each space together to find the answer 

 

Example Question #9 : How To Do Other Word Problems

The square of what number is 75 divided by 3?

Possible Answers:

Correct answer:

Explanation:

To answer this question we must first divide the original number by the number following it to get 

Once we have this number we then square root it to find the answer 

Example Question #10 : How To Do Other Word Problems

What is the absolute value of -57?

Possible Answers:

Correct answer:

Explanation:

Absolute values are always positive so the absolute value of a negative number is just the number without the minus sign.

In this case the answer is 

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