ACT Math : How to add odd numbers

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : Integers

Solve:  

Possible Answers:

Correct answer:

Explanation:

Add the ones digits:

Since there is no tens digit to carry over, proceed to add the tens digits:

The answer is .

Example Question #82 : Integers

At a certain high school, everyone must take either Latin or Greek. There are  more students taking Latin than there are students taking Greek. If there are  students taking Greek, how many total students are there?

Possible Answers:

Correct answer:

Explanation:

If there are  students taking Greek, then there are  or  students taking Latin. However, the question asks how many total students there are in the school, so you must add these two values together to get:

 or  total students.

Example Question #1 : Integers

Find the sum of 13 and 19.

Possible Answers:

Correct answer:

Explanation:

Rewrite the question in a mathematical expression.

Add the ones digit.

Since this number is larger than , carry over the  in tens digit when adding the next term.

Add the tens digit with the carry over.

Combine the tens digit and the ones digit. The answer is .

Example Question #2 : Integers

Possible Answers:

 

 

 

Correct answer:

 

Explanation:

In order to get an odd result from an addition, we must have one odd and one even number, thus you know from the first point about  that only one of the two values is odd. Now, to get an even result, you can have two evens or two odds. So, let's presume that  has two odd values, this means that  must be even. Thus, you have:

Now, if we presume that  has two even values, we must then know that  is odd.  Thus, we have:

First of all, you can eliminate the two answers that say that a given value is positive or negative. This cannot be told from our data. Next, it cannot be the case that  is even. It will always be odd (hence, the correct answer is this). Finally, it cannot be that  is even always. In the second case above, you will have two even numbers added together, given you an even. Then, you will add in an odd, giving you an odd.

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