SAT Math: Arithmetic

Consecutive Integers

If the sum of 5 consecutive positive integers is 145, what is the value of the largest integer? 


Note: In the math section of the SAT, you will encounter questions that do not have answer choices.  Instead of bubbling in a letter, you will bubble in your answer.  These questions are called grid in questions, and you should always guess an answer for them because there is no penalty for getting the question wrong!


Knowsys Method

Read the question carefully.  First, let's identify key terms.  An integer is a whole number (positive, negative, or zero).  Consecutive integers follow in a sequence and have a difference equal to 1 between each number.  An example of five consecutive integers is 3, 4, 5, 6, 7.  Be sure to note that you are looking for the largest number in this series of consecutive integers.

Identify the bottom line.  The largest number in a series of consecutive integers that all add up to 145.

Assess your options.  There are two methods that you could use to solve this problem.  The first method is to use division to find the middle number in the series.  The second method is to use an equation.  See both methods explained below.  

Attack the problem. 

Method 1: Division

Any time you see a problem set up like this one, you can divide the sum by the number of integers to get the value of the middle integer.  Divide 145 by 5 to get 29.  Then add 2 to 29 to get 31, the largest integer. 

Method 2: Set up an equation

You know that there is a difference of 1 between each integer, so if the largest integer in the series is n, then the next largest integer would be n - 1, and the third largest would be n - 2, and so on.

Set up an equation in which all five integers add up to 145.  Your equation should look like this:

    n + (n - 1) + (n - 2) + (n - 3) + (n - 4) = 145

Combine like terms and solve for n.

    5n - 10 = 145
          +10    +10
           5n = 155
           ÷5     ÷5
             n =  31

Loop back.  Have you found the largest number in the series of consecutive integers?  Yes.  Now that you are sure that you have solved for the bottom line, bubble in your answer choice.

The answer to this question is: 31

This is a medium level question.


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