SAT Math: Arithmetic


If the sum of 3 consecutive integers is 300, what is the value of the middle integer?

A.  99

B.  100

C.  101

D.  150

E.  297


Knowsys Method

Read the question carefully.  What is actually going on in this problem?  Three different whole numbers that are consecutive are added together in order to get the number 300.

Identify the bottom line.  You only need to find the middle number.

Assess your options.   You could pick three different numbers in a row and start adding them up to see which set will give you the answer 300, but that will take a lot of guess work.  Instead, there is a much easier method.  You only want to find the middle number.  Simply divide the sum by the number of integers in the set.

Attack the problem.  Your sum is 300 and there are 3 different integers.  Divide 300 by 3 and you find the middle number.  The answer is 100.  

This method will always work.  If it seems too simple to you, you can double check it now so that you will feel confident of your answer on the test. What are the 3 integers?  These numbers are 99 + 100 + 101 = 300.  Your middle number is still 100.

Loop back.  You found the middle integer, not the lowest or highest in your list of consecutive integers, so you are ready to select your answer. 

The correct answer is (B).

This question is a medium level question.


Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  


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