SAT Math: Arithmetic

The sum of 9 consecutive integers is 3150.  What is the value of the least of these integers?


Knowsys Method

Read the problem carefully.  This is a grid in question.  Instead of bubbling in a letter, you will bubble in your answer.  You should always guess on grid in questions because, unlike multiple choice questions, grid in questions do not have a wrong answer penalty.

Identify the bottom line.   the value of the least integer = ? 

Assess your options.  You could start guessing and trying, but the more effective method will be to use a method.  In this type of problem, there is a method that will make it super simple.  Do you know it?  

Attack the problem.  

The issue of the least or the greatest or any integer in between does not matter until we actually have a starting point.  These questions will always involve an odd number of integers (here, 9).  So, all we have to do is divide the sum by the number of integers to get the average integer. Sound familiar?  It should!  This is just another use of the average formula.  

The Average Formula: 

average formula.gif

In this particular problem we know the sum = 3150 and the number is 9.  Let's just plug in to get:

20140211 SAT average question.gif

When we solve for x, we get 350.

That tells us that the middle number (= the median) = 350.  Since we want the LEAST integer, count back 4 more:  349, 348, 347, 346.  Found it!  

Note:  If the problem had asked for the GREATEST integer, we would have counted up 4:  351, 352, 353, 354.  

Loop back.  Verify that you solved for the bottom line.

The correct answer is 346.  Grid it in.

Level = Medium  

Want some help reviewing the math concepts you need to master?  Try these Knowsys resources:

  1. Knowsys Pre-Algebra Flashcards
  2. Knowsys Algebra I Flashcards
  3. Knowsys SAT & ACT Math Practice book.  

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