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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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SAT Math: Data Analysis

Median

Screen Shot 2014-01-23 at 4.56.27 PM.jpg

The table above shows the number of students enrolled at Allenville Middle School from 2005 to 2011.  If the median enrollment over these seven years was 789, and no two years had the same number of students enrolled, what is the lowest possible value for y?

Knowsys Method

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!

Read the problem carefully.   Review the definitions of important terms.  The median is the middle number in a set of numbers.

Identify the bottom line.  lowest possible y = ?

Assess your options.  There is only one possible method for solving this problem, and it is demonstrated below.

Attack the problem.  Whenever you are working with medians, you should start by putting the list of numbers in order.

737  755  776  789  804  811  

Now you need to determine where y should fall in the list.  The problem tells you that 789 is the median,  and no two years had the same enrollment, so y must be greater than 789.  The smallest that y can be, therefore, is 790.

Loop back.  Check to verify that you have solved for the bottom line.

The correct answer is 790.

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.  

Subscribe to Knowsys SAT & ACT Blog by Email