Source: Official Guide Revised GRE 1st Ed. Part 6; Set 4; #7

1

It if were discovered that the value

It if were discovered that the value of imports shown for 2007 was incorrect and should have been $5 billion instead, then the average (arithmetic mean) value of imports per year for the 10 years shown would have been approximately how much less? $200 million, $50 million, $20 million, $7 million, $5 million

3 Explanations

2

Gravatar Niloufar Hafizi, Magoosh Tutor

Hello Peng,

Good question! How come we cannot cancel out intermediate years the way we did in Question 5 from this same data set?

In Q5, we are asked about the **average of the changes in the values of imports** between 2000 and 2009. So we were calculating the average in this way:

* Average of changes = [(Change from 2000 to 2001) + (Change from 2001 to 2002) + (Change from 2002 to 2003) + (Change from 2003 to 2004) + (Change from 2004 to 2005) + (Change from 2005 to 2006) + (Change from 2006 to 2007) + (Change from 2007 to 2008) + (Change from 2008 to 2009)]/9 changes

--->

* [(2000 import value - 2001 import value) + (2001 import value -2002 import value) + (2002 import value - 2003 import value) + (2003 import value - 2004 import value) + (2004 import value - 2005 import value) + (2005 import value - 2006 import value) + (2006 import value - 2007 import value) + (2007 import value - 2008 import value) + (2008 import value - 2009 import value)]/9

Simplifies to:

* (2000 import value - 2009 import value)/9

See how all of the values except for the 2000 import value and the 2009 import value cancel out because we are averaging the changes in the values of the imports? If we were asked about the average of the values of the imports each year, we would not be able to do this.

This question in fact does ask for the actual average of the import values for the years 2000 to 2009 -- not for the average of the yearly changes. So we are averaging values for each year, not changes:

* Average of values = (2000 import value + 2001 import value + 2002 import value + 2003 import value + 2004 import value + 2005 import value + 2006 import value + 2007 import value + 2008 import value + 2009 import value)/10

Nothing cancels out. They're all individual values that have to be taken into consideration for the average.

Hope that helps explain the differences in set-up!

Apr 22, 2015 • Comment

2

Gravatar Jonathan , Magoosh Tutor

Hi Alicia,
The question is asking about the average for the 10-year period shown. Each year has its own positive value. For example, in 2004 we have 4 billion and in 2009 we have 9 billion. The average for the 10 years is the sum of the 10 numbers for each of 2000 through 2009 divided by 10.

When we change the number for 2007, we are changed one number included in that sum -- we are decreasing the total by 2 billion. 2 billion divided by 10 is 200 million, so that's how much the average decreases. I hope this helps? :)

Mar 29, 2015 • Comment

2

Gravatar Chris Lele, Magoosh Tutor

Oct 9, 2012 • Comment

PENG WANG

Hi Chris, thanks for the explanation. But I don't understand why the answer is not 0? I mean, when we calculated the total change over the ten years, we have added and subtracted the import for 2007, so why does the import for 2007 affect the total sum?

Jul 28, 2014 • Reply

Alicia Scott

I have the same question as Wang. We didn't use individual year numbers in the original problem, so why would the year 2007 change the answer?

Mar 15, 2015 • Reply

Add Your Explanation

You must have a Magoosh account in order to leave an explanation.

Learn More About Magoosh