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# ETS Additional Test 1st edition, Section 6, #5

**24**

*(Admin note: The text of this question may be found in Section 6, Page 84 of the first edition of the GRE PDF practice book, archived here: https://web.archive.org/web/20110605194015/http://www.ets.org/s/gre/pdf/practice_book_GRE_pb_revised_general_test.pdf)*

Usually I can get these average questions...not sure why I'm struggling on this one!

What is the best way to approach this question?

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200Textbook Approach:To do this one "by the book," we need to do some quick calculations with averages. Let's take a look at how we'd set up our scratch paper. As always, Record What You Know:Next let's do a quick average review:

Average = Sum of All Numbers ÷ Number of Numbers

The next step is to fill in the blanks we know here to try to figure out what we don't know:

What's the missing info here? The sums! So let's calculate those next.

23 ∙ 100 = Sum of 100 Numbers

27 ∙ 50 = Sum of 50 Numbers

2300 = Sum of 100 Numbers

1350 = Sum of 50 Numbers

Now let's ask ourselves what we'd need to do to calculate the average of all 150. Remind yourself of the average equation:

Average = Sum of All Numbers ÷ Number of Numbers

Average of all 150 Numbers = Sum of all 150 Numbers ÷ 150

Do we know the sum of all 150 numbers? Yes. It's 3650. So:

Average of all 150 Numbers = 3650 ÷ 150

Average of all 150 Numbers = 24 ¹/3

Problem Solving/Logic Approach:Notice what's going on with our averages here. We're bringing up the overall average by adding a new set of numbers. We start with 100 numbers and an average of 23. The new 50 numbers have an average of 27.We wish to compare the overall average to 25.

Key observation: What would it take to bring the overall average up to 25? Will 50 more numbers with an average of 27 be enough to bring the whole average up to 25?

No, it would take

100 more numbers with an average of 27 to bring the overall average up to 25.

Think about it this way: the average of 23 and 27 is 25. If we have more 23s than 27s, we're going to be stuck closer to 23 in the overall average.

Therefore, without doing any calculations, you can observe that the overall average won't get up to 25, and the answer is B.