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VeritasKarishma, Bunuel
Hi, Need to practice more questions like this.. Can you guys help?

Use the GC advanced search feature to find more questions on averages:
https://gmatclub.com/forum/advanced-search/
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HI,
i hope i am right here:
what i did is, since adding 39 is mean +2, and adding 15 is mean -1:
39-m/n+1=+2
15-m/n+1=-1
solving for N=> N=7
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Given: When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1.

Asked: What is the value of n?
Let the average of n people be x.

When a person aged 39 is added to a group of n people, the average age increases by 2.
nx + 39 = (n+1)(x+2) = nx + 2n + x + 2
2n + x =37

When a person aged 15 is added instead, the average age decreases by 1.
nx + 15 = (n+1)(x-1) = nx + x - n - 1
x - n = 16

n = (37-16)/3 = 7

IMO A
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Let the average age be A years and let there be n people in the group

When a person aged 39 joins the group, new sum = An+39, and new average (An+39)/(n+1) = (A+2) Simplyfing this we get 37 = 2n+A

When a person aged 15 joins the group instead, new sum = An+15, and new average (An+15)/(n+1) = (A-1) Simplyfing this we get 16 = -n+A

Subtracting the two equations we get, 21=3n or n=7

Hence, option A.

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KarishmaB, Bunuel
How should one improve his/her logic so that many questions like these can be answered faster rather than trying to solve them by equations ?
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How should one improve his/her logic so that many questions like these can be answered faster rather than trying to solve them by equations ?

Hi kntombat,

Most GMAT questions are based on an established pattern of some kind (and sometimes more than one) - so thinking in terms of patterns can help you to move faster through a variety of different Quant and Verbal questions. With Average Formula questions, the patterns are typically about Arithmetic (specifically, "division"). When you divide one number by another number (which is what the Average Formula ultimately is), you usually do NOT end up with an integer. That decimal (or fraction or remainder) often provides a big clue about the denominator of that fraction. IF, when doing that division, you actually DO end up with an integer, then that too provides a big clue (this time about how the denominator relates to the numerator - the denominator has to be a factor of the numerator). With certain PS questions, the answer choices can also be used to avoid working through step-heavy, Algebraic calculations, meaning that you should also take advantage of that additional 'information' any time it's available.

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How should one improve his/her logic so that many questions like these can be answered faster rather than trying to solve them by equations ?


Very good question! and this is really hard to be able to not get bogged down and rather to step out and see if there is a better approach than the first thing that jumps out at you. It takes skill and practice and patience and confidence. Most people will not be able to do this on the test unless they feel very confident and comfortable but frankly, most people don't need to do it either as they won't reach a very hard question like that.
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How should one improve his/her logic so that many questions like these can be answered faster rather than trying to solve them by equations ?

I like to work with logical approaches so I never start with "let the number of people be x" or something like that. Note that it is a skill that takes time so I wish schools focussed on these but they don't. But if one has a few months in hand, these approaches can certainly be learned. The upside is that they come in handy throughout your life. You start making sense of complicated looking concepts and formulas (especially in Finance & Stats).
I do discuss a lot of these approaches in my blog: https://anaprep.com/blogs/

Check the video discussing Arithmetic Mean here: https://youtu.be/W-qhIZ29UIs
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EMPOWERgmatRichC really not clear about the logic- If we add 15 and 39 yr olds then we basically add 2 people. Not clear on how and why you have just subtracted the two numbers and distributed 24 and that too by 3 . We do not even know whether 15 is average in order to say that 39-15 is an excess to be distributed among n+1 people. Overall the approach is not clear at all pls explain. avigutman


EMPOWERgmatRichC
Hi All,

We're told that the average age of a group of N people INCREASES BY 2 if one more person aged 39 joins the group and instead DECREASES BY 1 if one more person aged 15 joins the group. We're asked for the value of N. This question can be solved in a number of different ways, including with a bit of 'number logic' and TESTing THE ANSWERS.

To start, it's interesting the average increases or decreases by an exact INTEGER (often, we'd see a change that creates a decimal), so the numbers 39 and 15 impact the average in a specific way - and the DIFFERENCE in those values (39 and 15) is something that we have to consider. Including an extra 39 instead of an extra 15 would increase the SUM by 24... and again, would lead to an increase in average of 3. This implies that the NEW number of people (the original N people + 1) is a factor of 24. Based on the 5 answer choices, the likely answer is either 7 (which would be 8 people when the extra person is added) or 11 (which would be 12 people when the extra person is added).

Notice how 24 = (8)(3)... which would be the new number of people and the increase in the average (between when an extra 15 is included and when an extra 39 is included), so this is far more likely to be the situation that we're dealing with. Here's how to visualize that difference:

IF....
N=7 and the sum of those ages is X....
adding a 39 would give us a sum of (X+39)
adding a 15 instead would gives us a sum of (X+15)

The difference in those 2 situations is (X+39) - (X+15) = 24.
With 8 total people, the average would INCREASE by 24/8 = 3
This is exactly what happens in the situation described about, so this must be the answer.

Final Answer:
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Hi Elite097,

The prompt tells us two situations in which we add the age of a new person to an existing average:

-IF we add a '15' to the group, then the sum of the ages obviously increases by 15, but the average DECREASES by exactly 1.
-IF we add a '39' to the group, then the sum of the ages obviously increases by 39, but the average INCREASES by exactly 2.

The differences in those two pieces of information are what I discuss in my explanation (and to reiterate, we are thinking in terms of what happens if we add a 15 to the group).

IF we call the current sum "X", then adding 15 to that sum would give us (X+15). Adding a 39 INSTEAD of a 15 would increase that new sum by 24 (relative to what it was when we added the 15) and the new average would increase by 2 instead of decrease by 1 (which is a net-increase of 3 over what would happen if we included that extra 15).

Think about those differences: that net increase of 24 (re: from 15 to 39) leads to a net increase in the average of 3 (re: from a decrease of 1 to an increase of 2). We can use a variation on the Average Formula to organize that information:

(additional value added to sum)/(new number of terms) = +24/8 = new average increases by +3, meaning that adding another person increases the total number of people to 8 (and we started off with 7 people).

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