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KarishmaB
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When a person aged 39 is added to a group of n people, the average age 08 Apr 2019, 04:12
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rencsee
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What is the first thing you can say about the initial average? It must have been between 39 and 15. When a person aged 39 is added to the group, the average increases and when a person aged 15 is added, the average decreases.

Let’s look at the second case first. When the person aged 15 is added to the group, the average becomes (initial average – 1). If instead, the person aged 39 were added to the group, there would be 39 – 15 = 24 extra which would make the average = (initial average + 2). This difference of 24 creates a difference of 3 in the average. This means there must have been 24/3 = 8 people (after adding the extra person). The value of n must be 8 – 1 = 7.

Hi Bunuel,

I'm trying to understand the distribution of the numbers deviating from the average, but I'm far away from confident with this approach yet.

In case of this post, it is clear that the mean is between [15,39]

If (n*Av+39)/(n+1)=Av+2 -> adding 39, creates a difference of 2 in the Av (each number increased by 2)
If (n*Av+15)/(n+1)=Av-1 -> adding 15, creates a difference of 1 in the Av (each number decreased by 1)

using both of the given numbers -> 39-15=24 -> the Av is around 24 with a difference of 3 in the Av? How do we get this 3? Because we used both 39 and 15, the absolute difference from Av is 2+1?

I'm very confused here. Thank you for your help in advance!
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Think of it in another way:

There are n people.
When you add one person aged 15, you get n+1 people.
Say the average of these n+1 people is p. (which is 1 less than original)
If instead of 15 yrs old, this (n+1)th person were 39 yrs old, average would be 2 more than original. Can we say that this would be (p + 3) ?

So if you increase the age of a person from 15 to 39 (i.e. add 24), the average increases by 3. So you must be giving 3 extra to 8 people to account for the extra 24.

Hence (n+1) = 8
So n = 7
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When a person aged 39 is added to a group of n people, the average age 08 Apr 2019, 04:14
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energetics
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Imagine a number line (if you are familiar with VeritasKarishma posts on weighted average)... think about it like we are dealing with absolute value i.e. the 'distance' from the Average.

___1x<------->2x___
15 ------ Avg ------- 39

Adding 15 gives Avg - 1, the Avg is 'pulled' to the left because 15 is less than the Avg
Adding 39 gives Avg + 2, Avg is 'pulled' to the right because 39 is more than the Avg

Now, subtract the 15,

___1x<------->2x___
0 ------ Avg ------- 24

The 'pull' from 0 to the Avg is still 1, and the 'pull' from the Avg to 24 is still 2. This is because the distance covered stays the same in a ratio of 1x:2x.
Thus, the total from 0 to 24 would be 3x = 24 --> x = 8, hence n+1 = 8 and originally n = 7, A.


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Sound logic!
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When a person aged 39 is added to a group of n people, the average age 09 Jun 2019, 06:42
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VeritasKarishma, Bunuel
Hi, Need to practice more questions like this.. Can you guys help?
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When a person aged 39 is added to a group of n people, the average age 09 Jun 2019, 21:18
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asfandabid
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Hi, Need to practice more questions like this.. Can you guys help?
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Use the GC advanced search feature to find more questions on averages:
https://gmatclub.com/forum/advanced-search/
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When a person aged 39 is added to a group of n people, the average age 24 May 2020, 04:40
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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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When a person aged 39 is added to a group of n people, the average age 08 Feb 2022, 01:23
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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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When a person aged 39 is added to a group of n people, the average age 04 Mar 2022, 13:44
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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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When a person aged 39 is added to a group of n people, the average age 17 Oct 2022, 07:23
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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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When a person aged 39 is added to a group of n people, the average age 17 Oct 2022, 15:55
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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 ?
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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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When a person aged 39 is added to a group of n people, the average age 17 Oct 2022, 16:21
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kntombat
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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 ?
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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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When a person aged 39 is added to a group of n people, the average age Updated on: 24 Aug 2023, 05:37
Originally posted by KarishmaB on 18 Oct 2022, 23:24.
Last edited by KarishmaB on 24 Aug 2023, 05:37, edited 1 time in total.
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kntombat
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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 ?
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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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When a person aged 39 is added to a group of n people, the average age 10 Dec 2022, 07:19
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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


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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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A

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When a person aged 39 is added to a group of n people, the average age 10 Dec 2022, 13:51
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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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When a person aged 39 is added to a group of n people, the average age 02 Mar 2025, 04:53
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