It is currently 16 Jan 2018, 13:43

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# When a person aged 39 is added to a group of n people, the average age

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139205 [0], given: 12779

When a person aged 39 is added to a group of n people, the average age [#permalink]

### Show Tags

19 Aug 2015, 01:03
Expert's post
10
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

73% (01:29) correct 27% (02:28) wrong based on 168 sessions

### HideShow timer Statistics

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. What is the value of n?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

Kudos [?]: 139205 [0], given: 12779

Intern
Joined: 16 Jun 2015
Posts: 34

Kudos [?]: 24 [2], given: 0

Concentration: Strategy, Social Entrepreneurship
GMAT 1: 760 Q50 V42
WE: Information Technology (Other)
Re: When a person aged 39 is added to a group of n people, the average age [#permalink]

### Show Tags

19 Aug 2015, 01:34
2
KUDOS
1
This post was
BOOKMARKED

Let's assume that the total no. of people is n and the initial average is x.

So we can assume that the total sum of ages would be nx initially.

When the guy aged 39 is added to the total, the new sum of ages would be (nx+39). The new average now would be (nx+39)/n+1. We already know that now the average(x) is increased by 2. so we can equate the two above saying:

(nx+39)/(n+1) = x+2
solving this equation:
nx+39=(x+2)(n+1)
nx+39=nx +x +2n+2

we get,

2n+x=37

When the guy aged 15 is added to the total, the new sum of ages would be (nx+15). The new average now would be (nx+15)/n+1. We already know that now the average(x) is decreased by 1. so we can equate the two above saying:

(nx+15)/(n+1) = x-1

we get

x-n=16

solving the two equation simultaneously, we get n's value as 7.

Kudos [?]: 24 [2], given: 0

Manager
Joined: 21 Jan 2015
Posts: 149

Kudos [?]: 121 [0], given: 24

Location: India
Concentration: Strategy, Marketing
WE: Marketing (Other)
Re: When a person aged 39 is added to a group of n people, the average age [#permalink]

### Show Tags

19 Aug 2015, 01:55
1
This post was
BOOKMARKED
Bunuel wrote:
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. What is the value of n?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

Ans: A

Solution: lets say avg is x so total is (xn):
now with the first condition
(nx+39)/n+1 = x+2
2n+x = 37 Eq.1

with second condition
(nx+15)/n+1 = x-1
x-n = 16 Eq.2

by solving Eq1 and Eq2 we can find out n=7
_________________

--------------------------------------------------------------------
The Mind is Everything, What we Think we Become.
Kudos will encourage many others, like me.
Thanks

Kudos [?]: 121 [0], given: 24

Senior Manager
Joined: 28 Feb 2014
Posts: 295

Kudos [?]: 146 [3], given: 133

Location: United States
Concentration: Strategy, General Management
When a person aged 39 is added to a group of n people, the average age [#permalink]

### Show Tags

19 Aug 2015, 10:29
3
KUDOS
3
This post was
BOOKMARKED
When a person aged 39 is added to a group of n people, the average age increases by 2.
(Sum+39)/(n+1) = avg+2

When a person aged 15 is added instead, the average age decreases by 1.
(Sum+15)/(n+1) = avg-1

We can take the 1st equation and subtract from the 2nd equation to isolate n.
24=3n+3
n=7

(A) 7

Kudos [?]: 146 [3], given: 133

Current Student
Joined: 21 Nov 2014
Posts: 40

Kudos [?]: 10 [2], given: 35

Location: India
Concentration: General Management, Strategy
GMAT 1: 750 Q51 V40
WE: Operations (Energy and Utilities)
Re: When a person aged 39 is added to a group of n people, the average age [#permalink]

### Show Tags

19 Aug 2015, 11:56
2
KUDOS
2
This post was
BOOKMARKED
A simple and elegant solution.

As addition of 39, shifts mean by 2, and addition of 15, shifts mean by 1 to the other side, we have the mean lying between 39 & 15, and in a ratio of 2:1

39-15 = 24
24 divide by 3 is 8.

Meaning mean of the n terms is 15+8 = 39-16 = 23

Now, from first statement, When a person aged 39 is added to a group of n people, the average age increases by 2.

n*23 +39 = 25*(n+1)

n = 7

Ans. (A)

Kudos [?]: 10 [2], given: 35

Math Expert
Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139205 [1], given: 12779

Re: When a person aged 39 is added to a group of n people, the average age [#permalink]

### Show Tags

23 Aug 2015, 11:58
1
KUDOS
Expert's post
3
This post was
BOOKMARKED
Bunuel wrote:
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. What is the value of n?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

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.
_________________

Kudos [?]: 139205 [1], given: 12779

Retired Moderator
Joined: 12 Aug 2015
Posts: 2329

Kudos [?]: 988 [1], given: 678

GRE 1: 323 Q169 V154
When a person aged 39 is added to a group of n people, the average age [#permalink]

### Show Tags

08 Dec 2016, 20:40
1
KUDOS
1
This post was
BOOKMARKED
Here is my solution to this one -->
Let the original Mean = $$p$$
Thus original sum = $$p*n$$
Where $$n$$ is the number of people in the original set.
we need to get

As per question =>
$$\frac{p*n+39}{n+1} = p+2$$
$$p+2n=37$$-> Equation 1

Also
$$\frac{p*n+15}{n+1} = p-1$$

Hence $$p-n=16$$--> Equation 2

Hence using the two equations (1 and 2)
$$n=7$$

Hence A
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 988 [1], given: 678

Retired Moderator
Joined: 12 Aug 2015
Posts: 2329

Kudos [?]: 988 [0], given: 678

GRE 1: 323 Q169 V154
Re: When a person aged 39 is added to a group of n people, the average age [#permalink]

### Show Tags

09 Dec 2016, 03:14
One more method -->

Let Mean=p
APQ=> 2(n+1)=39-p
Hence p+2n=37

Also -1(n+1)=15-p
Hence p=16+n
Clearly Both of these Equations are as the above method.

To know Everything about Mean or Statistics in general, refer to this Post -->

_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 988 [0], given: 678

Non-Human User
Joined: 09 Sep 2013
Posts: 14272

Kudos [?]: 291 [0], given: 0

Re: When a person aged 39 is added to a group of n people, the average age [#permalink]

### Show Tags

28 Dec 2017, 10:07
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 291 [0], given: 0

Re: When a person aged 39 is added to a group of n people, the average age   [#permalink] 28 Dec 2017, 10:07
Display posts from previous: Sort by