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# The average (arithmetic mean) of 10, 30, and 50 is 5 more

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Math Expert
Joined: 02 Sep 2009
Posts: 46129
The average (arithmetic mean) of 10, 30, and 50 is 5 more [#permalink]

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01 Oct 2012, 05:05
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81% (00:40) correct 19% (00:43) wrong based on 929 sessions

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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and

(A) 15
(B) 25
(C) 35
(D) 45
(E) 55

Practice Questions
Question: 53
Page: 159
Difficulty: 600

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Re: The average (arithmetic mean) of 10, 30, and 50 is 5 more [#permalink]

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01 Oct 2012, 05:05
1
SOLUTION

The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and

(A) 15
(B) 25
(C) 35
(D) 45
(E) 55

The average of 10, 30, and 50 is $$\frac{10+30+50}{3}=30$$.

The average of 20, 40 and x must be 30-5=25, so the sum of these 3 numbers must be 3*25=75 --> 20+40+x=75 --> x=15.

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Re: The average (arithmetic mean) of 10, 30, and 50 is 5 more [#permalink]

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01 Oct 2012, 05:29
1
The average of 10 30 50 is $$\frac{A = 10+30+50}{3}$$ $$= 30$$
The second Average must be 5 less : 25. Using common sense or back solve we can obtain the solution.

Starting with A because we need a small value in the difference.

So,$$\frac{A = 20+40+15}{3}$$ $$= 25$$

thanks
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Re: The average (arithmetic mean) of 10, 30, and 50 is 5 more [#permalink]

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01 Oct 2012, 19:47
1
The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and
(A) 15
(B) 25
(C) 35
(D) 45
(E) 55

Average of 10,30,50 = 30
Average of 20,40 & x = 25
so 60 + x = 75----> x = 15
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Re: The average (arithmetic mean) of 10, 30, and 50 is 5 more [#permalink]

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04 Oct 2012, 00:47
3

Since 10, 30 and 50 are numbers in equally spaced sets, average is 30

Now 30 is 5 greater than 25 ....Thus average of 20, 40 and (x) is 25 ......This implies, sum of 3 numbers should be 75 to make the average = 25

Thus, answer is 15 = 75 - 20 - 40
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Joined: 07 Apr 2014
Posts: 119
Re: The average (arithmetic mean) of 10, 30, and 50 is 5 more [#permalink]

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10 Sep 2014, 19:08
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and

(A) 15
(B) 25
(C) 35
(D) 45
(E) 55

Practice Questions
Question: 53
Page: 159
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

10+30+50 = 90

90/3=30.

so mean of 20+40+x should be 25...

25*3=75(total),

60+x=75

x=15.
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The average (arithmetic mean) of 10, 30, and 50 is 5 more [#permalink]

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10 Sep 2014, 22:54
1
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and

(A) 15
(B) 25
(C) 35
(D) 45
(E) 55

Algebraic Method (Forming single equation for result)

$$\frac{10 + 30 + 50}{3} = \frac{20 + 40 + x}{3} + 5$$

x = 15

Shortcut (By observation) Method

10, 30, 50 are equally spaced; so average = 30

For the other set, required average would be 30 - 5 = 25

It means total = 75

Required number = 75 - (20+40) = 15
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Re: The average (arithmetic mean) of 10, 30, and 50 is 5 more [#permalink]

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30 May 2016, 05:24
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and

(A) 15
(B) 25
(C) 35
(D) 45
(E) 55

Let’s first determine the average of 10, 30, and 50, using the average formula.

average = sum/quantity

average = (10+30+50)/3

average = 90/3

average = 30

We can now rephrase the question to ask: "30 is 5 more than the average of 20, 40, and what value?" Let’s label the missing value as n and create an equation.

30 = (20+40+n)/3 + 5

25 = (20+40+n)/3

75 = 60 + n

15 = n

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Re: The average (arithmetic mean) of 10, 30, and 50 is 5 more [#permalink]

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30 May 2016, 06:15
[quote="Bunuel"]The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and

(A) 15
(B) 25
(C) 35
(D) 45
(E) 55
/quote]

avg of (10, 30, 50) = (10+30+50)/ 3 = 30.

Avg of next set = 25.

There are 3 nos. So sum of those 3 nos. = 25 * 3 = 75.
Third number = 75 - 20-40 = 15

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Re: The average (arithmetic mean) of 10, 30, and 50 is 5 more [#permalink]

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17 Dec 2016, 17:30
Here is my solution to this one =>

Mean(1) = 30 (Notice that it is an AP series so the median will be the mean)

Mean(2)=$$\frac{60+x}{3}$$

As per question
$$30=\frac{60+x}{3} +5$$
Hence x=15
Hence A

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Re: The average (arithmetic mean) of 10, 30, and 50 is 5 more [#permalink]

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28 Dec 2016, 17:42
$$a1 : \frac{90}{3} = 30$$
a2: $$25 = \frac{60 + x}{3}$$
x = 15
A
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Re: The average (arithmetic mean) of 10, 30, and 50 is 5 more [#permalink]

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01 Apr 2017, 09:48
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and

(A) 15
(B) 25
(C) 35
(D) 45
(E) 55

Practice Questions
Question: 53
Page: 159
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide for GMAT® Review, 13th Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

(10+30+50)/3 - (20+40+x)/3= 5
30-(60+x)/3=5
x=90-75=15
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Posts: 2559
Re: The average (arithmetic mean) of 10, 30, and 50 is 5 more [#permalink]

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13 Sep 2017, 09:02
Top Contributor
Bunuel wrote:
The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and

(A) 15
(B) 25
(C) 35
(D) 45
(E) 55

Let x = the missing (required number)
Average of 10, 30, and 50 = (10 + 30 + 50)/3 = 90/3 = 30
Average of 20, 40, and x = (20 + 40 + x)/3 = (60 + x)/3

The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and
So, 30 = (60 + x)/3 + 5
Subtract 5 from both sides to get: 25 = (60 + x)/3
Multiply both sides by 3 to get: 75 = 60 + x
Solve: x = 15

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Re: The average (arithmetic mean) of 10, 30, and 50 is 5 more   [#permalink] 13 Sep 2017, 09:02
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