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# What is the average (arithmetic mean) of a, b, and c ?

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Math Expert
Joined: 02 Sep 2009
Posts: 50586
What is the average (arithmetic mean) of a, b, and c ?  [#permalink]

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10 Jul 2018, 20:29
00:00

Difficulty:

35% (medium)

Question Stats:

72% (00:59) correct 28% (01:25) wrong based on 43 sessions

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What is the average (arithmetic mean) of a, b, and c ?

(1) a + 2b + 3c = 10

(2) 3a + 2b + c = 14

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What is the average (arithmetic mean) of a, b, and c ?  [#permalink]

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10 Jul 2018, 20:40
1
Bunuel wrote:
What is the average (arithmetic mean) of a, b, and c ?

(1) a + 2b + 3c = 10

(2) 3a + 2b + c = 14

Basically we need the value of $$a+b+c$$, to determine the average

Statement 1: $$a+2b+3c=10$$ cannot be factorized to get $$a+b+c$$. Insufficient

Statement 2: $$3a+2b+c=14$$ cannot be factorized to get $$a+b+c$$. Insufficient

Combining 1 & 2: add the two equations to get $$4a+4b+4c=24 => a+b+c=6$$. Sufficient

Option C
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Re: What is the average (arithmetic mean) of a, b, and c ?  [#permalink]

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10 Jul 2018, 21:12
Bunuel wrote:
What is the average (arithmetic mean) of a, b, and c ?

(1) a + 2b + 3c = 10

(2) 3a + 2b + c = 14

Combining (1) (2), we have
a + 2b + 3c +3a + 2b + c =4(a+b+c)=24
Now, AM(a,b,c)=$$\frac{(a+b+c)}{3}$$=$$\frac{24}{4*3}$$
So, AM of a,b, and c is 2.
Sufficient.

Ans. (C)
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PKN

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Re: What is the average (arithmetic mean) of a, b, and c ?  [#permalink]

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12 Jul 2018, 09:48
Bunuel wrote:
What is the average (arithmetic mean) of a, b, and c ?

(1) a + 2b + 3c = 10

(2) 3a + 2b + c = 14

Avg=(a+b+c)/3

From Equation A, we neither find value of individual variable(a,b,c) nor we can find the sum (a+b+b+c)

From Equation B also we can not find value of individual variable(a,b,c) or the sum (a+b+b+c)

Using both equation:-
4(a+b+c)=10;
=> (a+b+c)=10/4

so the avg will be 10/12
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Re: What is the average (arithmetic mean) of a, b, and c ?  [#permalink]

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12 Jul 2018, 09:52
Hi PKGMAT,
4(a+b+c)=10+14=24.

Posted from my mobile device
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Regards,

PKN

Rise above the storm, you will find the sunshine

Re: What is the average (arithmetic mean) of a, b, and c ? &nbs [#permalink] 12 Jul 2018, 09:52
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