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What is the average (arithmetic mean) of j and k ?

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What is the average (arithmetic mean) of j and k ? [#permalink]

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What is the average (arithmetic mean) of j and k ?

(1) The average (arithmetic mean) of j + 2 and k + 4 is 11.
(2) The average (arithmetic mean) of j, k, and 14 is 10.
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Re: What is the average (arithmetic mean) of j and k ? [#permalink]

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What is the average (arithmetic mean) of j and k ?

We need to find the value of \(\frac{j+k}{2}\).

(1) The average (arithmetic mean) of j + 2 and k + 4 is 11 --> \(\frac{(j+2)+(k+4)}{2}=11\) --> \(j+k=16\). Sufficient.
(2) The average (arithmetic mean) of j, k, and 14 is 10 --> \(\frac{j+k+14}{3}=10\) --> \(j+k=16\). Sufficient.

Answer: D.
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Re: What is the average (arithmetic mean) of j and k ? [#permalink]

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Re: What is the average (arithmetic mean) of j and k ? [#permalink]

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New post 21 Dec 2016, 17:33
Nice official Question.
Here is my solution to this one =>
In order to get the mean => we need the sum j+k

Statement 1=>
j+k=22-6=16
Hence sufficient

Statement 2=>
j+k=30-14=16
Hence sufficient

Hence D

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Re: What is the average (arithmetic mean) of j and k ? [#permalink]

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New post 02 Apr 2017, 07:20
Walkabout wrote:
What is the average (arithmetic mean) of j and k ?

(1) The average (arithmetic mean) of j + 2 and k + 4 is 11.
(2) The average (arithmetic mean) of j, k, and 14 is 10.



To find: (j+k)/2
(1) (j+2+k+4)/2 = 11
j+k+6=22
j+k=22-6

Sufficient

AD

(2) (j+k+14)/3=10
Again we get the value for j+k.

Sufficient

D
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Re: What is the average (arithmetic mean) of j and k ? [#permalink]

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New post 02 Apr 2017, 08:06
Walkabout wrote:
What is the average (arithmetic mean) of j and k ?

(1) The average (arithmetic mean) of j + 2 and k + 4 is 11.
(2) The average (arithmetic mean) of j, k, and 14 is 10.


Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

There are 2 variables \(i\), \(j\) and 0 equation are given from the conditions, so there is high chance (C) will be our answer.

For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority.

However, this question asks a relation between 2 variables, that is, \(\frac{j + k}{2}\). It might need less than 2 equations to solve.

Condition (1)
\(\frac{j + 2 + k + 4}{2} = 11\)
\(j + k + 6 = 22\)
\(j + k = 16\)
Hence, the average of \(j\) and \(k\) is \(\frac{j + k}{2} = 8\).

Condition (2)
\(\frac{j + k + 14}{3} = 10\)
\(j + k + 14 = 30\)
\(j + k = 16\)
Hence, the average of \(j\) and \(k\) is \(\frac{j + k}{2} = 8\).

Therefore, the correct answer is D.
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Re: What is the average (arithmetic mean) of j and k ?   [#permalink] 02 Apr 2017, 08:06
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