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Re: The average of 12 numbers 16. When one number is discarded and 15 is a [#permalink]

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19 Jun 2017, 11:48

Given data : The average of 12 number is 16, and one of the numbers(x) is removed.

The number which replaces x is 15, and this makes the overall average go up to 17(an increase of 1) x must be 12 lesser than 15 since the replacement of the number causes the average to go up 1. Hence, x = 15-12 = 3(Option A) _________________

Re: The average of 12 numbers 16. When one number is discarded and 15 is a [#permalink]

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19 Jun 2017, 19:39

Sum of 12 numbers=16*12=192 When one number is discarded and 15 is added then sum= 17*12=204 Let the number discarded be x 192-x+15=204 207-x=204 Hence x=3 A

Re: The average of 12 numbers 16. When one number is discarded and 15 is a [#permalink]

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24 Jun 2017, 14:48

\(Average = \frac{Sum}{Count}\)

\(12 = \frac{Sum}{16}\)

\(12 * 16 = Sum\)

\(Sum = 192\)

Now, we remove one number and add 15, and the new average is 17

\(12 = \frac{New Sum}{17}\)

\(12 * 17 = New Sum\)

\(New Sum = 204\)

So, difference between \(Sum\) and \(New Sum = 204 - 192 = 12\)

As we have added 15, we will substract above number from \(15 = 15-12 = 3\) Hence, the Answer is A _________________

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