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The average of 12 numbers 16. When one number is discarded and 15 is a

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

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The average of 12 numbers 16. When one number is discarded and 15 is added, the average becomes 17. What is the number that is discarded?

A. 3
B. 5
C. 6
D. 10
E. 12
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Jun 2017, 10:48, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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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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New post 19 Jun 2017, 10:19
A 3.

16*12 - x +15 = 17*12
192+15 -x = 204
207-204 = x
x = 3.

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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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New post 19 Jun 2017, 11:11
Antonio.Salazar2887 wrote:
The average of 12 numbers 16. When one number is discarded and 15 is added, the average becomes 17. What is the number that is discarded?

A. 3
B. 5
C. 6
D. 10
E. 12


\(\frac{12*16 - x + 15}{12} = 17\)

\(192 - x + 15 = 204\)

Or, \(x = 3\)

So, answer will be (A)
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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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New post 19 Jun 2017, 12:48
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)
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The average of 12 numbers 16. When one number is discarded and 15 is a [#permalink]

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New post 19 Jun 2017, 13:42
Antonio.Salazar2887 wrote:
The average of 12 numbers 16. When one number is discarded and 15 is added, the average becomes 17. What is the number that is discarded?

A. 3
B. 5
C. 6
D. 10
E. 12

Using (Average * number of terms) = Sum

Find the sum of first set of numbers.

Find the sum of the second set of numbers.

Set up an equation where the first sum is changed per the prompt, and equals the second sum.

1. (A)*(n) = S (the number of terms, 12, does not change)

Sum of first set of numbers: 16 * 12 = 192

Sum of second set of numbers: 17 * 12 = 204 (RHS)

2. Equation. From the first sum of 192, some number, x, is subtracted, and 15 is added (LHS):

192 - x + 15 = 204
-x = -3, or
x = 3

Answer A

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

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New post 19 Jun 2017, 18:11
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Antonio.Salazar2887 wrote:
The average of 12 numbers 16. When one number is discarded and 15 is added, the average becomes 17. What is the number that is discarded?

A. 3
B. 5
C. 6
D. 10
E. 12


Average to 12 numbers \(= 16\)

Sum of 12 numbers \(= 16 * 12 = 192.\) ---------- (i)

Average of 12 numbers (one number is discarded) and 15 is added \(= 17\)

Sum of 12 numbers (one number is discarded) and 15 is added \(= 17 * 12 = 204\)-------------- (ii)

Subtracting (ii) from (i), we get;

\(204 - 192 = 12\)

Difference between 15 and number discarded is 12. Let the number be x.

\(15 - x = 12\)

\(x = 15 - 12 = 3.\)

Hence the number discarded \(= 3.\) Answer (A) ...

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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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New post 19 Jun 2017, 20:39
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



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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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New post 24 Jun 2017, 15:48
\(Average = \frac{Sum}{Count}\)

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

\(12 * 16 = Sum\)

\(Sum = 192\)

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

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New post 06 Jul 2017, 17:47
Antonio.Salazar2887 wrote:
The average of 12 numbers 16. When one number is discarded and 15 is added, the average becomes 17. What is the number that is discarded?

A. 3
B. 5
C. 6
D. 10
E. 12


Since the average of 12 numbers is 16, the sum of those numbers is 12 x 16 = 192.

We can let x = the discarded number and we can create the following equation:

(192 - x + 15)/12 = 17

207 - x = 204

x = 3

Answer: A
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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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New post 06 Jul 2017, 18:36
Sum of 12 numbers = \(12*16 = 192\)

Discarding a number (x, say) and adding 15, we get = \(\frac{192 - x + 15}{12} = 17\)

\(192 - x + 15 = 204\)

\(-x = 204 - 192 - 15\)

\(x = 3\). Ans - A.
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Re: The average of 12 numbers 16. When one number is discarded and 15 is a   [#permalink] 06 Jul 2017, 18:36
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