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M02-04

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Bunuel
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M02-04 [#permalink] New post   16 Sep 2014, 00:17
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83% (01:23) correct 17% (02:05) wrong based on 648 sessions
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For the past \(k\) days, Liv has baked an average (arithmetic mean) of 55 cupcakes per day. Today, Bibi helped Liv, and together they baked 100 cupcakes, raising the average to 60 cupcakes per day. What is the value of \(k\)?


A. 8
B. 9
C. 10
D. 12
E. 13
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Bunuel
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Re M02-04 [#permalink] New post   16 Sep 2014, 00:17
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For the past \(k\) days, Liv has baked an average (arithmetic mean) of 55 cupcakes per day. Today, Bibi helped Liv, and together they baked 100 cupcakes, raising the average to 60 cupcakes per day. What is the value of \(k\)?


A. 8
B. 9
C. 10
D. 12
E. 13


The total number of cupcakes baked in \(k\) days was \(55k\), which means that the total number of cupcakes baked in \(k+1\) days was \(55k+100\). The new average is \(\frac{55k+100}{k+1} = 60\).

Thus, \(55k + 100 = 60k + 60\) and \(k = 8\).


Answer: A
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Re: M02-04 [#permalink] New post   18 Mar 2015, 05:56
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Hi,
I approached the prob in this way.

Average of 60 indicates that 5 more needs to be added in k days and 60 on the last day.

The question says 5k + 60 = 100
Therefore, k = 8

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Channarong22
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Re: M02-04 [#permalink] New post   06 Jun 2016, 23:13
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I think this is a high-quality question and I agree with explanation.
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Re: M02-04 [#permalink] New post   25 Jan 2020, 08:58
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Bunuel wrote:
For the past \(k\) days the average (arithmetic mean) number of cupcakes baked by Liv was 55 per day. Today Bibi helped Liv and together they baked 100 cupcakes, which raised the average to 60 cupcakes per day. What is the value of \(k\)?

A. 8
B. 9
C. 10
D. 12
E. 13



All we care about is the increase.

So when they baked together the average went up to 60. So that means for last day 60 will be counted towards the average. Subtract that and you get 40.

Now 40 was used to increase average from 55 to 60. That means increase of 5. How many times you can distribute 5 out of 40? 8 times.

Answer A.
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Re: M02-04 [#permalink] New post   17 Mar 2020, 01:54
very well explained, i got this question wrong in gmat club test, thought as work/rate problem, then realized averaging.
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Re: M02-04 [#permalink] New post   12 Aug 2023, 02:05
I think this is a high-quality question and I agree with explanation.
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Re: M02-04 [#permalink] New post   12 Aug 2023, 05:53
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M02-04 [#permalink]
12 Aug 2023, 05:53
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