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The ‘Amazing Soft Drink’ company interviewed 'k' consumers for market

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The ‘Amazing Soft Drink’ company interviewed 'k' consumers for market [#permalink]

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The ‘Amazing Soft Drink’ company interviewed 'k' consumers for market research study. The study found that \(\frac{2}{5}\) of consumers preferred Zing cola to Diet Zing Cola. Of those who preferred Diet Zing, \(\frac{1}{6}\) preferred Caffeine free Diet Zing. How many consumers, in terms of 'k' , did not prefer Caffeine free Diet Zing?

A. \(\frac{k}{11}\)
B. \(\frac{k}{10}\)
C. \(\frac{7k}{15}\)
D. \(\frac{9k}{10}\)
E. \(\frac{10k}{11}\)
[Reveal] Spoiler: OA

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The ‘Amazing Soft Drink’ company interviewed 'k' consumers for market [#permalink]

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HolaMaven wrote:
The ‘Amazing Soft Drink’ company interviewed 'k' consumers for market research study. The study found that \(\frac{2}{5}\) of consumers preferred Zing cola to Diet Zing Cola. Of those who preferred Diet Zing, \(\frac{1}{6}\) preferred Caffeine free Diet Zing. How many consumers, in terms of 'k' , did not prefer Caffeine free Diet Zing?

A. \(\frac{k}{11}\)
B. \(\frac{k}{10}\)
C. \(\frac{7k}{15}\)
D. \(\frac{9k}{10}\)
E. \(\frac{10k}{11}\)



Hi...

Two ways..

1) proper method..
Let's find how many prefer..
1/6 of free diet... Free diet- how many?? 1-2/5 = 3/5 of 'k'..
So 1/6 of 3/5 of k= \(\frac{1}{6}*\frac{3}{5}*k=\frac{k}{10}\)
Total who do not prefer =k- k/10=9k/10
D

2) give a value to K..
Let k =10..
3/5 of 10 or 6 prefer diet..
1/6 of these prefer free diet =6*1/6=1..
So who do not prefer=10-1=9..

Substitute k as 10 and find which matches.
D =9k/10=9*10/10=9
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The ‘Amazing Soft Drink’ company interviewed 'k' consumers for market [#permalink]

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New post 18 Aug 2017, 04:32
1. \(\frac{2}{5}\) preferred Zing Cola to Diet Zing Cola, thus those who prefer Diet Zing is \(\frac{3}{5}\).
2. From this \(\frac{3}{5}\), \(\frac{1}{6}\) prefer caffeine free. Thus, compared with K, this would be \(\frac{3}{5}\) * \(\frac{1}{6}\), which is \(\frac{1}{10}\)
3. Asked : what ratio of people who don't like the caffeine? 1 - \(\frac{1}{10}\) : \(\frac{9}{10}\)
Is it true 600-700 question? Or do I miss something?
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Re: The ‘Amazing Soft Drink’ company interviewed 'k' consumers for market [#permalink]

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New post 18 Aug 2017, 04:45
septwibowo wrote:
1. \(\frac{2}{5}\) preferred Zing Cola to Diet Zing Cola, thus those who prefer Diet Zing is \(\frac{3}{5}\).
2. From this \(\frac{3}{5}\), \(\frac{1}{6}\) prefer caffeine free. Thus, compared with K, this would be \(\frac{3}{5}\) * \(\frac{1}{6}\), which is \(\frac{1}{10}\)
3. Asked : what ratio of people who don't like the caffeine? 1 - \(\frac{1}{10}\) : \(\frac{9}{10}\)
Is it true 600-700 question? Or do I miss something?





It is not asking to find the ratio. It is asking to find the fraction of people who dont like caffeine so answer is only \(\frac{9k}{10}\)
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Re: The ‘Amazing Soft Drink’ company interviewed 'k' consumers for market [#permalink]

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New post 18 Aug 2017, 04:48
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HolaMaven wrote:
septwibowo wrote:
1. \(\frac{2}{5}\) preferred Zing Cola to Diet Zing Cola, thus those who prefer Diet Zing is \(\frac{3}{5}\).
2. From this \(\frac{3}{5}\), \(\frac{1}{6}\) prefer caffeine free. Thus, compared with K, this would be \(\frac{3}{5}\) * \(\frac{1}{6}\), which is \(\frac{1}{10}\)
3. Asked : what ratio of people who don't like the caffeine? 1 - \(\frac{1}{10}\) : \(\frac{9}{10}\)
Is it true 600-700 question? Or do I miss something?





It is not asking to find the ratio. It is asking to find the fraction of people who dont like caffeine so answer is only \(\frac{9k}{10}\)


Ah sure! thanks!
So, all we have to do is to add this ration with the number of respondents : \(\frac{9}{10}\) * k, which is \(\frac{9k}{10}\).
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Re: The ‘Amazing Soft Drink’ company interviewed 'k' consumers for market [#permalink]

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New post 18 Aug 2017, 05:08
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HolaMaven wrote:
The ‘Amazing Soft Drink’ company interviewed 'k' consumers for market research study. The study found that \(\frac{2}{5}\) of consumers preferred Zing cola to Diet Zing Cola. Of those who preferred Diet Zing, \(\frac{1}{6}\) preferred Caffeine free Diet Zing. How many consumers, in terms of 'k' , did not prefer Caffeine free Diet Zing?

A. \(\frac{k}{11}\)
B. \(\frac{k}{10}\)
C. \(\frac{7k}{15}\)
D. \(\frac{9k}{10}\)
E. \(\frac{10k}{11}\)



One can also assume a value for k and then do it. Say k = 30

Since 2/5th preferred Zing, 3/5th preferred Diet Zing. So 18 preferred it.
Of these 18, 1/6th preferred Caffeine Diet Zing so 3 preferred it. This means 27 did not.

Put k = 30. Whichever option gives 27, is the answer.

Answer (D)
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Re: The ‘Amazing Soft Drink’ company interviewed 'k' consumers for market   [#permalink] 18 Aug 2017, 05:08
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