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# In a certain city, the ratio of the number of people who purchase news

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Math Expert
Joined: 02 Sep 2009
Posts: 56306
In a certain city, the ratio of the number of people who purchase news  [#permalink]

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10 Dec 2018, 03:36
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Difficulty:

75% (hard)

Question Stats:

53% (02:18) correct 47% (02:13) wrong based on 125 sessions

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In a certain city, the ratio of the number of people who purchase newspaper X to the number of people who purchase newspaper Y is 7:1. What percent of the population purchases newspaper Y?

(1) Twenty-seven percent of the population purchases neither newspaper X nor newspaper Y.

(2) Seventy percent of the people who purchase newspaper Y also purchase newspaper X.

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Re: In a certain city, the ratio of the number of people who purchase news  [#permalink]

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10 Dec 2018, 04:08
1
Let the population of the city be P.
No of people who purchase newspapers is 8x (7x + x)
No of people who don't purchase newspapers is P-8x

Required percentage $$\frac{x}{P}*100$$

Statement 1) Twenty-seven percent of the population purchases neither newspaper X nor newspaper Y.

0.27P = P-8x
8x = 0.63P
$$x = \frac{0.63P}{8}$$

Required percentage: $$\frac{x}{P}*100$$ = $$\frac{0.63P}{8P}*100$$

$$\frac{63}{8}$$%

SUFFICIENT

Statement 2) Seventy percent of the people who purchase newspaper Y also purchase newspaper X.

Only newspaper X = 6.3x
Only newspaper Y = 0.3x
Both = 0.7x

INSUFFICIENT to get the required percentage.

OPTION: A
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Re: In a certain city, the ratio of the number of people who purchase news  [#permalink]

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10 Dec 2018, 16:24
1
eswarchethu135 wrote:
Let the population of the city be P.
No of people who purchase newspapers is 8x (7x + x)
No of people who don't purchase newspapers is P-8x

Required percentage $$\frac{x}{P}*100$$

Statement 1) Twenty-seven percent of the population purchases neither newspaper X nor newspaper Y.

0.27P = P-8x
8x = 0.63P
$$x = \frac{0.63P}{8}$$

Required percentage: $$\frac{x}{P}*100$$ = $$\frac{0.63P}{8P}*100$$

$$\frac{63}{8}$$%

SUFFICIENT

Statement 2) Seventy percent of the people who purchase newspaper Y also purchase newspaper X.

Only newspaper X = 6.3x
Only newspaper Y = 0.3x
Both = 0.7x

INSUFFICIENT to get the required percentage.

OPTION: A

imo, the number of people who do not purchase any newspaper= Total population- (the no. of people who buy newspaper x + the no. of people who buy newspaper y - who buy both), because the no of people who buy both are being counted twice. So, Statement 2 is needed to answer the question.

So, 0.27P=P-8x+y should be the equation, where y= no. of people who buy both newspapers.

IMO, option C.
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Re: In a certain city, the ratio of the number of people who purchase news  [#permalink]

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09 Jan 2019, 07:35
1
This is my thought process. I humbly request any of you to correct it. We are asked to find the number of people who buy newspaper y and not the number of people who only buy newspaper y. So why do we need to find the intersection? After excluding the people who buy neither newspapers, we know the percent of the newspaper bought. From that we can calculate the fraction of people who bought newspaper y.

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Re: In a certain city, the ratio of the number of people who purchase news  [#permalink]

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13 Jan 2019, 03:24
anant327 wrote:
This is my thought process. I humbly request any of you to correct it. We are asked to find the number of people who buy newspaper y and not the number of people who only buy newspaper y. So why do we need to find the intersection? After excluding the people who buy neither newspapers, we know the percent of the newspaper bought. From that we can calculate the fraction of people who bought newspaper y.

Any follow up on this question Bunuel
Re: In a certain city, the ratio of the number of people who purchase news   [#permalink] 13 Jan 2019, 03:24
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