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basketball and golf

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by j_shreyans » Wed Sep 17, 2014 2:05 am
In a certain country, 60 percent of the population likes basketball, and 30 percent of the population likes both basketball and golf. What percentage of the people who like basketball also like golf?

A)20%
B)33%
C)40%
D)50%
E)67%

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by GMATGuruNY » Wed Sep 17, 2014 3:07 am
j_shreyans wrote:In a certain country, 60 percent of the population likes basketball, and 30 percent of the population likes both basketball and golf. What percentage of the people who like basketball also like golf?

A)20%
B)33%
C)40%
D)50%
E)67%
Let the total number of people = 100.
Since 60% like basketball, the number who like basketball = (60/100)(100) = 60.
Since 30% like both basketball and golf, the number who like both = (30/100)(100) = 30.
Implication:
Of the 60 people who like basketball, 30 also like golf.
Thus:
(total who like both)/(total who like basketball) = 30/60 = 1/2 = 50%.

The correct answer is D.
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by [email protected] » Wed Sep 17, 2014 8:09 pm
Hi j_shreyans,

Mitch's approach is a great way to solve this problem - it allows you to TEST a VALUE for the total population, then figure out (and compare) the two subgroups in a really easy way.

The algebra approach isn't too bad though:

X = Total population
.6X = percentage of population that likes basketball
.3X = percentage of populations that likes BOTH basketball and gold

*Note: the prompt does NOT say that 60% of the population likes JUST basketball; this means that the 30% who like BOTH sports are included in the 60% who like basketball*

"What percentage of people who like basketball also like golf?"

%Both/%basketball = .3X/.6X = .3/.6 = 3/6 = 1/2 = 50%

Final Answer: D

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by apkmnp » Thu Sep 18, 2014 4:16 am
Hi,

Just trying to look it through the Venn Diagram format for simpler understanding.


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by Brent@GMATPrepNow » Thu Sep 18, 2014 11:28 am
j_shreyans wrote:In a certain country, 60 percent of the population likes basketball, and 30 percent of the population likes both basketball and golf. What percentage of the people who like basketball also like golf?

A)20%
B)33%
C)40%
D)50%
E)67%
Another approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of people, and the two characteristics are:
- likes basketball or doesn't like basketball
- likes golf or doesn't like golf

Since the question asks us to find a PERCENTAGE, let's let the population = 100
This means we can set up our diagram as follows:
Image

60 percent of the population likes basketball
This means that a TOTAL of 60 people like basketball.
So, we'll add that to our diagram:
Image

30 percent of the population likes both basketball and golf
So, 30 people like BOTH
Add that to our diagram:
Image

What percentage of the people who like basketball also like golf?
There 60 people who like basketball. 30 of those 60 people, also like golf.
30/60 = [spoiler]50% = D[/spoiler]

Cheers,
Brent

---------------------------------

NOTE: This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

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Easy Data Sufficiency questions
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Medium Data Sufficiency questions
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- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
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- https://www.beatthegmat.com/mba/2011/05/ ... question-3
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