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Livesaving test - Overlapping Groups

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by BlueDragon2010 » Wed Feb 26, 2014 5:27 am
Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?

A) 60
B) 80
C) 100
D) 120
E) 140
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by Patrick_GMATFix » Wed Feb 26, 2014 5:38 am
You can use Venn diagrams, the groups formula (group 1 + group 2 + neither - both = total), or the groups table (sometimes called a matrix) to solve overlapping sets. In many cases, you can even work back from the answer choice (this technique is called reverse engineering, back solving or plug-in-the-answers).

I go through the question in detail in the full solution below (taken from the GMATFix App).

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by Brent@GMATPrepNow » Wed Feb 26, 2014 8:14 am
Patrick has done a great job demonstrating a technique sometimes referred to as 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.
Here, we have a population of swim club members, and the two characteristics are:
- passed the lifesaving test or did not pass the lifesaving test
- took a preparatory course or did not take a preparatory course

These types of overlapping sets questions are very popular on the GMAT, so all students should know how to solve them.

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 the 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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Difficult Data Sufficiency questions
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- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
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by Abhishek009 » Wed Feb 26, 2014 9:00 am
BlueDragon2010 wrote:Thirty percent of the members of a swim club have passed the lifesaving test.

30% has passed the test , so 70% has failed in the test.

Now we have the Information -
BlueDragon2010 wrote:12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
So we can say 30 % = 30 + 12 swimmers

So, 70% = 42

1% = 42/70

100% = ( 42/70 )*100

So there were 60 swimmers in the club...

Answer is [spoiler](A)[/spoiler]
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by GMATGuruNY » Wed Feb 26, 2014 10:12 am
BlueDragon2010 wrote:Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?

A) 60
B) 80
C) 100
D) 120
E) 140
A double-matrix would work well here.
An alternate approach:

Since 30% of the members have passed the test, 70% have not.
These 70% are composed of 12 members who took the course and 30 members who did not, for a total of 42 members.
Thus, 70% of the total number of members in the swim club -- in other words, 70% of the correct answer choice -- must be equal to 42.
The correct answer must be A:
70% of 60 = 42.

The correct answer is A.
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by [email protected] » Wed Feb 26, 2014 6:44 pm
Hi BlueDragon2010,

For this question, you can the Tic-Tac-Toe Board (and you don't even need to fill in the entire grid!).

The first sketch includes the information from the prompt.

The second sketch includes the two deductions...


Image

The bottom-middle box contains two pieces of information that are equal:

.7X = 42

We can solve for X....X = 60, so we can answer the given question.

Final Answer: A

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by Scott@TargetTestPrep » Sat Jul 18, 2015 6:38 pm
BlueDragon2010 wrote:Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?

A) 60
B) 80
C) 100
D) 120
E) 140
Solution:

We are given that 30 percent of the members of the swim club have passed the lifesaving test. If we use variable T for the total number of members, we can say:

0.3T = number of members who passed the test

Since we know that 0.3T is the number of members who passed the test, we can determine that 0.7T members did not pass the test. Next we are given that among the members who have not passed the test, 12 have taken the preparatory course and 30 have not taken the course. With this information we can set up the following equation:

12 + 30 = 0.7T

42 = 0.7T

420 = 7T

60 = T

Thus, there are 60 members in the swim club.

Answer: A

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by nikhilgmat31 » Wed Jul 29, 2015 5:27 am
70 % of x = 30 + 12
70/100 * x = 42

x= 60
Answer is A
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