A certain health club offers only yoga classes and spin classes. If al

It always becomes so easy with a matrix box. Just plug in the data given and get the result.

Can someone explain this with simple explanation

Here's a step-by-step approach using the Double Matrix method.

Here, we have a population of health club members, and the two characteristics are:
- taking yoga or not taking yoga
- taking spin classes or not taking spin classes

So, we can set up our diagram as follows:

IMPORTANT: Notice that I placed a zero in the bottom right corner because we are told that all club members take at least one type of class
In other words, there are zero members who take neither yoga nor spin classes.

Also notice that I made the total population of club members = 100. This is okay since the target question asks us to find a certain PERCENT.

Target question: What percent of members take yoga classes?

In other words, we want to find the sum of the top two boxes.


Statement 1: 30% of members take both types of classes.
So, we can place 30 of the 100 members in the top-left box.

Does this provide enough information to find the sum of the top two boxes?
No.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 40% of members take only spin classes.
So, we can place a 40 in the bottom left box.


This means that a total of 40 of the 100 members do NOT take yoga.


From this, we can conclude that the remaining 60 members DO take yoga.

In other words, 60% of the members take yoga.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer =

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Prompt analysis
There are yoga class and spin class. There are members who either joins spin or yoga or both classes.
That means 100 = N(y only) + N(s only) + N(y and s)
Superset
The value of percentage of member will be in the range of 0-100%

Translation
In order to find the exact value, we need:
1# the exact percentage of people taking yoga classes
2# The rest of the parameter in in the prompt analysis

Statement analysis
St 1: N(y and s) = 30. Therefore N(y only) +N (s only) = 70. Cannot say anything about the rest two variable. INSUFFICIENT
St 2: N(s only) = 40 .therefore N(y only) +N(y and s) = 60. Cannot say anything about the rest two variable. INSUFFICIENT

St 1 & St 2: N(y and s) = 30 and N(s only) = 40. Therefore N(y only) = 30. ANSWER.
Option C

Since number of people who take neither = 0 (Given:all club members take at least one type of class), then we need to find members who take Yoga

40% of members take only spin classes--> remaining 60 % take yoga classes (i.e. those members who take yoga only + those members who take both yoga and spin =60%)

Hence B alone is suff.

The only thing that makes this challenging is the wording of statement 2
"only spin"

Since we're told each club member participates in at least one club activity, 0% participates in neither yoga or spin.

Statement 2 tells us that 40% participate in spin but not yoga. We can conclude the total percentage that don't participate in yoga is 40%.

Therefore 60% participate in yoga.

Statement 2 is sufficient.

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