In a group of x students, w students are taking Chemistry but not French, y students are taking French but not Chemistry, and z students are NOT taking French. Which of the following represents the number of students who are taking Chemistry?
A) x - y - z - w
B) x - y + z + w
C) x - y - z + w
D) x + y - z - w
E) x - y + z - w
Answer: C
Difficulty level: 650 - 700
Source: www.gmatprepnow.com
*I'll post a solution in 2 days
Challenge question: In a group of x students, w students are
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We know w students have taken Chemistry. Now out of the total x, students we need to find that how many of the remaining students can take Chemistry.
Since y have taken French, so they are out and we are left with (x - y) probable for Chemistry. Also given that z have not taken French and assuming that (w≠z), removed this z students to get the final leftover students as (x - y - z).
So, the total students who can take Chemistry = x-y-z+w.
Hence, C is the correct answer. Regards!
Since y have taken French, so they are out and we are left with (x - y) probable for Chemistry. Also given that z have not taken French and assuming that (w≠z), removed this z students to get the final leftover students as (x - y - z).
So, the total students who can take Chemistry = x-y-z+w.
Hence, C is the correct answer. Regards!
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- Brent@GMATPrepNow
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Let's apply the Double Matrix Method, a technique that can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).Brent@GMATPrepNow wrote:In a group of x students, w students are taking Chemistry but not French, y students are taking French but not Chemistry, and z students are NOT taking French. Which of the following represents the number of students who are taking Chemistry?
A) x - y - z - w
B) x - y + z + w
C) x - y - z + w
D) x + y - z - w
E) x - y + z - w
Answer: C
Difficulty level: 650 - 700
Source: www.gmatprepnow.com
*I'll post a solution in 2 days
Here, we have a population of students, and the two characteristics are:
- taking French or not taking French
- taking Chemistry or not taking Chemistry
In a group of x students, w students are taking Chemistry but not French, y students are taking French but not Chemistry, and z students are NOT taking French.
We can set up our matrix as follows:
Which of the following represents the number of students who are taking Chemistry?
In other words, we want to determine the SUM of the boxes in the left-hand column.
So, let's note this on our diagram to remind us that this is our goal...
Now focus your attention on the two boxes in the LOWER ROW.
We know that the SUM of those two boxes is z
So, if one box contains w students, then the other box must contain z-w students, which we'll add to our diagram...
Now focus your attention on the two boxes in the RIGHT-HAND COLUMN.
When we add those boxes, we get: y + z - w...
This means that, out of a total of x students, (y + z - w) are taking NOT taking Chemistry
So, the number of students TAKING Chemistry = x - (y + z - w)
= x - y - z + w
Answer: C
ASIDE: 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 this 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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Difficult Data Sufficiency questions
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Cheers,
Brent
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- Jeff@TargetTestPrep
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We can use the formulas:Brent@GMATPrepNow wrote:In a group of x students, w students are taking Chemistry but not French, y students are taking French but not Chemistry, and z students are NOT taking French. Which of the following represents the number of students who are taking Chemistry?
A) x - y - z - w
B) x - y + z + w
C) x - y - z + w
D) x + y - z - w
E) x - y + z - w
1) Total = Chemistry only + French only + both + neither
x = w + y + both + neither
2) Not taking French = Chemistry only + neither
z = w + neither
z - w = neither
So we have:
x = w + y + both + (z - w)
x = y + z + both
x - y - z = both
Finally, we can use the formula:
Chemistry = Chemistry only + both
Chemistry = w + (x - y - z)
Chemistry = x - y - z + w
Answer: C
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