Bunuel wrote:
A group of 20 people are drinking coffee. The total number taking cream in their coffee is 7 less than twice the total number taking sugar. The number taking both cream and sugar is the same as the number taking neither. How many people in the group take cream?
A. 9
B. 10
C. 11
D. 12
E. 13
PS20487
One approach is to use the
Double Matrix Method.
This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of coffee drinkers, and the two characteristics are:
- takes cream or does not take cream
- takes sugar or does not take sugar
Aside: We can also use Venn diagrams and formulae to solve overlapping sets questions. However, as difficulty levels increase, it becomes harder to apply those other approaches, whereas the Double Matrix Method works every time. 20 people are drinking coffee. The total number taking cream in their coffee is 7 less than twice the total number taking sugar. The number taking both cream and sugar is the same as the number taking neither. Let
x = the number of people taking sugar
This means
2x - 7 = the number of people taking cream
Let
k = the number of people taking both cream and sugar
So,
k = the number of people taking neither cream nor sugar
We get the following:
There are 20 people in total. So, if x of them are taking sugar, then
20 - x of them are NOT taking sugar
Likewise, if (2x - 7) of them are taking cream, then 20 - (2x - 7) of them are NOT taking cream
Simplify to get:
27 - 2x of them are NOT taking cream
Add this to our diagram to get:
KEY POINT: If we let W = the value in the TOP-RIGHT box, something nice happens:Since the two boxes in the RIGHT-HAND column add to 20 - x, we can conclude that:
W + k = 20 - x Likewise, since the two boxes in the TOP row add to 2x - 7, we can conclude that
W + k = 2x - 7Since both of these equations are set equal to
W + k, it must be the case that:
20 - x = 2x - 7Add x to both sides:
20 = 3x - 7 Add 7 to both sides:
27 = 3xSolve:
x = 9 How many people in the group take cream? We already know that
2x - 7 people take cream
Since
x = 9, the number of people who take cream = 2(
9) - 7 =
11 Answer: C
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:
EXTRA PRACTICE QUESTION
More questions to practice with:
EASY:
https://gmatclub.com/forum/of-the-120-p ... 15386.html MEDIUM:
https://gmatclub.com/forum/in-a-certain ... 21716.html HARD:
https://gmatclub.com/forum/a-group-of-2 ... 24888.html KILLER:
https://gmatclub.com/forum/a-certain-hi ... 32899.html