A group of 20 people are drinking coffee. The total number taking crea

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 - 7
Since both of these equations are set equal to W + k, it must be the case that: 20 - x = 2x - 7
Add x to both sides: 20 = 3x - 7
Add 7 to both sides: 27 = 3x
Solve: 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

let "c" represents total number of people taking cream
let "s" represents total number of people taking sugar
let "cs" represents total number of people taking cream+ sugar
let "n" represents total number taking niether.

given,
I. total number taking cream in their coffee is 7 less than twice the total number taking sugar
==> c=2s-7 ------------ (i)

II. The number taking both cream and sugar is the same as the number taking neither
==> cs=n ----------(ii)

III. A group of 20 people are drinking coffee
==> c+s-cs+n = 20 -----------(iii)
putting (ii) in (iii) we get==> c+s=20 --------------- (iv)
putting value of c from (i) in (iv) we get
2s-7+s=20 or s= 9 -------- (v)
putting value of s(=9) in (iv) or (i) we get c=11 = answer= option C

Solution

Given

In this question, we are given that

• 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

To find
We need to determine

• The number of people, in the group, who take cream

Approach and Working out

• Number of people who drink coffee = 20

o Number of people who drink coffee with sugar = x
o Number of people who drink coffee with cream = 2x - 7
o Number of people who drink only coffee = y
o Number of people who drink coffee with both cream and sugar = y

• 20 = x + 2x – 7 – y + y

o 3x = 27
o Thus, x = 9

• Therefore, 2x – 7 = 2*9 – 7 = 18 – 7 = 11

Thus, option C is the correct answer.

Correct Answer: Option C
_________________

Number of people who drink coffee = 20
Number of people who drink coffee with sugar = S
Number of people who drink coffee with cream,C = 2S - 7
No of people with both = No of people with neither = Y

If we work with options, we realize that C has to be odd : because : even C = 2S-7 , shall give in S in decimal which is not possible :
e.g : C=12 :S will be: 19/2, not possible
Only odd answers A,C,E
9= 2s-7 : S = 8
C+S = 17,
But not possible,as 20-17 :3 /y =1.5

13 = 2s-7 : s =10
C+s : 23, Eliminate

Answer 11:
Lets check
11=2s-7 s => 9
c+s : 18
left: 20-18 =2 /y , i.e y=1

chetan2u:

one question in genral,

these types of questions can be solved either by venn diagram or by 2 table

how to distinguish , which one to be chose?

Actually double matrix is the extension of the vent diagram.
The Venn diagram of two circles will have 4 zones
Outside both the circles —- none of the two
Overlap — common to the two
Area under a single circle — only one

Exactly the same 4 areas are there in 2*2 matrix.


You can use any which you find comfortable.
_________________

Dear Chetan !!!

Thanks for your reply.

Actually intent for asking this question is that I started solving these questions from the Venn diagram and if I am unable to get the answer from it within 1 min or so, then I try the 2X2 Matrix.

but both seem to be the same. actully am loosing about 1 min to find out which one to be used.

Total number of people drinking coffee = 20
Total number of people who use cream = 2x - 7
Total number of people who use sugar = x

Therefore we can conclude the total number of people who DON'T use sugar = 20 - x
Therefore we can conclude the total number of people who DON'T use cream = 20 - (2x-7) = 27 - 2x

The number taking both cream and sugar is the same as the number taking neither. Let this number = n

What is 2x - 7?

We need to find the value of x. We can create the following equation:

\((20 - x) - n = (2x-7) - n\)

\(27 = 3x\)

\(9 = x\)

\(2(9) - 7 = 11\)

Answer is C.
_________________

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Hi Brent BrentGMATPrepNow, great expanation visually. One question that if I equate 20 - x = 27 - 2x then I got x = 7? Why is that and could you help? thanks.

How/why did you create the equation 20 - x = 27 - 2x?

Hi Brent BrentGMATPrepNow, was thinking to find the value of x. What's the logic behin and how to equate the right one here? thanks

I equated 20 - x and 2x - 7 because they were both set equal to W + k.

So, W + k = 20 - x and W + k = 2x - 7
Then it must also be true that: 20 - x = 2x - 7

Let's assume the number of people taking sugar in their coffee is x.
According to the problem, the total number taking cream in their coffee is 7 less than twice the total number taking sugar. So the number of people taking cream would be (2x - 7).

The number of people taking both cream and sugar is the same as the number taking neither. This means that the number of people taking both cream and sugar is 0.

We can use the principle of inclusion-exclusion to solve this problem. The principle states that:

Total = A + B - (A ∩ B)

Where:
A = Number of people taking cream
B = Number of people taking sugar

Total = Number of people in the group = 20

Substituting the values in the equation:
20 = (2x - 7) + x - (0)

Simplifying the equation:
20 = 3x - 7

Bringing the constant term to the right side:
20 + 7 = 3x = 27

Dividing both sides by 3:
x = 9

Now that we know x, we can find the number of people taking cream:
Number of people taking cream = 2x - 7 = 2(9) - 7 = 18 - 7 = 11

Therefore, there are 11 people in the group who take cream in their coffee.