Problem Solving

Hi RiyaR,

This is an example of an Overlapping Sets question. Normally, in these types of questions, I prefer to use the tic-tac-toe board. Here though, the prompt refers to the exact 5 groups in the Overlapping Sets Formula:

(Gp. A) + (Gp. B) - Both + Neither = Total

Gp. A = All those who take cream
Gp. B = All those who take sugar

Let's call...
X = the number who take sugar

According to the prompt...
2X - 7 = the number who take cream

Since the number who take BOTH is the SAME as the number who take NEITHER, we can call each of those by the same variable: Y

So, plugging all of this (along with the total number of people = 20) into the equation, we get....

(2X - 7) + X - Y + Y = 20

3X - 7 = 20
3X = 27
X = 9

Now we know the number of people who take sugar (9) and the number who take cream (11).

Looking at the answer choices, we can take advantage of an interesting shortcut. We're asked for the "number of people who take NEITHER", but we know that this is the SAME number as the number of people who take BOTH. Since 9 people take sugar, 9 is the MAXIMUM number of people who could take BOTH! Look at the answers; there's only 1 possibility....9. No more work needs to be done.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

RiyaR wrote: ↑

Wed Sep 03, 2014 10:55 am

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 number taking neither. how many peopl in the group take neither?
A)9
B) 10
C)11
D)12
E)13

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:



Now let's focus on the value in the TOP-RIGHT box
Since the two boxes in the RIGHT-HAND column add to 20 - x, we can conclude that (20 - x) - k is the value in the TOP-RIGHT box




Likewise, since the two boxes in the TOP row add to 2x - 7, we can conclude that (2x - 7) - k is the value in the TOP-RIGHT box


Notice that we have two different ways to express the value in the TOP-RIGHT box
So, it must be the case that those quantities are equal
In other words: (20 - x) - k = (2x - 7) - k
Simplify each side: 20 - x - k = 2x - 7 - k
Add k to both sides: 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: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you’re familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent