Data Sufficiency

BTGModeratorVI wrote: ↑

Tue Feb 16, 2021 8:26 am

If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

(1) 60 percent of the guests who ordered dessert also ordered coffee.
(2) 90 percent of the guests who ordered coffee also ordered dessert.

Answer: C
Source: official guide

Let's use the Double Matrix method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of guests, and the two characteristics are:
- ordered dessert or did not order dessert
- ordered coffee or did not order coffee

Target question: What percent of the guests ordered coffee?
Since the target question is asking for a percent, let's say that there are 100 guests in total.

Given: 75 percent of the guests ordered dessert
Since we're saying that there is a total of 100 guests, we know that 75 of them ordered dessert.
This also tells us that 25 guests did not order dessert.
So, we can set up our diagram as follows:

Notice that I have let x = the total number of guests who ordered coffee.

Statement 1: 60 percent of the guests who ordered dessert also ordered coffee.
75 guests ordered dessert. 60% of 75 = 45, so 45 guests ordered coffee AND dessert.
So, we get:

As you can see, we still don't have enough information to determine the value of x (the number of guests who ordered coffee)
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 90 percent of the guests who ordered coffee also ordered dessert.
We get:

As you can see, we still don't have enough information to determine the value of x (the number of guests who ordered coffee)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When we combine the statements, we see that we have 2 different pieces of information describing the top-left box.

This means that 0.9x = 45
Solve to get x = 50
In other words, 50 guests ordered coffee, which means 50% of the guests ordered coffee.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

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.

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