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Sets

This topic has 2 expert replies and 0 member replies
vinay1983 Legendary Member
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Sets

Post Thu Sep 12, 2013 2:32 am
lf 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.

OA C

Can this be solved by any other method other than Venn diagram, maybe Double matrix?

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GMAT/MBA Expert

Post Thu Sep 12, 2013 7:26 am
Quote:
If 75 percent of the guests at a certain banquet ordered dessert, what percent of the guests ordered coffee?

1.) 60% of the guests who ordered dessert also ordered coffee.
2.) 90% of the guests who ordered coffee also ordered dessert.
Let D = total who ordered dessert.
Let C = total who ordered coffee.
Let B = total who ordered both dessert and coffee.
Plug in guests = 100.

Then D = .75*100 = 75.

Statement 1:
Tells us that B = .6*75 = 45. Not sufficient to determine C.

Statement 2:
Tells us the .9C = B. Not sufficient to determine C.

Statements 1 and 2 together:
.9C = 45.
C = 50.
Sufficient.

The correct answer is C.

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GMAT/MBA Expert

Post Thu Sep 12, 2013 6:51 am
vinay1983 wrote:
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.

We can, indeed, 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

To learn more about this technique, watch our free video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

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

Cheers,
Brent

PS: Once you learn how the Double Matrix Method works, try these additional practice questions:
- http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1
- http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2
- http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3
- http://www.beatthegmat.com/ds-quest-t187706.html
- http://www.beatthegmat.com/overlapping-sets-questions-t183320.html
- http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html
- http://www.beatthegmat.com/ds-french-japanese-t222297.html

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