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If 75 percent of the guests at a certain banquet ordered

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by BTGmoderatorLU » Wed Jul 18, 2018 3:02 pm

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Difficulty—

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.

The OA is C.

What mistake am I making?

A- # of people who order dessert.
B- # of people who order coffee.
AnB - # of people who order both dessert and coffee.

Given: A = 75
Statement 1: AnB = 0.6*70 = 45.
Given that we know AuB = A + B - AnB.
100 = 75 + B - 45 --> B = 75. Hence statement 1 should be sufficient.

What am I doing wrong here!? So confused! Please help. Thank you so much!

When I solve this problem by using the 2x2 grid, it's obvious that there is not enough information. But when I try to just use the formula it gives me sufficient info.
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Source: — Data Sufficiency |
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by GMATGuruNY » Wed Jul 18, 2018 4:03 pm
BTGmoderatorLU 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.
Let the total number of guests = 100.
Since 75% of the guests ordered dessert, we get:
Total desert = 0.75(100) = 75.

Let C = total who ordered coffee.
Let B = total who ordered both dessert and coffee.

Statement 1: 60% of the guests who ordered dessert also ordered coffee.
Thus:
B = 0.6(75) = 45.
Not way to determine the value of C.
INSUFFICIENT.

Statement 2: 90% of the guests who ordered coffee also ordered dessert.
Thus:
0.9C = B.
Not way to determine the value of C.
INSUFFICIENT.

Statements 1 and 2 together:
Since 0.9C = B and B=45, we get:
0.9C = 45.
C = 50.
SUFFICIENT.

The correct answer is C.
What mistake am I making?

A- # of people who order dessert.
B- # of people who order coffee.
AnB - # of people who order both dessert and coffee.

Given: A = 75
Statement 1: AnB = 0.6*70 = 45.
Given that we know AuB = A + B - AnB.
100 = 75 + B - 45 --> B = 75. Hence statement 1 should be sufficient.
The equations in red do not account for the number of guests who ordered NEITHER DESSERT NOR COFFEE
The following equation is correct:
Total Guests = (Total Dessert) + (Total Coffee) - Both + Neither
In Statement 1, the following values can be inserted into the blue equation above:
Total Guests = 100
Total Dessert = 75
Both = 45
Since we are left with two unknowns -- Total Coffee and Neither -- the blue equation cannot be solved.
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If 75 percent of the guests at a certain banquet ordered

by Brent@GMATPrepNow » Thu Jul 19, 2018 6:14 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.
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:
Image
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:
Image
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:
Image
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.
Image
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

----------------------------------
To learn more about the Double Matrix Method, watch our free 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
- the-aam-aadmi-party-t272242.html
- finance-majors-non-finance-majors-overl ... 67425.html

Medium Problem Solving questions
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- of-the-applicants-passes-a-certain-test-15-t270255.html
- opening-night-and-late-patrons-t264869.html
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Difficult Problem Solving questions
- ratio-problem-t268339.html
- overlapping-sets-question-t265223.html
- fractions-t264254.html
- overlapping-sets-t264092.html
- mba/2011/05/09/random-double-matrix-question-2

Easy Data Sufficiency questions
- for-what-percent-of-those-tested-for-a- ... 70596.html
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Medium Data Sufficiency questions
- sets-matrix-ds-t271914.html
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- mba/2011/05/05/random-double-matrix-question-1

Difficult Data Sufficiency questions
- double-set-matrix-question-t271423.html
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- mba/2011/05/16/random-double-matrix-question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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