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?
Sets
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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.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.
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: https://www.gmatprepnow.com/module/gmat- ... ems?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:
- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
- https://www.beatthegmat.com/ds-quest-t187706.html
- https://www.beatthegmat.com/overlapping- ... 83320.html
- https://www.beatthegmat.com/finance-majo ... 67425.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html
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Let D = total who ordered dessert.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 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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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