In a restaurant, 75% of the customers ordered dessert, what percent of the customers ordered coffee?
(1) 93% of the customers who ordered dessert also ordered coffee.
(2) 80% of the customers who ordered coffee also ordered dessert.
I know that the answer, just looking at it,would be C...but how would you go about solving it?
x>0?
(1)|x|?x^2
(2)x<|x^1|
prep question
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Hey!
I think you have not entered the entire Q, as there can be few customers who ordered nothing!
Please check your Q with that of the actual.
Regards,
Mukherjee
I think you have not entered the entire Q, as there can be few customers who ordered nothing!
Please check your Q with that of the actual.
Regards,
Mukherjee
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Let the total number of guests = 100.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 = the number who ordered dessert.
C = the number who ordered coffee.
B = the number who ordered BOTH.
Since 75% of the guests ordered dessert, we get:
D = 0.75 * 100 = 75.
Statement 1: 60% of the guests who ordered dessert also ordered coffee.
In other words, 60% of the 75 guests who ordered dessert ordered BOTH dessert AND coffee.
Thus:
0.6 * 75 = B
B = 45.
No way to determine the value of C.
INSUFFICIENT.
Statement 2: 90% of the guests who ordered coffee also ordered dessert.
In other words, 90% of the guests who ordered coffee ordered BOTH coffee AND dessert.
Thus:
0.9C = B.
No way to determine the value of C.
INSUFFICIENT.
Statements combined:
Since 0.9C = B and B = 45, we get:
0.9C = 45
C = 50.
SUFFICIENT.
The correct answer is C.
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As you can see, Mitch has posted the original question...
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
----------------------------------
To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919
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Cheers,
Brent
Another approach for this question is to 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.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
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
----------------------------------
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
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html
Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- 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/ds-french-ja ... 22297.html
Difficult Problem Solving questions
- 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
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- https://www.beatthegmat.com/ds-quest-t187706.html
Medium Data Sufficiency questions
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- https://www.beatthegmat.com/a-manufacturer-t270331.html
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Difficult Data Sufficiency questions
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- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3
Cheers,
Brent