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# Guests at a recent party ate a total of fifteen hamburgers.[Very Tough]

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Guests at a recent party ate a total of fifteen hamburgers. Each guest who was neither a student nor a vegetarian ate exactly one hamburger. No hamburger was eaten by any guest who was a student, a vegetarian, or both. If half of the guests were vegetarians, how many guests attended the party?

(1) The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate for non-vegetarians.

(2) 30% of the guests were vegetarian non-students.

Try solving this inside 2 min.

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This Question is a really nut cracker. How many of you spent more than 3-4 min on this question & still could not figure out the right answer? I am guessing quite a lot of you. The idea of this question was not make you feel bad. But to make you realize that there will be questions ( 1 or 2) like these in the exam. So if you are not able to solve a question 2min, you should probably move on to the next question and not waste your precious time.

Incase of questions, such as this, it always a good idea to make a Data Grid to visualize the problem easily. Let the total be X.

 Veg Non Veg Total Students Non Students 15 Total X/2 X/2 X ( since halfare veg/nonveg)

Let us pick up Statement 1 : The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate for non-vegetarians.

VEG Students: VEG Non Students = 2:3, which is half as the ratio for Non Veg Students : Non veg Non Students => 4:3.
Total Non Veg = X/2
total non veg non students => { ( Non veg Non Students/ ( Non veg Non Students+ Non veg Students ) } * Total Non Veg
or => 3/7 * X/2 = 15 ( which is given as 15)

 Veg Non Veg Total Students Non Students (3/7) * X/2 = 15 Total X/2 X/2 X ( since halfare veg/nonveg)

This does seems to SUFFICIENT to solve this problem. Hence Statement 1 is sufficient.
Let us pick Statement 2 : 30% of the guests were vegetarian non-students.
The equation would look like Veg Non Students = 0.3 * X. But we cannot calculate X with this statement. Hence INSUFFICIENT.

answered Sep 27, 2014 by Partner (696 points)
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Jyotsna Mehta