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# Guests at a recent party ate a total of fifteen hamburgers.

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Manager
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Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

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12 Apr 2008, 14:34
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.

i dont know the OA so send ur reasoning.

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Director
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Re: hi walker pls do it ? [#permalink]

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12 Apr 2008, 15:58
2
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I think answer to this DS question is A.

It is because of fact that question tells us that "No hamburger was eaten by any guest who was a student, a vegetarian, or both".

Student and Vegetarian ate = 0
Student and Non Vegetarian ate = 0
Non student and Vegetarian ate = 0
Only people Non-Student and Non-Vegetarian ate = 1 burger each, that means there were 15 non-student and non vegetarian people were there in party.

Also given to us that half of them are vegetarian, so that also means half are non-vegetarian.

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

Create A matrix (See the attached document).

Say there are x vegetarian student (from question that also means we have x non-vegetarian student).
As per this statement vegetarian students = 2x/5 and vegetarian non-students = 3x/5
Number of Non-vegetarian student = x - 15, as 15 were non-vegetarian non-student as calculated above.

As per this statement we have (x-15)/15 = 4/3 (Twice the rate of vegetarian students).
This will give us value of x and total number of guest = 2x.

DO NOT solve to get x and putting back the values as that is not required.

Statement 2:
Tells us that 30% of the guests were vegetarian non-students. But we don't know what is total number of guest so this alone is insufficient.

Attachments

Sample_Matrix.doc [25 KiB]

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Re: hi walker pls do it ? [#permalink]

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12 Apr 2008, 21:03
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Expert's post
Thanks, abhijit_sen.
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Re: hi walker pls do it ? [#permalink]

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12 Apr 2008, 23:30
thanks

abhijet thanks a ton

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Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

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06 Oct 2012, 05:08
Hi,

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

Student / Non-student = 2 /3 - > half the ratio for Non-veg then how to i convert it?

Ratio 3/5 -> twice this ratio would be ?

Also please correct me if the below is wrong

Pepper to Salt = 2:5 -> then
if the pepper is reduced by half then ratio becomes 1:10
If the pepper is doubled then ratio becomes 4:5

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Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

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06 Oct 2012, 08:36
Jp27 wrote:
Hi,
The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate for non-vegetarians.

Student / Non-student = 2 /3 - > half the ratio for Non-veg then how to i convert it?

Ratio 3/5 -> twice this ratio would be ?
Simply multiply the ratio by 2: so 2/3 is converted to 4/3 and 3/5 will be 6/5.

Jp27 wrote:
Also please correct me if the below is wrong

Pepper to Salt = 2:5 -> then
if the pepper is reduced by half then ratio becomes 1:10
If the pepper is doubled then ratio becomes 4:5

If pepper is reduced by half, the ratio will be 1:5. You can think it this way: first you have two parts pepper and 5 parts salt. Then you take away half of the pepper, so one part. What's left is one part pepper and 5 parts salt. You dont double the salt.

4:5 is correct.

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Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

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06 Oct 2012, 10:17
Zinsch123 wrote:
Jp27 wrote:
Hi,
The vegetarians attended the party at a rate of 2 students to every 3 non-students, half the rate for non-vegetarians.

Student / Non-student = 2 /3 - > half the ratio for Non-veg then how to i convert it?

Ratio 3/5 -> twice this ratio would be ?
Simply multiply the ratio by 2: so 2/3 is converted to 4/3 and 3/5 will be 6/5.

Jp27 wrote:
Also please correct me if the below is wrong

Pepper to Salt = 2:5 -> then
if the pepper is reduced by half then ratio becomes 1:10
If the pepper is doubled then ratio becomes 4:5

If pepper is reduced by half, the ratio will be 1:5. You can think it this way: first you have two parts pepper and 5 parts salt. Then you take away half of the pepper, so one part. What's left is one part pepper and 5 parts salt. You dont double the salt.

4:5 is correct.

Hey Zinsch123 - Thanks for your response.

There was a typo in my earlier post please allow to me to correct it...

Pepper to Salt = 2:5 -> then
if the pepper is reduced by half then ratio becomes 2(1/2):5 = 2:10
If the pepper is doubled then ratio becomes 4:5 -> this is correct (math here is 2*2:5=4:5) and you approve.

So coming back to the other doubts ->
2 students to every 3 non-students,half the rate for non-vegetarians. -> What is the math here?
2 students to every 3 non-students, double the rate for non-vegetarians. ->What is the math here?

Last edited by Jp27 on 06 Oct 2012, 21:32, edited 1 time in total.

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Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

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06 Oct 2012, 10:51
Not sure if my approach is right. I am slightly unsure on how I represented the information given in the Statement 1 on the rate(see below for the matrix on that). Statement 2 looks obviously insuff.
Attachments

Hamburgers.png [ 11.94 KiB | Viewed 3668 times ]

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Last edited by Pansi on 06 Oct 2012, 11:07, edited 1 time in total.

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Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

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06 Oct 2012, 11:06
Thought more on what exactly does halving the rate means :

Assume - Distance = 30 miles, Time Taken = 10 hrs. So Rate/Speed = Distance/Time= (30/10) = 3 miles/hr
Now halving the rate gives 1.5miles/hr. Now the D/T= (0.5)x (30/10)= 1.5 miles/hr.
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Re: Guests at a recent party ate a total of fifteen hamburgers. [#permalink]

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06 Oct 2012, 21:48
Pansi wrote:
Not sure if my approach is right. I am slightly unsure on how I represented the information given in the Statement 1 on the rate(see below for the matrix on that). Statement 2 looks obviously insuff.

I think you need to re-visit those cells in the 2nd row

From A statement -> Veg to Veg-Non-Stud = 2a to 3a so in your table x=2a y =3a
Now half the rate for Non- Veg here => 4b:3b (Im not sure how to get this ratio); In your table these values are wrong = : 4b (instead of z):3b

you already know 3b=15, b=5 hence 4b =20 - get the total Non-veg now by adding this row -> 35
Since this is exactly half of the total G = 70 (you have got 40).

I though I'll share because this as these Questions might appear in PS also.

And Also I understand rate thingy you gave about ratios but any idea on the below Qs?

2 students to every 3 non-students,half the rate for non-vegetarians. -> What is the math here?
2 students to every 3 non-students, double the rate for non-vegetarians. -> is this math correct? multiply by 2 here to get 4:3

Cheers

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Re: Guests at a recent party ate a total of fifteen hamburgers.   [#permalink] 06 Oct 2012, 21:48
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