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A survey was conducted to determine the popularity of 3 food

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A survey was conducted to determine the popularity of 3 food

by viveksahay » Fri Sep 27, 2013 3:25 am
I found this question while writing GMAT Prep Exam Pack 1

A survey was conducted to determine the popularity of 3 food among students. The data collected from 75 students is summarized as below

48 like Pizza
45 like Hoagies
58 like tacos
28 like pizza and hoagies
37 like hoagies and tacos
40 like pizza and tacos
25 like all three food

What is the number of students who like none or only one of the foods ?

A. 4
B. 16
C. 17
D. 20
E. 23

I got this one right but I spent a lot of time playing with numbers. Can someone please show a faster way.

OA is D
Last edited by viveksahay on Fri Sep 27, 2013 7:18 pm, edited 1 time in total.
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by theCodeToGMAT » Fri Sep 27, 2013 4:23 am
viveksahay wrote:I found this question while writing GMAT Prep Exam Pack 1

A survey was conducted to determine the popularity of 3 food among students. The data collected summarized as below

48 like Pizza
45 like Hoagies
58 like tacos
28 like pizza and hoagies
37 like hoagies and tacos
40 like pizza and tacos
25 like all three food

What is the number of students who like none or only one of the foods ?

A. 4
B. 16
C. 17
D. 20
E. 23

I got this one right but I spent a lot of time playing with numbers. Can someone please show a faster way.

OA is D
Are you sure you arent missing any values? I got stuck after finding people who likes "only" one.

What mistake i made?

Edited after the question was corrected: Answer = 20 [spoiler]{D} [/spoiler]..
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Last edited by theCodeToGMAT on Fri Sep 27, 2013 8:14 pm, edited 1 time in total.
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by vinay1983 » Fri Sep 27, 2013 5:21 am
Where did I go wrong here?

T = 48+45-58-(28+37+40)+25+x
=151-(105)+25
=151-130
=21

Somehow the question seems lacking some values!I might be wrong though
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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by viveksahay » Fri Sep 27, 2013 7:00 am
I have a different solution than yours but am still clueless about how to find those who like none..
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by fourteenstix » Fri Sep 27, 2013 12:04 pm
viveksahay wrote:I have a different solution than yours but am still clueless about how to find those who like none..
I don't think it's possible. We need the total number of students in order to solve for "none".
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by Brent@GMATPrepNow » Fri Sep 27, 2013 12:07 pm
fourteenstix wrote: I don't think it's possible. We need the total number of students in order to solve for "none".
Agreed!

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by Java_85 » Fri Sep 27, 2013 12:31 pm
IMO 16 is the possible right answer, To answer this question we also need the number of people who don't like any of this foods and the question doesn't provide enough info about it!
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by viveksahay » Fri Sep 27, 2013 7:26 pm
Apologies about my mistake. I had missed the total number of students while copying the question on the forum. I have updated the question. 75 is the total number of students.

I have also uploaded the updated solution.

Thanks
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by saswata1985 » Fri Sep 27, 2013 9:37 pm
Hi,

It took me 1 min 29 secs to answer this question.

In addition to the information provided in the question, I culled out the following set of figures to arrive at the answer: (No of students who liked only one of the food items + none)

Only Hoagies - 4
Only Pizza - 5
Only Tacos - 5
None - 4

Please note that out of total no of students who liked Pizza, Hogies and Tacos
we deduct the number of people who liked All three (25) from each of the figures provided for students like Pizza and Hoagies or Pizza and Tacos or Tacos and Hoagies.

For instance if we are to determine the number of students who like Only Pizza and Hoagies ie (28-25=3), Only Pizza and Tacos ie (40 - 25 = 15) and Only Hoagies and Tacos ie ( 37-25 = 12).

Now having arrived at the figures where in we have people who like "all three"; "Only two" when complete the blank spaces in the circles to arrive at "only one" of the three items we get:

Only Hoagies = (45-25-12-3) = 5; Only Pizzas =(48-25-15-3) = 5 and Only Tacos = (58-25-12-15) = 6

Now should we add up all the above figures

All three + Only Two of the items + Only one of the Items = 25 + (3+15+12) + (5+5+6) = 71

Since 71 out of 75 students have one, two or all of the food items, we arrive at the number 4 for the student who do not have anything. ie our 'neither' category students.

Now if we add this 4 to Only one item category students we arrive at:

4 + (5+5+6) = 20 (option D)

This can be solved in a jiffy using a simple diagram as the above is a verbal description of the same.

Hope you find the above explanation useful.
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by GMATGuruNY » Sat Sep 28, 2013 3:37 am
viveksahay wrote:I found this question while writing GMAT Prep Exam Pack 1

A survey was conducted to determine the popularity of 3 food among students. The data collected from 75 students is summarized as below

48 like Pizza
45 like Hoagies
58 like tacos
28 like pizza and hoagies
37 like hoagies and tacos
40 like pizza and tacos
25 like all three food

What is the number of students who like none or only one of the foods ?

A. 4
B. 16
C. 17
D. 20
E. 23

I got this one right but I spent a lot of time playing with numbers. Can someone please show a faster way.

OA is D
Draw a VENN DIAGRAM representing the following:
75 Total
48 like pizza
45 like hoagies
58 like tacos
N = ?
Image

Complete the Venn diagram by working from the INSIDE OUT.

25 like all 3 foods:
Image

28 like pizza and hoagies
37 like hoagies and tacos
40 like pizza and tacos
Subtracting from these figures the 25 who like all 3 foods, we get:
Image

Subtracting the values in the diagram from P=48, H=45, and T=58, we get:
Image

Subtracting the values in the diagram from Total = 75, we get:
Image

Thus:
Only P + Only H + Only T + N = 5 + 5 + 6 + 4 = 20.

The correct answer is D.
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