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# Of the 8 people having a meal, 5 are having fries, 4 are having burger

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General GMAT Forum Moderator
Joined: 29 Jan 2015
Posts: 1129
Location: India
WE: General Management (Non-Profit and Government)
Of the 8 people having a meal, 5 are having fries, 4 are having burger  [#permalink]

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07 Jun 2017, 11:23
1
5
00:00

Difficulty:

(N/A)

Question Stats:

78% (01:47) correct 22% (01:50) wrong based on 94 sessions

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Of the 8 people having a meal, 5 are having fries, 4 are having burgers and 3 are having bacon. No other food is at the table. Each person is eating at least 1 item. If exactly 4 people are eating exactly 2 food items, how many people are eating all 3 items?

A- 0
B- 1
C- 2
D- 3
E- 4

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Manager
Joined: 23 May 2017
Posts: 240
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: Of the 8 people having a meal, 5 are having fries, 4 are having burger  [#permalink]

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07 Jun 2017, 11:32
1
2
Attachment:

FullSizeRender (18).jpg [ 90.85 KiB | Viewed 1765 times ]

Ans :A
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Director
Joined: 27 May 2012
Posts: 681
Re: Of the 8 people having a meal, 5 are having fries, 4 are having burger  [#permalink]

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05 Sep 2018, 07:39
1
rohan2345 wrote:
Of the 8 people having a meal, 5 are having fries, 4 are having burgers and 3 are having bacon. No other food is at the table. Each person is eating at least 1 item. If exactly 4 people are eating exactly 2 food items, how many people are eating all 3 items?

A- 0
B- 1
C- 2
D- 3
E- 4

Dear Moderator,
Found this overlapping set problem in the combination section, hope you will look into this. Thank you.
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- Stne

Math Expert
Joined: 02 Sep 2009
Posts: 52926
Re: Of the 8 people having a meal, 5 are having fries, 4 are having burger  [#permalink]

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05 Sep 2018, 07:46
stne wrote:
rohan2345 wrote:
Of the 8 people having a meal, 5 are having fries, 4 are having burgers and 3 are having bacon. No other food is at the table. Each person is eating at least 1 item. If exactly 4 people are eating exactly 2 food items, how many people are eating all 3 items?

A- 0
B- 1
C- 2
D- 3
E- 4

Dear Moderator,
Found this overlapping set problem in the combination section, hope you will look into this. Thank you.

_______________
Edited. Thank you.
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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 730
Of the 8 people having a meal, 5 are having fries, 4 are having burger  [#permalink]

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05 Sep 2018, 08:33
rohan2345 wrote:
Of the 8 people having a meal, 5 are having fries, 4 are having burgers and 3 are having bacon. No other food is at the table. Each person is eating at least 1 item. If exactly 4 people are eating exactly 2 food items, how many people are eating all 3 items?

A- 0
B- 1
C- 2
D- 3
E- 4

Immediate application of the simplifier:

$$A \cup B \cup C = A + B + C - \left[ {\sum {{\text{Exactly}}2} } \right] - 2 \cdot \left[ {{\text{Exactly3}}} \right]$$

In our case (see figure attached):

$$8 = {\text{F}} \cup {\text{Bu}} \cup {\text{Ba}}\mathop = \limits^{\left( * \right)} 12 - 4 - 2x\,\,\,\,\, \Rightarrow \,\,\,? = x = 0$$

(All numerical alternative choices - we may explore a particular case, as we did.)

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.
Attachments

05Set18_3w.gif [ 27.81 KiB | Viewed 420 times ]

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Of the 8 people having a meal, 5 are having fries, 4 are having burger   [#permalink] 05 Sep 2018, 08:33
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