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Of the 8 people having a meal, 5 are having fries, 4 are having burger 07 Jun 2017, 12:23
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A
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Question Stats:

79% (01:34) correct 21% (01:43) wrong based on 221 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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A
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Of the 8 people having a meal, 5 are having fries, 4 are having burger 07 Jun 2017, 12:32
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Ans :A
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Of the 8 people having a meal, 5 are having fries, 4 are having burger 05 Sep 2018, 08:39
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rohan2345
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
Show more


Dear Moderator,
Found this overlapping set problem in the combination section, hope you will look into this. Thank you.
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Of the 8 people having a meal, 5 are having fries, 4 are having burger 05 Sep 2018, 08:46
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stne
rohan2345
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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_______________
Edited. Thank you.
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Of the 8 people having a meal, 5 are having fries, 4 are having burger 05 Sep 2018, 09:33
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rohan2345
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
Show more

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.
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Of the 8 people having a meal, 5 are having fries, 4 are having burger 24 Apr 2020, 07:14
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There are a total of 12 items on the table.. if 4 people are eating 2 items each which equals 8. 4 items remain and 4 people are at the table. so the answer is A.
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Of the 8 people having a meal, 5 are having fries, 4 are having burger 25 Apr 2020, 15:51
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rohan2345
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
Show more

We can use the formula:

Total = n(F) + n(B) + n(C) - n(exactly 2 sets) - 2*n(all 3 sets) + n(none)

8 = 5 + 4 + 3 - 4 - 2x + 0

8 = 8 - 2n

0 = n

Answer: A
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