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Of the 8 people having a meal...

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by BTGmoderatorLU » Wed Nov 22, 2017 2:19 pm
Of the 8 people having a meal, 5 are having fries, 4 are having burgers and 3 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

The OA is A.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
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by EconomistGMATTutor » Sat Nov 25, 2017 9:05 am
Hello LUANDATO.

Here, we will use the following formula:

$$\left|F\ o\ B\ o\ b\right|=\left|F\right|+\left|B\right|+\left|b\right|-\left(\left|F\ y\ B\right|+\ \left|F\ y\ b\right|+\ \left|B\ y\ b\right|\right)+\left|F\ y\ B\ y\ b\right|$$

where "F" are the people having fries, "B" having burgers and "b" having bacon.

Replacing the data, we get $$5=5+4+3-\left(4\right)+\left|F\ y\ B\ y\ b\right|$$ So $$\left|F\ y\ B\ y\ b\right|=0.$$

The correct answer is A .

I hope this explanation may help you.

Feel free to ask me again if you a doubt,

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by Scott@TargetTestPrep » Sat Oct 05, 2019 3:57 pm
BTGmoderatorLU wrote:Of the 8 people having a meal, 5 are having fries, 4 are having burgers and 3 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

The OA is A.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.
We can use the formula:

Total = #(Fries) + #(Burgers) + #(Bacons) - #(Exactly 2 items) - 2 x #(All 3 items)

If we let T = number of people who eat all 3 items, we can create the equation:

8 = 5 + 4 + 3 - 4 - 2T

0 = 2T

0 = T

Answer: A

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