If among 200 students, 105 like pizza and 134 like burger, then the nu

Question

If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can be ?

A. 23
B. 26
C. 28
D. 93
E. 96

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ArunSharma12 · Accepted Answer

img.png a + c = 105 b + c = 134 a + b + 2c = 239 a+ b + c + x = 200 c - x = 39 c = 39 + x 105 - a = 134 - b b = 29 + a which means b can not be a value less than 29, this removes options A,B and C. when b = 93, then a = 64 and c = 41 when b = 96, then a = 67 and c = 38 we know c is value greater than 39, so b is 93. Ans: D

yashikaaggarwal · Answer

The maximum no. Of people eating only burger is 134-39=95
(105+134=239 and 239-200=39)
And the minimum no. Is 134-105=29
Which are not in the option at all. Can you state what no. Is to be justified here? Maximum or minimum. Or correct me if I am wrong somewhere.

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jatinmittal91 · Answer

Max number of stds eating only burger is 134-39=95 (105+134=239 and 239-200=39)
and the min. no. is 134-105=29
The only option lie in this range is 93. Therefore, only D can be a possible answer.
Here, exact answer is not asked but the possible answer is asked.

Ans (D)

gurmukh · Answer

If we take a case where they are as exclusive as possible then minimum 39 people have to be common. 
(134+ 105) -200=39

Which makes minimum 95 people will like only burger.
134-39=95.
Now only option more than or equal to 95 is 96. Hence D become s the answer

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AnirudhaS · Answer

yashikaaggarwal , you have done the heavy lifting already!

See the question -

The answer lies between 29 and 95. The only choice which can be true is 93.

jatinmittal91 · Answer

Sorry brother but the answer is 93 and option D is 93.
You did everthing right but your concluding statement is wrong. The answer should be between 29 and 95, i.e 93.

AnirudhaS · Answer

Actually no the answer should be between 29 and 95. If all of the people who like pizza also like burger, then you will reach the 134-105 = 29. You have done it right already, i would have asked him to see your solution!

What our friend has done wrong is he has found out intersection of pizza and burger, which is 39. (134+105-200 = 39).

yashikaaggarwal · Answer

Yes Get it now. Thank You

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preetamsaha · Answer

Let the number of students who like both pizza and burger be ‘m’ .

The number of students who like neither of them be n

From venn diagram 105 – m + m + 134 – m + n = 200 => m – n = 39

∴The possible values of (m, n) are (39, 0) (40, 1)…….(105, 66)

∴ The number of students who like only burger is lies in the range   =

∴ From options, 93 is a possible answer

ANSWER D

exc4libur · Answer

200=105+134-both+neither
neither-both=-39
both=neither+39
both≥39

134-105≤b_only≤134-39
29≤b_only≤95

ans (D)

RahulHGGmat · Answer

Hi  Bunuel ,

Greetings of the day and Happy New Year.

I am trying to solve this question but was stuck on it. I checked all the solutions provided by people but was unsure whether they were right or not. Hence, I would request you to illuminate your expertise on it and help me by providing the solution of this problem.

Many Thanks in advance.

CEdward · Answer

Great question about the fundamentals of set theory involving two sets. I guess I am overly happy that I got it right.

If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can be ?

A. 23
B. 26
C. 28
D. 93
E. 96

This implies that 95 students in total DO NOT like pizza:

Pizza Not Pizza Total
Burger 134
Not Burger 66
Total 105 95 200

We can see from the above that 95 is the maximum possible answer so let's rule out A/B/C.
Is 96 possible? No...max is 95.

93 is the answer (fill in the rest of the cells to make sure).

Answer is D

MBAApp27 · Answer

Key word in this question is "can be" they're not looking for what it actually is, they are testing to see what fits the range between the minimum and maximum of the only burger.

Let's calculate.

200= Like Pizza + Like Burger - both

200= 105+134-both

Both=39

That is the minimum overlap.

The maximum number of people who will only like burgers would be 95. To minimize how many only Burger we get we would do 134-105 which is 29.

Therefore our range of people 29<= x<= 95,

A,B,C are eliminated and E is out of range. Answer is D

HarshavardhanR · Answer

https://gmatclub.com/forum/download/file.php?id=85471 --- Harsha GMAT-Club-Forum-c80v6rrs.png

If among 200 students, 105 like pizza and 134 like burger, then the nu

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If among 200 students, 105 like pizza and 134 like burger, then the nu

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