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In a survey among students, it was found that 48% preferred coffee, 54

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Bunuel
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In a survey among students, it was found that 48% preferred coffee, 54 [#permalink] New post   03 Nov 2019, 02:37
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In a survey among students, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee ans tea, 32% smoked and drank tea and 30% smoked and drank coffee. Only 6% did none of these. If the total number of students is 2000 then, the ratio of number of students who like only coffee to the number who like only tea is

A. 5:3
B. 8:9
C. 2:3
D. 3:2
E. None of these


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Re: In a survey among students, it was found that 48% preferred coffee, 54 [#permalink] New post   03 Nov 2019, 03:15
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x are those who prefer all three.
100-6= 48+54+64-28-32-30+x
x=18

Students who like Only coffee= 48-28-30+18=8

Students who like Only tea= 54- 28-32+18=12

Ratio= 8/12=2/3


Bunuel wrote:
In a survey among students, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee ans tea, 32% smoked and drank tea and 30% smoked and drank coffee. Only 6% did none of these. If the total number of students is 2000 then, the ratio of number of students who like only coffee to the number who like only tea is

A. 5:3
B. 8:9
C. 2:3
D. 3:2
E. None of these


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Re: In a survey among students, it was found that 48% preferred coffee, 54 [#permalink] New post   03 Nov 2019, 03:28
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Bunuel wrote:
In a survey among students, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee ans tea, 32% smoked and drank tea and 30% smoked and drank coffee. Only 6% did none of these. If the total number of students is 2000 then, the ratio of number of students who like only coffee to the number who like only tea is

A. 5:3
B. 8:9
C. 2:3
D. 3:2
E. None of these


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Let number of people who like Coffee, Tea & Smoke be C, T & S respectively.
Let the number of people who like all the 3 = X
As per the below Venn diagram,


Formula: Total(%) = '0' Category + C + T + S - (Exactly 2 category) - 2(Exactly 3 Category)
--> 100 = 6 + 48 + 54 + 64 - (28 - X + 30 - X + 32 - X) - 2X
--> 100 = 6 + 166 - 90 + X
--> 100 = 82 + X
--> X = 18

Required ratio = (18 - 10) : (18 - 6) = 8 : 12 = 2 : 3

IMO Option C
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InVinoVeritas2
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Re: In a survey among students, it was found that 48% preferred coffee, 54 [#permalink] New post   25 Jan 2020, 02:00
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Hi there,

Can anybody explain to me where the -2x comes from?

Formula: Total(%) = '0' Category + C + T + S - (Exactly 2 category) - 2(Exactly 3 Category)
--> 100 = 6 + 48 + 54 + 64 - (28 - X + 30 - X + 32 - X) - 2X

Thank you very much!
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RawJoker
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In a survey among students, it was found that 48% preferred coffee, 54 [#permalink] New post   21 Feb 2020, 18:00
InVinoVeritas2 wrote:
Hi there,

Can anybody explain to me where the -2x comes from?

Formula: Total(%) = '0' Category + C + T + S - (Exactly 2 category) - 2(Exactly 3 Category)
--> 100 = 6 + 48 + 54 + 64 - (28 - X + 30 - X + 32 - X) - 2X

Thank you very much!



As you can see, when we add C + T + S in the equation above, we include 'X' three times individually within 'C', 'T' and 'S'. (Please refer to the diagram above for clarity)
Therefore to avoid counting the 'X' values thrice, we have subtracted twice the value of 'X' at a later stage in the equation so that 'X' is taken up only once in the calculation.

Hope this helps. Cheers!
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azamatboden
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Re: In a survey among students, it was found that 48% preferred coffee, 54 [#permalink] New post   26 Jul 2022, 10:33
Can someone explain to me why we are not using the fact that the number of students is 2000?
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Re: In a survey among students, it was found that 48% preferred coffee, 54 [#permalink] New post   25 Oct 2023, 04:08
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Re: In a survey among students, it was found that 48% preferred coffee, 54 [#permalink]
25 Oct 2023, 04:08
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