Question

Directions: Refer to the data below and answer the questions that follow.
In a survey among students at all the IlMs, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee and 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 find
The percentage of those who like coffee or tea but not smoking among those who like at least one of these is

• A. More than 30
• B. Less than 30
• C. Less than 25
• D. None of these

Answer 1

The correct option is A More than 30

If you try to draw a figure for this question, the figure would be something like:


Let $x$ be number of students, who like all three coffee, tea and smoking.
Since, $6\%$ of students does not like any three, so remaining $94\%$ likes at least one of the three category.
We can then solve this as:
$x-10+28-x+x+30-x+x+2+32-x+x-6=94$
$\Rightarrow x+76=94\Rightarrow x=18$.
Note: In this question, since all the values for the use of the set theory formula are given, we can find the missing value of students who liked all three as follows:
$94=48+54+64-28-32-30+$ All three $\Rightarrow$ All three = 18 As you can see this is a much more convenient way of solving this question, and the learning you take away for the 3 circle situation is that whenever you have all the values known and the only unknown value is the center value - it is wiser and more efficient to solve for the unknown using the formula rather than trying to solve through a venn diagram.
Based on this value of x we get the diagram completed as:

The answers then are:
$\frac{30}{94}\Rightarrow$ more than 30%. Option (a) is correct,