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 at least one of these is

• A. 100
• B. 90
• C. 80
• D. 94

Answer 1

The correct option is D 94

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

We can then solve this as:
$x-10+28-x+x+30-x+x+2+32-x+x-6=94$
$\to x+76=94\to x=18$.
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 $\to$ 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 answer then is:
94%. Option (d) is correct.