Logical Reasoning Discussion

**Common Information**

In a drawing competition, students were asked to draw geometric figures of their choice. The following Venn diagram represents the number of students and their choices of geometric figures. Each geometric figure on the Venn diagram represents the set of students who chose to draw that particular geometric figure.

Q. |
How many students drew polygons with sum of internal angles less than $200^\circ$ |

✖ A. |
30 |

✖ B. |
40 |

✔ C. |
50 |

✖ D. |
60 |

**Solution:**

Option(**C**) is correct

In order to solve this question set, let us first try and understand the diagram and what it represents.

There are four closed figures in the diagram – a triangle, a rectangle, a circle and a parallelogram. Each of these figures represents a set of students who have chosen to draw that particular geometrical figure.

Next, we move on to the numbers and the lower case letters in the diagram. The addition of all the numbers (that are labelled using lower case letters) in one particular figure represents the total number of students in that set. The reason why these numbers are separated is because they have different representations. Every letter (and its number) represents some section of the set which is different from the other sections.

Consider the circular set and its letters *j*, *m*, *a*, *h*, *f* and *i*. Here is what each of these letters represents:

*j* – Number of students common to the circle set and the rectangle set

*m* – Number of students common to the circle, rectangle and the triangle sets

*a* – Number of students common to all the sets

*h* – Number of students common to the circle set and the triangle set

*f* – Number of students common to the circle set and the parallelogram set

*i* – Number of students who belong only to the circle set

This is how the entire diagram has been laid out. The significance of the lower case letters in solving the questions is therefore, primary.

Now, let us move on to the solution of the question.

Of all the shapes, only triangle has sum of internal angles less than $200^\circ$

∴ All zones lying within set *T *satisfy this condition,

$= k + g + b + e + m + a + h$

$= 3 + 7 + 13 + 9 + 5 + 12 + 1$

$= \textbf{50}$

**Saikat Basu**

*()
*

Good One, Q is "How many students drew polygons with sum of internal angles less than 200 Degrees" - not "How many students drew polygons ONLY with sum of internal angles less than 200 Degrees".

For Ex, People who draw both Triangle and Rectangle, are also counted.