In the figure given below the triangle represents pens, the rectangle represents pencils and the circle represents erasers. Number in each area represents the number of items in that area. How many pens are pencils?
21
In this Venn diagram the triangle represents pens, the rectangle represents pencils and the circle represents erasers, and every number written inside a region gives the count of items falling in exactly that region.
The question "how many pens are pencils" asks for the items that belong to both the pen group and the pencil group at once, that is the whole area where the triangle and the rectangle overlap.
That overlap is not a single cell: it splits into the part inside the triangle and rectangle but outside the circle, and the inner part where the triangle, rectangle and circle all cross together.
Both of these sub-regions count as pens-and-pencils, because adding the erasers group on top does not remove an item from being both a pen and a pencil.
The two overlapping sub-regions carry the counts \(5\) and \(16\), so the required total is \(5 + 16 = 21\).
The care needed here is to include every sub-region shared by the triangle and rectangle, whether or not the circle also passes through it.
Hence the number of pens that are pencils is 21.
Similar Questions
In the figure given below the rectangle represents airplanes, the circle represents white and the triangle represents car. The number in each area represents the number of items in that area.
Which of the following statement is NOT correct?
I. Number of white which are car and airplanes both are 9.
II. Number of airplanes which are not car are 24.
In the figure given below the triangle represents balls, the circle represents chairs and the rectangle represents wickets. The number in each area represents the number of items in that area.
Which of the following statement is correct?
I. Number of wickets which are only chairs are 10.
II. Total number of balls are 14 less than the total number of wickets.
In the figure given below the circle represents colour, the rectangle represents black and the triangle represents pink. The number in each area represents the number of items in that area.
How many colour are pink?
Identify the diagram that best represents the relationship among the given classes.
Carpenter, Male, Female
Important Questions from Venn Diagram Problems
In a group of 73 friends, 14 friends go to Gym and Karate classes both, whereas 7 friends neither go to Gym class nor to Karate class. If a total of 36 friends go to Gym class, then how many friends go to only Karate class?
In an examination 20% students failed in Mathematics and 15% failed in English. If 10% failed in both and those who passed in both numbered 300, then the total number of students who appeared in the examination was
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Which category is represented by the number '5'?
- In the following diagram, the circle stands for 'policemen', the square stands for 'sportspersons' and the 'triangle' stands for 'tax-payers' the numbers given in the different segments represent the number of persons in that category.
How many policemen are tax-payers but are NOT sportspersons?
The letter that represents the artists who are the doctors and dancers only is
