Mathematics
Grade-4-
Easy

Question

Nancy is making a repeating pattern for the rule "Triangle, Square, Pentagon, and Hexagon."

If this pattern repeats 15 times, then how many squares are there in this pattern?

  1. 3    
  2. 4    
  3. 5    
  4. 6    

Hint:

We are given a repeating pattern of four shapes. The four shapes are triangle, pentagon and hexagon. The rule to write shapes is “Triangle, Square, Pentagon and Hexagon”. We are asked to number of squares in the pattern, if it’s repeated 15 times.

The correct answer is: 4


    The given pattern in words is Triangle, Square, Pentagon, Hexagon, Triangle, Square, Pentagon, Hexagon
    We are asked the number of squares in the pattern, if the pattern is repeated 15 times.
    Here, the pattern repeated 15 times means pattern repeated up to 15th place.
    Four shapes are repeating. And, the fourth shape is a Hexagon.
    So, all multiples of four will have Hexagon in their position.
    15 is not a multiple of 4. The closest multiple of 4 to 15 is 16.
    As square appears for every four shape, it appears 4 times for 16.
    But, we have repeated the shapes 1 place less than 16. The shape before Hexagon is Pentagon. So, at 15th place there is a pentagon.
    The shape before Pentagon is a square. So, at 14th place there will be a square. It is included in the pattern.
    So, there are 4 squares when pattern is repeated 15 times.

    We have to be careful about the sequence of the pattern.

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