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Question

Rina, while waiting for her friend Tina, started playing with matchsticks. As the wait time was more, Rina makes the figure “262226” using the matchsticks by the time Tina reaches. Tina accidentally steps on the pattern and all the matchsticks were spread all over.What was the number of matchsticks Rina wasted?


A

21

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B

26

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C

32

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D

36

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Solution

The correct option is C

32



From the image above, we see that 5 matchsticks are required to make 2 and 6 matchsticks are needed to make 6.
So if the number of twos is taken as 'a' and the number of sixes is taken as 'b'.
The number of matchsticks needed to make the two's =5×a=5a
The number of matchsticks needed to make the six's =6×b=6b
Total number of matchsticks = 5a+6b
In number 262226, there are four 2's and two '6's.
Hence, a = 4 and b = 2

Therefore, the total number of matches required =5a+6b=5×4+6×2
= 20+12 = 32


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