Question

With the help of match-sticks, Zalak prepared a pattern as shown below. When $97$ matchsticks are used, the serial number of the figure will be ...........

• A. Figure 32
• B. Figure 95
• C. Figure 49
• D. Figure 48

Answer 1

The correct option is D Figure 48

Pattern associated with the number of matchsticks:
Figure 1: No. of sticks $=3=3+0$
Figure 2: No. of sticks $=5=3+2$
Figure 3: No. of sticks $=7=3+2+2$
Figure 4: No. of sticks $=9=3+2+2+2$
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The rule associated with it can be given as no. of sticks $=3+2(n-1)$ where $n$ is the number of the figure.
Now there are $97$ matchsticks
$⟹3+2(n-1)=97$
$⟹3+2n-2=97$
$⟹2n=96$
$⟹n=48$

Hence, serial number of the figure having $97$ matchsticks is $48$.