GATE Civil 2022 Set 2 | GA | Question: 10

Question

An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point $\text{P}$ facing east.

The ant first turns $72^{\circ} $ anticlockwise at $\text{P},$ and then does the following two steps in sequence exactly FIVE times before halting.

 

1. moves forward for $10 \; \text{cm.}$
2. turns $144^{\circ}$ clockwise.

The pattern made by the trace left behind by the ant is

       A.  

       B. 

       C. 

       D. 

Answer 1

Using the above information, given in the question, we can easily draw the trace of an ant movement.

 

Here, ${\color{Blue}{\text{PS = SQ = QT = TR = RP = 10 cm}}}$

Correct Answer $:\text{C}$

Answer 2

We can also solve this question using option elimination. The ant is rotating $72^\circ$ anticlockwise from point $P$, which means that Option A and Option B get eliminated. Now, only Option C and Option D remain as possible answers. But Option D gets eliminated because we are repeating the two given steps only for five times (as per the question). Option D shows more than five sides, whereas Option C has exactly five sides. Hence, the correct answer is: \[ \boxed{\text{Option C}} \]

Answer 3

For solving such types of questions, you dont need exact angles, so if 72 degrees become 71 or 73. It's completely fine. Just estimate what can be a 72 degrees on the basis of the known figures of 90, 180 and 45 degrees. And draw the figure. After repeating 5 times we'll get the shape of star. But to save time always check with options continuously. So, After 2-3 times only we'll understand it is a star i.e option C.

Answer 4

the action is repeated 5 times
so there should be only 5 edges in the diagram
So B&D options are eliminated

Now checking A and C:
The directions are already given in the options

Option A:
PQ=QR
If you are standing at Q and take a 144 clockqise, you will go down. But in the option QR is going up

So discarded

Option B:
PS=SQ
While standing at S, if you take 144 clockwise, you will go down.
Hence Option B is correct