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Worked Examples

Example-1

Given below are five alternative figures marked as (A), (B), (C), (D) and (E) followed by four alternative answers marked as (1), (2), (3) and (4). Select the answer that depicts three of the alternative figures which when fitted together will form a complete square.

 

Description: 112960.png

  1. ABC
  2. BCD
  3. CDE
  4. BCE

Solution

No combination can be formed by using figure (A) so as to get a square. Next, we start with figure (B). Figures (B) and (C) can be combined as shown below:

 

Description: 112970.png

 

Figure (E) can now be easily fitted into this combination to form a square as shown:

 

Description: 112979.png

 

Clearly, figures (B), (C) and (E) when fitted together will form a complete square.

 

Hence, the answer is (4).
 

 

Example-2

Select three out of the following five alternative figures which together form one of the four alternatives (1), (2), (3) and (4) and when fitted together will form a complete square.

 

Description: 112988.png

  1. ABC
  2. BCD
  3. ABE
  4. ACD

Solution

Figure (A) combines with figure (B) to form a figure shown below:

 

Description: 112997.png

 

Now, we can fit figure (E) to form a complete square as shown below:

 

Description: 113019.png

 

Clearly, figures (A), (B) and (E) when fitted together will form a complete square.

 

Hence, the answer is (3).
 

 

Example-3

Given below are five alternative Figures marked (A), (B), (C), (D) and (E). Select the figure which does not fit into any of the remaining alternative figures to form a complete square.

 

Description: 113027.png

Solution

Clearly, figure (A) fits into figure (C) to form a complete square and also figure (B) fits into figure (E) to form a complete square as shown:

 

Description: 113039.png

 

Figure (D) does not fit into any of the alternative figures to form a complete square.

 

Therefore, figure (D) is the answer.
 

 

Example-4

Given below is a problem figure marked (X) followed by four other alternative figures marked (1), (2), (3) and (4). Select a figure from amongst the alternative figures which exactly fit into figure (X) to form a complete square.

 

Description: 113047.png

Solution

On close observation, we find that only figure (2) exactly fits into figure (X) to form a complete square as shown:

 

Description: 113058.png

 

Hence, the answer is (2).

 

Similar to the construction of squares, we have problems on construction of equilateral triangles.

 

The solving of such problems will become easier after studying the following example.
 

 

Example-5

Select three out of the following five alternative figures which together form one of the four alternatives (1), (2), (3) or (4) and when fitted together will form a complete equilateral triangle.

 

Description: 113071.png

  1. ABC
  2. BCD
  3. ABD
  4. A1E

Solution

We first select the largest figure which contains at least one angle of 60°. Clearly, Figure (B) is such a figure. Now, figure (C) fits into it as shown:

 

Description: 113080.png

 

Finally, the figure shown in figure (D) fits into the above combination to form a complete equilateral triangle as shown:

 

Description: 113089.png

 

Hence, figures (B), (C) and (D) fit into each other to form a complete equilateral triangle. So, the answer is (2).
 





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