# Analytical Reasoning Shortcuts, Examples

**Analytical Reasoning Important Questions - Page 2**

*In ‘Analytical Reasoning’, we analyse the problems related to the counting of some geometrical figures in a given complex figures. The objective can be met by a systematic analysis of the complex figure given. *

*The steps involved in the analysis of the complex figure would be clear from the following examples:*

## Analytical Reasoning Solved Example

Count the number of triangles in the problem figure.Examples 1)

* Solution:* As a first step, all the intersecting points in the problem figure are labeled as shown.

Now count the number of simplest triangles. These are ABD, BED, CBF, BEF, FIH, FHE, GDH, DHE and their number is 8.

Next count the triangles which are formed by the combination of two of these simple triangles. These are DBF, BFH, FHD and BHD and their number is 4.

Now since, the triangles formed with the combination of three or more triangles do not exist, the total number of triangles in the figure is 8 + 4 = 12. So (c) is the correct answer.

* Example 2)* Find the number of straight lines in the figure.

* Solution:* First the given problem figure is labeled as shown.

Now, count the horizontal lines, namely AC, HD and GE and their number is 3.

Now, count the vertical lines AG, BF and CE and their number is also 3.

Finally, count the six (6) slanting lines namely – BH, CG, DF, BD, AE and HF.

Thus, the total number of straight lines = 3 + 3 + 6 = 12

Hence, **(a)** is the answer.

* Example 3)* Count the number of squares in the given problem figure.

* Solution:* As usual we first label the given problem figure as shown. Now, the squares formed with two components are-namely, ABJI, BCKJ, CDLK, IJGH, JKFG and KLEF. Their number in 6.

Similarly, a square made of four components is only 1, i.e.., CJFL

Finally, the squares composed of eight components are ACFH and BDEG. So their number is 2.

∴ The total number of squares = 6 + 1 + 2 = 9.

So,

**(b)**is the answer.

* Example 4)* Count the number of straight lines in the given problem figure.

* Solution:* The given problem figure may be labeled as shown:

Now we have

(i) Three (3) horizontal lines namely, AC, HD and GE.

(ii) Three (3) slanting lines namely, AG, BF and CE. And

(iii) Six (6) slanting lines namely, BH, CG, DF, BD, AE and HF.

∴ Total No. of lines = 3+3+6 = 12

∴ So (a) in the correct answer.

* Example 5)* Find the number of parallograms in the given problem figure.

* Solution:* First the given figure is labeled as shown.

Now,

(i) We have 6 simplest parallelograms namely, ABKJ, BCLK, CDEL, JKHI, KLOGH, LEFG.

(ii) The parallelograms composed of two components are ACLJ, BDEK, CKFG, EFHK; LGIJ, HIAB and, BCGH and their number is 7.

(iii) The parallogram composed of four components are ACGI and BDFH and their number is 2.

(iv) The parallogram composed of six elements is ADFI, i.e.., one only.

∴ The total number of parallelograms = 6+7+2+1 = 16

∴ The answer is (c).

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