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Non-Verbal Reasoning - Analytical Reasoning

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13.

Find the number of triangles in the given figure.

A.	10	B.	19
C.	21	D.	23

Answer & Explanation

Answer: Option C

Explanation:

The figure may be labeled as shown. The simplest triangles are ABI, BIC, AIJ, CIJ, AHJ, CDJ, JHG, JDE, GJF and EJF i.e. 10 in number. The triangles composed of two components each are ABC, BCJ, ACJ, BAJ, AJG, CJE and GJE i.e. 7 in number. The triangles composed of four components each are ACG, ACE, CGE and AGE i.e. 4 in number. Total number of triangles in the figure =10+ 7 + 4 = 21.

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14.

Find the number of triangles in the given figure.

A.	5	B.	6
C.	8	D.	10

Answer & Explanation

Answer: Option D

Explanation:

The figure may be labeled as shown. The simplest triangles are AJF, FBG, GCH, HDI and IEJ i.e. 5 in number. The triangles composed of three components each EBH, AIC, EFC, ADG and BJD i.e. 5 in number. Thus, there are 5 + 5 = 10 triangles in the figure.

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15.

Find the minimum number of straight lines required to make the given figure.

A.	9	B.	11
C.	15	D.	16

Answer & Explanation

Answer: Option B

Explanation:

The figure may be labeled as shown. The horizontal lines are DE, FH, IL and BC i.e. 4 in number. The slanting lines are AC, DO, FN, IM, AB, EM and HN i.e. 7 in number. Thus, there are 4 + 7 = 11 straight lines in the figure.

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16.

Find the number of triangles in the given figure.

A.	10	B.	12
C.	14	D.	16

Answer & Explanation

Answer: Option C

Explanation:

The figure may be labeled as shown. The simplest triangles are ABJ, ACJ, BDH, DHF, CIE and GIE i.e. 6 in number. The triangles composed of two components each are ABC, BDF, CEG, BHJ, JHK, JKI and CJI i.e. 7 in number. There is only one triangle JHI which is composed of four components. Thus, there are 6 + 7 + 1 = 14 triangles in the given figure.

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17.

Find the number of triangles in the given figure.

A.	28	B.	32
C.	36	D.	40

Answer & Explanation

Answer: Option C

Explanation:

The figure may be labeled as shown. The simplest triangles are AML, LRK, KWD, DWJ, JXI, IYC, CYH, HTG, GOB, BOF, FNE and EMA i.e. 12 in number. The triangles composed of two components each are AEL, KDJ, HIC and FBG i.e. 4 in number. The triangles composed of three components each are APF, EQB, BQH, GVC, CVJ, IUD, DUL and KPA i.e. 8 in number. The triangles composed of six components each are ASB, BSG, CSD, DSA, AKF, EBH, GGJ and IDL i.e. 8 in number. The triangles composed of twelve components each are ADB, ABC, BCD and CDA i.e. 4 in number. Total number of triangles in the figure = 12 + 4 + 8 + 8 + 4 = 36.

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18.

What is the number of triangles that can be formed whose vertices are the vertices of an octagon but have only one side common with that of octagon?

A.	64	B.	32
C.	24	D.	16

Answer & Explanation

Answer: Option B

Explanation:

When the triangles are drawn in an octagon with vertices same as those of the octagon and having one side common to that of the octagon, the figure will appear as shown in (Fig. 1).

Now, we shall first consider the triangles having only one side AB common with octagon ABCDEFGH and having vertices common with the octagon (See Fig. 2).Such triangles are ABD, ABE, ABF and ABG i.e. 4 in number.

Similarly, the triangles having only one side BC common with the octagon and also having vertices common with the octagon are BCE, BCF, BCG and BCH (as shown in Fig. 3). i.e. There are 4 such triangles. This way, we have 4 triangles for each side of the octagon. Thus, there are 8 x 4 = 32 such triangles.

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