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# Analytical Reasoning Questions

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Choose the correct option.

Find the number of triangles in the given figure.

A18

B20

C24

D27

ENone of these

Explanation:

The figure may be labelled as shown.
The simplest triangles are IJO, BCJ, CDK, KQL, MLQ, GFM, GHN and NIO i.e. 8 in number.

The triangles composed of two components each are ABO, AHO, NIJ, IGP, ICP, DEQ, FEQ, KLM, LCP and LGP i.e.10 in number.

The triangles composed of four components each are HAB, DEF, LGI, GIC, ICL and GLC i.e. 6 in number.

Total number of triangles in the figure = 8 + 10 + 6 = 24.

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Choose the correct option.

Find the number of triangles in the given figure.

A20

B24

C28

D32

ENone of these

Explanation:

The figure may be labelled as shown.
The simplest triangles are ABG, BIG, BIC, CIH, GIH, CDH, HED, GHJ, HJE, FEJ, GFJ and AGF i.e. 12 in number.

The triangles composed of two components each are ABF, CDE, GBC, BCH, GHG, BHG, GHF, GHE, HEF and GEF i.e. 10 in number.

The triangles composed of three components each are ABH, AFH, CDG and GDE i.e. 4 in number.

The triangles composed of four components each are BHF and CGE i.e. 2 in number.

Total number of triangles in the figure = 12 + 10 + 4 + 2 = 28.

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Choose the correct option.

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

A11

B14

C16

D17

ENone of these

Explanation:

The figure may be labelled as shown.
The horizontal lines are AK, BJ, CI, DH and EG i.e. 5 in number.

The vertical lines are AE, LF and KG i.e. 3 in number.

The slanting lines are LC, CF, FI, LI, EK and AG i.e. 6 in number.

Thus, there are 5 + 3 + 6 = 14 straight lines in the figure.

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Choose the correct option.

Find the number of triangles in the given figure.

A11

B13

C15

D17

ENone of these

Explanation:

The figure may be labelled as shown.
The simplest triangles are AFB, FEB, EBC, DEC, DFE and AFD i.e. 6 in number.

The triangles composed of two components each are AEB, FBC, DFC, ADE, DBE and ABD i.e. 6 in number.

The triangles composed of three components each are ADC and ABC i.e. 2 in number.

There is only one triangle i.e. DBC which is composed of four components.

Thus, there are 6 + 6 + 2 + 1 = 15 triangles in the figure.

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5 / 31

Choose the correct option.

Find the number of triangles in the given figure.

A5

B6

C8

D10

ENone of these

Explanation:

The figure may be labelled 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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Choose the correct option.

Find the number of triangles in the given figure.

A18

B20

C28

D34

ENone of these

Explanation:

The figure may be labelled as shown.
The simplest triangles are AEI, AIH, BEJ, BJF, CFK, CKG, DGL, DLH, EOJ, FOJ, FOG, LOG, HOL and HOE i.e. 14 in number.

The triangles composed of two components each are EAH, FBE, BEO, EOF, BFO, FCG, GDH, HOD, HOG and GOD i.e. 10 in number.

The triangles composed of three components each are EFH, EHG, FGH and EFG i.e. 4 in number.

Thus, there are 14 + 10 + 4 = 28 triangles in the given figure.

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Choose the correct option.

Find the number of triangles in the given figure.

A12

B18

C22

D26

ENone of these

Explanation:

The figure may be labelled as shown.
The simplest triangles are AHB, GHI, BJC, GFE, GIE, IJE, CEJ and CDE i.e. 8 in number.

The triangles composed of two components each are HEG, BEC, HBE, JGE and ICE i.e. 5 in number.

The triangles composed of three components each are FHE, GCE and BED i.e. 3 in number.

There is only one triangle i.e. AGC composed of four components.

There is only one triangle i.e. AFD composed of nine components.

Thus, there are 8 + 5 + 3 + 1 + 1 = 18 triangles in the given figure.

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Choose the correct option.

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

A9

B11

C15

D16

ENone of these

Explanation:

The figure may be labelled 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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Find the number of triangles in the given figure.

A4

B5

C6

D7

ENone of these

Explanation:

The figure may be labelled as shown.

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10 / 31

Choose the correct option.

Find the number of triangles in the given figure.

A16

B18

C14

D15

ENone of these

Explanation:

The figure may be labelled as shown.
The simplest triangles are BFG, CGH, EFM, FMG, GMN, GHN, HNI, LMK, MNK and KNJ i.e. 10 in number.

The triangles composed of three components each are FAK and HKD i.e. 2 in number.

The triangles composed of four components each are BEN, CMI, GLJ and FHK i.e. 4 in number.

The triangles composed of eight components each are BAJ and OLD i.e. 2 in number.

Thus, there are 10 + 2 + 4 + 2 = 18 triangles in the given figure.

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