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Analytical Reasoning Questions

1. Find the number of triangles in the given figure.

A. 8
B. 10
C. 12
D. 14

Explanation:

The figure may be labeled as shown.

The simplest triangles are AHG, AIG, AIB, JFE, CJE and CED i.e. 6 in number
The triangles composed of two components each are ABG, CFE, ACJ, and EGI i.e. 4 in number.
The triangles composed of three components each are ACE, AGE, and CFD i.e. 3 in number
There is only one triangle i.e. AHE composed of four components.
Therefore, There are 6 + 4 + 3 + 1 = 14 triangles in the given figure

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2. Find the number of squares in the below figure.

A. 13
B. 15
C. 14
D. 17

3. Find the number of parallelograms in the below figure

A. 18
B. 20
C. 19
D. 16

Explanation:

The simplest Parallelogram are OPTS, PQUT, QRVU, STXW, TUYX, UVZY, these are 6 in number.
The Parallelogram composed of two components each are OQUS, PRVT, SUYW, TVZX, OPXW, PQYX, QRZY, these are 7 such Parallelogram.
And the Parallelogram composed of three components each are ORVS, SVZW these are 2 Parallelogram.
Therefore, the Parallelogram composed of four components each are OQYW, PRZX these are 2 Parallelogram.
Only 1 Parallelogram of six components is ORZW.
So there are 6+7+2+2+1 = 18.

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4. 

A. 16
B. 18
C. 14
D. 15

Explanation:

There are total 10+2+4+2 = 18 triangles in this figure.

5. What will be the number of hexagonal in the following figure?

A. 4
B. 6
C. 2
D. 5

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6. What will be the number of hexagonal in the following figure?

A. 19
B. 18
C. 16
D. 17

Explanation:

7. Find the number of triangles in the given figure.

A. 22
B. 24
C. 26
D. 28

Explanation:

The figure may be labeled as shown.

The simplest triangles are AGH, GFO, LFO, DJK, EKP, PEL, and IMN i.e. 7 in number. The triangles having two components each are GFL, KEL,
AMO, NDP, BHN, CMJ, NEJ, and HFM i.e. 8 in number. The triangles having three components each are IOE, IFP, BIF and CEI i.e. 4 in number.
The triangles having four components each are ANE and DMF i.e. 2 in number. The triangles having five components each are FCK, BGE and
ADL i.e. 3 in number. The triangles having six components each are BPF, COE, DHF, and AJE i.e. 4 in number.
Total number of triangles in the figure = 7 + 8 + 4 + 2 + 3 + 4 = 28

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8. What is the minimum number of different colours required to paint the given figure such that no two adjacent regions have the same color?

A. 1
B. 6
C. 5
D. 2

9. Find the number of triangles in the given figure.

A. 16
B. 22
C. 28
D. 32

Explanation:

The figure may be labeled as shown.

The simplest triangles are AFJ, FJK, FKB, BKG, JKG, JGC, HJC, HIJ, DIH, DEI, EIJ, and AEJ i.e. 12 in number. The triangles composed of two components each are JFB, FBG, BJG, JFG, DEJ, EJH, DJH and DEH i.e. 8 in number. The triangles composed of three components each are AJB, JBC, DJC, and ADJ i.e. 4 in number. The triangles composed of six components each are DAB, ABC, BCD and ADC i.e. 4 in number.

Thus, there are 12 + 8 + 4 + 4 = 28 triangles in the figure.

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10. Find the number of parallelograms.

A. 8
B. 10
C. 15
D. None of These

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