# Logical Reasoning and Analytical Ability (Test 3)

## Upsc Civil Services Entrance Exams : General Studies Test

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Logical Reasoning and Analytical Ability
| Logical Reasoning | | Analytical Reasoning |
Q.1
Find the number of triangles in the given figure.

A. 22
B. 24
C. 26
D. 28
Explaination / Solution:

The figure may be labelled 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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Q.2
Find the number of triangles in the given figure.

A. 11
B. 13
C. 15
D. 17
Explaination / Solution:

The figure may be labelled as shown.

The simplest triangles are AKI, AIL, EKD, LFB, DJC, BJC, DHC and BCG i.e. 8 in number.

The triangles composed of two components each are AKL, ADJ, AJB and DBC i.e. 4 in number.

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

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

Thus, there are 8+ 4 + 2 + 1= 15 triangles in the figure.

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Q.3
Find the number of triangles in the given figure.

A. 5
B. 6
C. 8
D. 10
Explaination / Solution:

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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Q.4

Find the number of triangles in the given figure.

A. 15
B. 16
C. 17
D. 18
Explaination / Solution:

The figure may be labelled as shown.

The simplest triangles are ABF, BFG, BCG, CGH, GHD, GED, EFG and AFE i.e. 8 in number.

The triangles composed of two components each are ABG, BGE, AGE, ABE and GCD i.e. 5 in number.

The triangles composed of three components each are BCD, CDE, BED and BCE i.e. 4 in number.

Thus, there are 8 + 5 + 4 = 17 triangles in the figure.

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Q.5

Find the number of triangles in the given figure.

A. 20
B. 24
C. 28
D. 32
Explaination / Solution:

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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Q.6

Find the number of triangles in the given figure.

A. 27
B. 25
C. 23
D. 21
Explaination / Solution:

The figure may be labelled as shown.

The simplest triangles are GLK, DLJ, DJM, HMN, QRE, IRA, IPA and FPO i.e. 8 in number.

The triangles having two components each are BDO, CDQ, DLM, PRA, KFI, NEI, HJI, GJI, DKI and DNI i.e. 10 in number.

The triangles having four components each are DIE, DFI, DOA, DQA andGHI i.e. 5 in number.

The triangles having six components each are DCA and DBA i.e. 2 in number.

DEF is the only triangle having eight components.

ABC is the only triangle having twelve components.

Thus, there are 8+10+ 5 + 2+1 + 1 = 27 triangles in the figure.

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Q.7

Find the number of quadrilaterals in the given figure.

A. 6
B. 7
C. 9
D. 11
Explaination / Solution:

The figure may be labelled as shown.

The quadrilaterals in the figure are ABCD, ABDE, ABDF, ABDH, CDHA, CDEA, CDFA, DEAG, DEFA, FAGD and AGDH.

The number of quadrilaterals in the figure is 11.

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Q.8

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

A. 3
B. 4
C. 5
D. 6
Explaination / Solution:

The figure may be labelled as shown.

The regions A, C, E and G can have the same colour say colour 1.

The regions B, D, F and H can have the same colour (but different from colour 1) say colour 2.

The region 1 lies adjacent to each one of the regions A, B, C, D, E, F, G and H and therefore it should have a different colour say colour 3.

The regions J, L and N can have the same colour (different from colour 3) say colour 1.

The regions K, M and O can have the same colour (different fromthe colours 1 and 3). Thus, these regions will have colour 2.

The region P cannot have any of the colours 1 and 2 as it lies adjacent to each one of the regions J, K, L, M, N and O and so it will have colour 3.

The region Q can have any of the colours 1 or 2.

Minimum number of colours required is 3.

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Q.9

Count the number of squares in the given figure.

A. 11
B. 21
C. 24
D. 26
Explaination / Solution:

The figure may be labelled as shown.

The squares composed of two components each are BNQM, CORN, DPSO, MQTL, NRUQ, OSVR, PFWS, QUJT, RVIU and SWHV i.e. 10 in number.

The squares composed of four components each are ABQL, BCRQ, CDSR, DEFS, LQJK, QRIJ, RSHI and SFGH i.e. 8 in number.

The squares composed of eight components each are BRJL, CSIQ and DFHR i.e. 3 in number.

The squares composed of sixteen components each are ACIK, BDHJ and CEGI i.e. 3 in number.

Thus, there are 10 + 8 + 3 + 3 = 24 squares in the figure.

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Q.10

Count the number of rectangles in the given figure.

A. 20
B. 18
C. 16
D. 15
Explaination / Solution:

The figure may be labelled as shown.

The rectangles composed of two components each are HIJE, EKJ,F, FMNG, GPQH, AEOH, EBFO, OFCG and HOGD i.e. 8 in number.

The rectangles composed of four components each are ABFH, BCGE, CDHF, DAEG and EFGH i.e. 5 in number.

The rectangles composed of six components each are IJFG, KLGH, MNHE and PQEF i.e. 4 in number.

The rectangles composed of eight components each are IJMN, KLPQ and ABCD i.e. 3 in number.

Thus, there are 8 + 5 + 4 + 3 = 20 rectangles in the given figure.

(Here note that the squares are also counted amongst rectangles)

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