Analytical reasoning test-2

Answer: Option A

Explanation

After labelling the figure, we get the following,

• Simplest triangles AEI, EOJ, OHI, HAI, EBJ, BFJ, FOJ, OEJ, HOL, OGL, GDL, DHL, OFK, FCK,CGK, and GOK (16)
• Triangles with two components each HAE, AEO, EOH, OHA, OEB,EBF, BFO, FOE, DHO, HOG, OGD, GDH, GOF, OFC, FCG, and CGO (16)
• Triangles with four components each HEF, EFG, FGH, GHE, ABO, BCO, CDO, and DAO (8)
• Triangles with eight components each DAB, ABC, BCD and CDA (4)

Total number of triangles in the figure is 16 + 16 + 8 + 4 = 44

Also we need to count the number of squares in this figure,

• Squares with two components each HIOL, IEJO, JFKO, and KGLO (4)
• Squares with four components each AEOH, EBFO, OFGC and HOGD (4)
• Square with eight components is EFGH (1)
• Square with sixteen components is ABCD (1)

Total number of squares in the figure is 4 + 4 + 1 + 1 = 10

Hence option A is correct.

Answer: Option C

Explanation

After labelling the figure, we get the following,

• Simplest triangles BGM, GHM, HAM, ABM, GIN, IJN, JHN, HGN, IKO, KLO, LJO, JIO, KDP, DEP, ELP, LKP, BCD and AFE (18)
• Triangles with two components each ABG, BGH, GHA, HAB, HGI, GIJ, IJH, JHG, JIK, IKL, KLJ, LJI, LKD, KDE, DEL, and ELK (16)
• Triangles with four components each BHI, GJK, ILD, AGJ, HIL and JKE (6)

Total number of triangles in the figure is 18 + 16 + 6 = 40

Also we need to count the number of squares in this figure,

• Squares with two components each MGNH, NIOJ, and OKPL (3)
• Squares with four components each BGHA, GIJH, IKLJ, and KDEL (4)

Total number of squares in the figure is 3 + 4 = 7

Hence option C is correct.

Answer: Option C

Explanation

After labelling the figure, we get the following,

• Simplest triangles ABI, BGI, GHI, HAI, BCJ, CFJ, FGJ, CDK, DEK, EFK and FCK (12)
• Triangles with two components each ABG, BGH, GHA, HAB, BCF,CFG, FGB, GBC, CDE, DEF, EFC, and FCD (12)
• Triangles with four components each AGC, BFD, HBF and CGE (6)

Total number of triangles in the figure is 12 + 12 + 4 = 28

Also we need to count the number of squares in this figure,

• Squares with two components each BJGI and CKFJ (2)
• Squares with four components each ABGH, BCFG and CDEF (3)

Total number of squares in the figure is 2 + 3 = 5

Hence option C is correct.

Answer: Option C

Explanation

We shall join the centres of all the circles by horizontal and vertical lines and then label the resulting figure as shown.

• The simplest squres are ABED, BCFE, DEHG, EFIH, GHKJ, and HILK (6)
• Squares composed of four simple squares are ACIG and DFEL (2)

Total number of squares in the figure is 6+2=8

Hence option C is correct.

Answer: Option A

Explanation

After labelling the figure, we get the following,

• Simplest triangles BPN, PNE, ABM, EFG, MLK, GHI, QRO, RSO, STO and QTO (10)
• Triangles with two components each BPE, TQR, QRS, RST, and STQ (5)
• Triangles with three components each MPO and GPO (2)
• Triangles with six components each LPJ, HPJ, and MPG (3)
• Triangle with twelve components is LPH (1)

Total number of triangles in the figure is 10 + 5 + 2+ 3 + 1 = 21

Also we need to count the number of squares in this figure,

• Squares with two components each KJOM and JIGO (2)
• Squares with four components each ANOM, NFGO and CDEB (3)
• Square composed of four components is QRST (1)
• Square composed of ten components is AFIK (1)

Total number of squares in the figure is 2 + 3 + 1 + 1 = 7

Hence option A is correct.