Analytical reasoning test-2

Answer: Option D

Explanation

After labelling the figure, we get the following,

• Simplest squares are QVYU, VRWY, YWSX, and UYXT (4)
• Squares with four components each IMYP, MJNY, YNKO, PYOL, and QRST (5)
• Square with twelve components is MNOP (1)
• Square with sixteen components is IJKL (1)
• Square with twenty four components is AEGK (1)

Total number of squares in the figure is 4 + 5 + 4 + 1 + 1 + 1+ 1 =17

Hence option D is correct.

Answer: Option B

Explanation

After labelling the figure, we get the following,

• Simplest squares are BCNM, CDON, PQIJ, and QRHI (4)
• Squares with four components each MNTS, NOUT, STQP and TURQ (4)
• Squares with five components each ACTL, CEFT, TFGI and LTIK (4)
• Squares with six components each BDUS and SUHJ (2)
• Square with eight components is MORP (1)
• Square with twenty components is AEGK (1)

Total number of squares in the figure is 4 + 4 + 4 + 2 + 1 + 1 = 16

Hence option B is correct.

Answer: Option C

Explanation

After labelling the figure, we get the following,

• Squares with two components each BJMI, CKMJ, DLMK, and AIML (4)
• Squares with three components each EBMA, BFCM, MCGD, and AMDH (4)
• Squares with four components each VWBA, XYCB, ZA1DC and B1C1AD (4)
• Squares with seven components each NOJL, PQKI, RSLJ, and TUIK (4)
• Square with eight components is ABCD (1)
• Square with twelve components is EFGH (1)

Total number of squares in the figure is 4 + 4 + 4 + 4 + 1 + 1 = 18

Hence option C is correct.

Answer: Option C

Explanation

After labelling the figure, we get the following,

• Simplest triangles IJQ, JKQ, KLQ, LMQ, MNQ, NOQ, OPQ, and PIQ (8)
• Triangles with two components each ABQ, BCQ, CDQ, DEQ, EFQ, FGQ, GHQ, HAQ, IKQ, KMQ, MOQ, and OIQ (12)
• Triangles with four components each ACQ, CEQ, EGQ, GAQ, IKM, KMO, MOI and OIK (8)
• Triangles with eight components each ACE, CEG, EGA and GAC (4)

Total number of triangles in the figure is 8 + 12 + 8 + 4 = 32

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

• Squares with two components each IJQP, JKLQ, QLMN, and PQNO (4)
• Squares with four components each ABQH, BCDQ, QDEF and HQFG (4)
• Square with eight components is IKMO (1)
• Square with sixteen components is ACEG (1)

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

Hence option C is correct.

Answer: Option D

Explanation

The various spaces in the figure in the figure may be labelled as shown.

• The spaces P, Q and R have to be shaded by three different colours definitely (since each of these three spaces lies adjacent to the other two).
• Now in order that no two adjacent spaces be shaded by the same colour, the spaces T, U and S must be shaded with the colours of the spaces P, Q and R respectively.
• Also the spaces X,V and W must be shaded with the colours of the spaces R,P and Q respectively.

Thus, minimum three colours are required.

Hence option D is correct