counting figures model question set 1 Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (b)

Answer: (a)

The figure may be labelled as shown

The Simplest ||gms are LMHJ and BDFM i.e.,2 in number.

The ||gms composed of two components each are ABML and MFGH i.e.,2 in number.

The ||gms composed of three components each are LBHI, LBEF, BDGH, DFLA, BCFH, KLFH, ABHJ and LFGJ i.e.,8 in number.

The ||gms composed of six components each are LCFI, KBEH and ADGJ i.e.,3 in number.

∴ Total number of parallelograms in the given figure = 2 + 2 + 8 + 3 = 15.

Answer: (d)

The figure in the question may be labelled as shown in the figure below

In the inner most square, there are five squares namely □IXZU, □UZVJ, □XKWZ, □ZWLV, □IJKL.

In the middle square, there are five squares namely □ETZQ, □QZRF, □TZSG, □ZSHR, □EGHF.

In the outer most square, there are five squares namely □APZM, □MZNB, □PDOZ, □ZOCN, □ABCD.

∴ Total number of squares = 5 + 5 + 5 = 15

Answer: (b)

The figure may be labelled as shown

The squares composed of two components each are BJMI, CKMJ, DLMK and AIML i.e.,4 in number.

The squares composed of three components each are EBMA, BFCM, MCGD and AMDH i.e.,4 in number.

The squares composed of four components each are VWBA, XYCB, ZA$_1$DC and $B_1C_1$AD i.e.,4 in number.

The squares composed of seven components each are NOJL, PQKI, RSLJ and TUIK i.e.,4 in number.

There is only one square i.e., ABCD composed of eight components.

There is only one square i.e., EFGH composed of twelve components.

∴ Total number of squares in the given figure = 4 + 4 + 4 + 4 + 1 + 1 =18.

Answer: (a)

We may the label the figure as shown

The Simplest squares are QUYX, URVY, YVSW and XYWT i.e.,4 in number.

The squares composed of two components each are IMYP, MJNY, YNKO and PYOL i.e.,4 in number.

The squares composed of three components each are AEYH, EBFY, YFCG and HYGD i.e.,4 in number.

There is only one square i.e., QRST composed of four components.

There is only one square i.e., IJKL composed of eight components.

There is only one square i.e., ABCD composed of twelve components.

∴ Total number of squares in the given figure = 4 + 4 + 4 + 1 +1 + 1 =15