counting figures model question set 2 Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (d)

Answer: (a)

The figure in question looks like as shown below after labelling it.

Smallest Triangles = ΔGAH, ΔHFL, ΔLCI, Δ IDJ ΔJBK, ΔKEG = 6

Largest Triangles = ΔABC, ΔEFD = 2

∴ Total Triangles = 6 + 2 = 8

Answer: (b)

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 given figure.

Answer: (c)

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

The simplest squares are ABED, BCFE, DEHG, EFIH, GHKJ and HILK i.e., 6 in number.

The squares composed of four simple squares are ACIG and DFLJ i.e., 2 in number.

Thus, 6 + 2 = 8 squares will be formed.

Answer: (c)

Given figure can be labelled as follows

In the above figure, triangles formed by single units are ΔABE, ΔAEO, ΔAOF, ΔAFC, ΔDEB, ΔDOE, ΔDFO and ΔDCF i.e., 8 triangles.

Triangles formed by Combining 2 units are ΔABO, ΔAEF, ΔAOC, ΔBOD, ΔDEF, ΔDOC, ΔAED and ΔADF i.e., 8 triangles.

Triangles formed by Combining 3 units are ΔABF, ΔAEC, ΔBDF and ΔEDC i.e., 4 triangles.

Triangles formed by Combining 4 units are ΔABC, ΔBCD, ΔABD and ΔACD i.e., 4 triangles.

∴ Total number of Triangles = 8 + 8 + 4 + 4 = 24