Question 1

Count the number of squares in the given figure.

Accepted Answer

The figure may be labelled as shown. The simplest squares are ABGF, BCHG, CDIH, DEJI, FGLK, GHML, HINM, IJON, KLQP, LMRQ, MNSR, NOTS, PQVU, QRWV, RSXW and STYX i.e. 16 in number. The squares composed of four components each are ACMK, BDNL, CEOM, FHRP, GISQ, HJTR, KMWU, LNXV and MOYW i.e. 9 in number. The squares composed of nine components each are ADSP, BETQ, FIXU and GJYV i.e. 4 in number. There is one square AEYU composed of sixteen components. There are 16 + 9 + 4 + 1 = 30 squares in the given figure.

Question 2

Count the number of triangles and squares in the given figure.

Accepted Answer

The figure may be labelled as shown. Triangles: The simplest triangles are JBO, BKO, KDO, DFO, FGO, GHO, HIO, IJO, ABJ, BCK, CKD and DEF i.e.12 in number. The triangles composed of two components each are IBO, BDO, DGO, GIO, ABO, CDO, CBO, CBD and DEO i.e. 9 in number. The triangles composed of four components each are IBD, BDG, DGI, GIB, ACO and COE i.e. 6 in number. There is only one. triangle i.e. ACE composed of eight components. Thus, there are 12 + 9 + 6 + 1 = 28 triangles in the given figure. Squares: The squares composed of two components each are BKOJ, KDFO, OFGH and JOHI i.e. 4 in number. There is only one square i.e. CDOB composed of four components. There is only one square i.e. BDGI composed of eight components. Thus, there are 4 + 1 + 1 = 6 squares in the given figure.

Question 3

Count the number of parallelogram in the given figure.

Accepted Answer

The figure may be labelled as shown. The simplest ||gms are ABFE, BCGF, CDHG, EFJI, FGKJ and GHLK. These are 6 in number. The parallelograms composed of two components each are ACGE, BDHF, EGKI, FHLJ, ABJI, BCKJ and CDLK. Thus, there are 7 such parallelograms. The parallelograms composed of three components each are ADHE and EHLI i.e. 2 in number. The parallelograms composed of four components each are ACKI and BDLJ i.e. 2 in number There is only one parallelogram composed of six components, namely ADLI. Thus, there are 6 + 7 + 2 + 2 + 1 = 18 parallelograms in the figure.

Question 4

Determine the number of rectangles and hexagons in the given figure.

Accepted Answer

The figure may be labelled as shown. Rectangles: The simplest rectangles are CVSR, VETS, RSWM and STKW i.e. 4 in number. The rectangles composed of two components each are CETR, VEKW, RTKM and CVWM i.e. 4 in number. The rectangles composed of three components each are ACRP, PRMO, EGHT and THIK i.e. 4 in number. The rectangles composed of four components each are CEKM, AVSP,PSWO, VGHS and SHIW i.e. 5 in number. The rectangles composed of five components each are AETP, PTKO, CGHR and RHIM i.e. 4 in number. The rectangles composed of six components each are ACMO and EGIK i.e. 2 in number. The rectangles composed of eight components each are AGHP, PHIO, AVWO and VGIW i.e. 4 in number. The rectangles composed of ten components each are AEKO and CGIM i.e. 2 in number. AGIO is the only rectangle having sixteen components. Total number of rectangles in the given figure = 4 + 4 + 4 + 5 + 4 + 2 + 4 + 2 + 1 = 30. Hexagons: The hexagons in the given figure are CDEKLM, CEUKMQ, CFHJMQ, BEUKNP and BFHJNP. So, there are 5 hexagons in the given figure.

Question 5

Count the number of triangles and squares in the given figure.

Accepted Answer

The figure may be labelled as shown. Triangles : The simplest triangles are BPN, PNE, ABM, EFG, MLK, GHI, QRO, RSO, STO and QTO i.e. 10 in number. The triangles composed of two components each are BPE, TQR, QRS, RST and STQ i.e. 5 in number. The triangles composed of three components each are MPO and GPO i.e. 2 in number. The triangles composed of six components each are LPJ, HPJ and MPG i.e. 3 in number. There is only one triangle LPH composed of twelve components. Total number of triangles in the figure = 10 + 5 - 2 + 3 + 1 = 21. Squares : The squares composed of two components each are KJOM and JIGQ i.e. 2 in number. The squares composed of three components each are ANOM, NFGO and CDEB i.e.3 in number. There is only one square i.e. QRST composed of four components. There is only one square i.e. AFIK composed of ten components. Total number of squares in the figure = 2 + 3 + 1 + 1 = 7.

Question 6

Find the number of quadrilaterals in the given figure.

Accepted Answer

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.

Question 7

Count the number of squares in the given figure.

Accepted Answer

The figure may be labelled 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.

Question 8

Count the number of squares in the given figure.

Accepted Answer

The figure may be labelled as shown. The squares composed of two components each are ABKJ, BCLK, CDEL, LEFG, KLGH and JKHI i.e.6 in number. There is only one square i.e. CEGK composed of four components. The squares composed of eight components each are ACGI and BDFH i.e. 2 in number. There are 6 + 1 + 2 = 9 squares in the figure.

Question 9

What is the minimum number of colours required to fill the spaces in the given diagram without any two adjacent spaces having the same colour?

Accepted Answer

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 S, T and U respectively i.e. with the colours of the spaces R, P and Q respectively. Thus, minimum three colours are required.

Question 10

Count the number of convex pentagons in the adjoining figure.

Accepted Answer

A convex pentagon has no angles pointing inwards. More precisely, no internal angles can be more than 180°. The figure may be labelled as shown. The pentagons in the figure, are ABDFH, CDFHB, EFHBD, GHBDF, ACDFG, CEFHA, EGHBC, GABDE, BDEGH, DFGAB, FHACD and HBCEF. Clearly, these are 12 in number.

Question 11

Count the number of parallelogram in the given figure.

Accepted Answer

The figure may be labelled as shown. The simplest parallelograms are LMHJ and BDFM i.e. 2 in number. The parallelograms composed of two components each are ABML and MFGH i.e. 2 in number. The parallelograms composed of three components each are LBHI, LBEF, BDGH, DFLA, BCFH, KLFH, A6HJ and LFGJ i.e. 8 in number. The parallelograms composed of six components each are LCFI, KBEH and ADGJ i.e. 3 in number. Total number of parallelograms in the figure = 2 + 2 + 8 + 3 = 15.

Question 12

What is the number of triangles that can be formed whose vertices are the vertices of an octagon but have only one side common with that of octagon?

Accepted Answer

32

Question 13

How many blocks in a mile?

Accepted Answer

About 15 - 20 blocks become a 1 mile. City blocks differ in sizes. They do not have a standard measurement. Every geographical area has its own average city block size. A city block is a rectangular area in a city with several buildings with the streets around. It is also called "block" which, in a dictionary, is defined as an informal unit of distance from one intersection to the next.

Question 14

What does this symbol mean '&'?

Accepted Answer

'&' is a Logical Symbol and is called as Ampersand. ^ is called Caret - is called Bar v is called Reversed Caret.

Question 15

8(6+5) - 10 =?

Accepted Answer

8(6+5) - 10 = ? ? = 8(11) - 10 ? = 88 - 10 ? = 78.

Question 16

How many lines of symmetry does a Pentagon have?

Accepted Answer

A regular Pentagon have 5 sides and 5 lines of symmetry. The number of lines of symmetry in a regular polygon is equal to the number of sides.

Question 17

A line is an undefined term because it

Accepted Answer

contains an infinite number of points

Question 18

What is Latus Rectum of Parabola?

Accepted Answer

line segment

Question 19

What do you understand by - 'If K is there L has to be there'

Accepted Answer

This would not mean that K and L will always be together. It just implies that, if K is there, then L will also be there. At the same time, it can happen that L is there but K isn't. Remember, the condition is on K, not on L.

Question 20

A university library budget committee must reduce exactly five of eight areas of expenditure—I, J, K, L, M, N, O and P—in accordance with the following conditions: If both I and O are reduced, P is also reduced. If L is reduced, neither N nor O is r…

Accepted Answer

This question concerns a committee’s decision about which five of eight areas of expenditure to reduce. The question requires you to suppose that K and N are among the areas that are to be reduced, and then to determine which pair of areas could not also be among the five areas that are reduced. The fourth condition given in the passage on which this question is based requires that exactly two of K, N, and J are reduced. Since the question asks us to suppose that both K and N are reduced, we know that J must not be reduced: Reduced :: K, N Not reduced :: J The second condition requires that if L is reduced, neither N nor O is reduced. So L and N cannot both be reduced. Here, since N is reduced, we know that L cannot be. Thus, adding this to what we’ve determined so far, we know that J and L are a pair of areas that cannot both be reduced if both K and N are reduced: Reduced :: K, N Not reduced :: J, L Answer choice (B) is therefore the correct answer.

Analytical Reasoning Questions