RRB General Ability and Intelligence - Analytical Reasoning
Exam Duration: 45 Mins Total Questions : 30
How many straight lines are there in the following figure?
- (a)
9
- (b)
11
- (c)
15
- (d)
48
This figure is labelled as shown:
Horizontal lines are DE, FH, IL and BC i.e. 4 in number. Slanting lines are IM, FN, DO, AC, AB, EM and HN i.e. 7 in number.Total number of lines is 4 + 7 = 11.
What is the number of straight lines in the following figure?
- (a)
10
- (b)
12
- (c)
13
- (d)
17
We can label the figure as shown:
In this figure:
the horizontal lines are AC, HD and GE i.e. 3 in number the vertical lines are AG, BF and CE i.e. 3 in number and the slanting lines are AE, CD, AD, CG, DE and GD i.e. 6 in umber.
Thus, there are 3 + 3 + 6 = 12 lines in all
Count the number of triangles and squares in the following figure:
- (a)
28 triangles, 10 squares
- (b)
28 triangles, 8 squares
- (c)
32 triangles, 10 squares
- (d)
32 triangles, 8 squares
We may label the figure as shown
Triangles:
The simplest triangles are IJO, JKO, KLO, LMO, MNO, NOO, OP~ and, Pl Le. 8 in number.
The triangles composed of two components are ABO, BCO, COO, DEO, EFO, FGO, GHO, HAO, IKO, KMO, MOO and 010 Le. 12 in number.
The triangles composed of four components are ACO, CEO, EGO, GAO, IKM, KMO, MOl and OIK Le. 8 in number.
The triangles composed of eight components are ACE, CEG, EGA and GAC i.e. 4 in number.
Thus, there are 8 + 12 + 8 + 4 = 32 triangles.
Squares:
Squares composed of two components are IJOP, JKlO, LMNO and OPQN Le. 4 in number.
Squares composed of four components are ABOH, BC 00, ODEF and HOFG Le. 4 in number.
The only square composed of eight components is IKMO.
There is only one square composed of sixteen components which is ACEG.
Hence, there are 4 + 4 + 1 + 1 = 10 squares in the figure.
Count the number of triangles in the following figure:
- (a)
15
- (b)
16
- (c)
17
- (d)
18
We label the figure as shown:
Count the number of simplest triangles. These are AFC, AFB, BGF, CGF, CGE, BGD, EHG, and DHG. Thus there are 8 such triangles.
Next, count the number of triangles which are composed of two smaH triangles each.
These are ABC, ACG, CGB, ABG and GDE. Thus, there are 5 such triangles.
Also, count the number of triangles each of which contains three small triangles.
These are BCD, CEB, EDC and EDB. Thus, there are 4 such triangles.
Consequently, there are 8 + 5 + 4 = 17 triangles in the figure.
How many rectangles does the following figure have?
- (a)
10
- (b)
12
- (c)
13
- (d)
14
The figure can be labelled as shown
The rectangles composed of two components are JKBH, lMDB, NOFD and PQHF ie. 4 in number.
The rectangles composed of four components are ACDH, BCEF, DEGH and FGAB i.e. 4 in number.
The rectangles composed of six components are HlMF, BNOH, POBD and JKDF Le. 4 in number.
The rectangles composed of eight components are JKNO and POlM Le. 2 in number.
Hence, the total number of rectangles in the figure = 4 + 4 + 4 + 2 '" 14
How many triangles are there in the figure below?
- (a)
5
- (b)
6
- (c)
8
- (d)
10
The figure is labelled as shown:
The simplest triangles are AJF. BFG. CGH. DHI and EJI Le. 5.
The triangles having three parts are AIC, ADG, EHB. EFC and DJB i.e. 5.
There are 10 triangles in the figure.
Count the number of squares in the figure given below:
- (a)
13
- (b)
16
- (c)
19
- (d)
20
We label the figure as shown:
The simplest squares are BCNM, CDON, HIRQ and SRIJ i.e. 4.
The squares composed of two components are MNUT, NOPU, UPQR and TURS Le. 4.
The squares composed of five components are CEFU, GIUF, IKLU and ACUL Le. 4.
The squares composed of six components are BDPT and TPHJ Le. 2.
There is only one square Le. MOQS composed of eight components.
There is only one square Le. AEGK composed of twenty components.'
Hence, there are 4 + 4 + 4 + 2 + 1 + 1 = 16 squares in the figure.
How many rectangles are there in the given figure?
- (a)
6
- (b)
7
- (c)
8
- (d)
9
The figure may be labelled as shown:
The simplest rectangles are BCJI, IJGH, CDEJ and JEFG Le. 4.
The rectangles composed of two components are BDEI, IEFH, CDFG and BCGH i.e.4.
The only rectangles composed of four components is BDFH.
Thus, there are 4 + 4 + 1 = 9 rectangles in the figure.
Count the number of triangles in the Following figure.
- (a)
8
- (b)
10
- (c)
11
- (d)
12
We label the figure as shown:
Simplest triangles are ABG, BCG, CDE,GCE, AGE and AFE i.e. 6.
Triangles composed of two triangles each, are ABC, ABE, ACE and BCE i.e. 4.
There are 6 + 4 = 10 triangles in the figure .
What is the number of triangles in the following figure?
- (a)
22
- (b)
24
- (c)
26
- (d)
28
We label the figure as below.
T~e simplest triangles are AGH, GFO, LFO, DJK, EKP, PEL and IMN i.e. 7.
The triangles having two components each, are GFL. KEL, AMO, NDP, BHN, CMJ, NEJ and HFM i.e. 8.. 'I
The triangles having three components each are IOE, IFP, BIF and CEI i.e. 4.
The triangles having four components each, are ANE and FMD i.e. 2.
The triangles having five components each, are FCK, BGE and ADL i.e. 3.
The triangles having six components each, are BPF and COE i.e. 2.
:. Total number of triangles in the figure = 7 + 8 + 4 + 2 + 3 + 2 = 26.
How many squares and triangles are there in the following figure?
- (a)
7, 18
- (b)
8, 18
- (c)
8, 15
- (d)
7, 17
The figure may be labelled as shown:
Determination of number of squares:
Squares having two components each, are REQO and GROP i.e. 2.
Squares having three components each, are OQEM and OMDP i.e. 2.
Squares having four components each, are STNL and HIJK i.e. 2.
DEFG is the only square having 10 components.
Thus, there are 2 + 2 + 2 + 1 = 7 squares in the figure.
Determination of number of triangles:
Simplest triangles are ALM, ANM, HIO. IOJ, JOK, HOK, QFC, NEQ, BPG and DLP ie. 8.
Triangles having two components each, a:S ALN, HIJ, IJK, JKH and IKH i.e. 5.
Triangles having three components each, are APO and AQO. Le. 2.
Triangles having six components each, are ABR and ARC i.e. 2.
ABC is the only triangle having 12 components.
Total number of triangles in the given figure = 8 + 5 + 2 + 2 + 1 = 18.
How many triangles are there in the following figure?
- (a)
9
- (b)
10
- (c)
11
- (d)
12
Label the figure as shown.
Simplest triangles are AFE, EFC, CFD, BFD and ABF Le. 5.
Triangles having two components are AFC, CFB, ABO and BAE Le. 4.
Triangles having three components are ADC and EBC Le. 2.
Triangles having five components are ABC i.e.1.
Total number of triangles in the figure = 5 + 4 + 2 + 1 = 12.
Count the number of triangles in the figure given below:
- (a)
11
- (b)
13
- (c)
15
- (d)
17
The figure is labelled as shown
The simplest triangles are AIK, AIL, EKD, FLB, CDJ, CBJ, CDH and CBG i.e. 8.
The triangles composed of two components are ADJ, ABJ, AKL and BCD i.e. 4.
The triangles composed of three components are ADC and ACB i.e. 2.
The only triangle composed of four components is ADB.
Thus, there are 8 + 4 + 2 + 1 = 15 triangles in the figure.
How many triangles are there in the figure given below?
- (a)
21
The figure may be labelled as shown.
Simplest triangles are ABL, BCD, DEF, FGP, PGH, HIQ, IJQ, JKR and KLR i.e. 9.
Triangles composed of two components are OGS, SGQ, SPI, SRI, KSQ, KSM, FGH, HIJ and JKL i.e. 9.
The only triangle composed of four components is KSG.
Triangles composed of five components are CGM, INE, INA and KOC i.e. 4.
Triangles composed of six components are GMK and KOG i.e. 2.
The only triangie composed of ten components is AlE and the only triangle composed of eleven components is CKG.
Total number of triangles in the figure = 9 + 9 + 1 + 4 + 2 + 1 + 1 = 27.
How many triangles and squares are there in the given figure?
- (a)
44 triangles, 10 squares
- (b)
14 triangles, 16 squares
- (c)
24 triangles, 6 squares
- (d)
24 triangles, 9 squares
The figure is labelled as shown below:
Determination of the number of triangles:
Simplest triangles are AIF, IFO, lEO, AlE, FBJ, BJG, JGO, FJO, GKC, HKC, HOK, GOK, OLH, LDH, ELD and ELO i.e. 16.
The triangles having two simple triangles each, are AFE, EDH, HCG, FBG, EOH, HOG, GOF, EOF, AEO, BOG, BOF, AOF, DOE, DOH, GOC and HOC i.e. 16.
The triangles having four simple triangles each, are AOD, DOC, COB, BOA, FEH, EGH, GFH and EFG i.e. 8.
The triangles having eight simple triangles each, are ADC, DBC. ABC and BAD i.e. 4.
The number of triangles in the figure = 16 + 16 + 8 + 4 = 44.
Determination of the number of squares:
The squares containing two triangles each, are GJOK, JOIF, 10LE and LOKH i.e. 4.
The squares containing four triangles each, are BFOG, AFOE, EOHD and GOHC i.e. 4.
EFGH is the only square containing eight triangles.
ABCD is the only square containing sixteen triangles.
The total number of squares in the figure = 4 + 4 + 1+ 1 = 10.
Count the number of triangles and squares in the figure given below:
- (a)
26 triangles, 5 squares
- (b)
26 triangles, 6 squares
- (c)
27 triangles, 6 squares
- (d)
27 triangles, 5 squares
The figure is labelled as shown below:
Triangles:
Simplest triangles are ABJ, BCK, CDK, DEF, BOJ. BOK, KOD. DOF, OFG, HOG, HIO and JOI i.e. 12.
Triangles composed of two components are BCD, ABO, ODE. BOI, BOD, DOG and GOI i.e. 7.
Triangles composed of four components are ACO, COE. DIG. BIG, BID and BDG i.e. 6.
The only triangle composed of eight components is ACE.
Thus, there are 12 + 7 + 6 + 1 = 26 triangles in the given figure.
squares:
T e squares composed of two components are KDFO. FOHG, JOHI and BKOJ i.e. 4.
The only square composed of four components is BCDO.
The only square composed of eight components is BDGI.
Thus, there are 4 + 1 + 1 = 6 squares in the figure.
Count the number of squares in the figure given below:
- (a)
11
- (b)
21
- (c)
24
- (d)
26
We labelled the figure as shown below:
The squares composed of two triangles each, are BMQN, LMQT, TQUJ, RNQU, NCOR, ROSV, URVI, OOPS, PFWS and SWHV i.e. 10.
The squares composed of four triangles each are ABQL, BCRQ, COSR, OEFS, SFGH, RSHI, QRIJ and LQJK i.e. 8. -
The squares composed of eight triangles each, are LBRJ, QCSI and ROFH i.e. 3.
The squares composed of sixteen triangles each, are ACIK, BOHJ and CEGI i.e. 3.
There are 10 + 8 + 3 + 3 = 24 squares in the figure.
How many squares does the following figure have?
- (a)
22
- (b)
20
- (c)
18
- (d)
16
The figure is labelled as shown below
The squares having two components each are BRZ'S, CSZ'T, DTZ'Q and AQZ'R i.e. 4.
The squares having three components each are FBZC, GCZO, HOZA and EAZB i.e. 4.
The squares having four components each, are APOO, ONMC, BCLK and BJIA i.e. 4.
The squares having seven components each, are UVSQ, WXTR, YZQS and A1B1RT i.e. 4.
ABOC is the only square having eight components.
EFGH is the only square having twelve components.
In all, there are 4 + 4 + 4 + 4 + 1 + 1 = 18 squares in the figure.
Study the following figure and answer the question
Count the number of triangles in the figure
- (a)
12
- (b)
16
- (c)
20
- (d)
24
The figure may be labelled as shown:
Tre simplest triangles are ABC, CDE, ACK, AKJ. HJK. CKH. CLH. HLF, LEF. CLE, HIJ and FGH i.e. 12.
The triangles composed of two components are AJH, CJH, ACH, ACJ, CHF, HEF, CEF and CEH i.e. 8.
Total number of triangles in the given figure = 12 + 8 = 20.
Study the following figure and answer the question
How many squares does the figure contain?
- (a)
5
- (b)
6
- (c)
7
- (d)
8
The figure may be labelled as shown:
Squares composed of two components are ABCK, CDEL, CLHK, HIJK and FGHL i.e. 5.
Squares composed of four components are ACHJ and CEFH i.e. 2.
Thus, there are 5 + 2 = 7 squares in the figure.
How many squares are there in the following figure?
- (a)
16
- (b)
17
- (c)
25
- (d)
27
The figure may be labelled as follows:
The simplest squares are ABGF, BCHG, CDIH, DEJI, FGLK, GHML, HINM,IJON,
KLQP, LMRQ, MNSR, NOTS, PQVU, QRWV, RSXW and STYX i.e. 16.
The squares composed of four simple squares are ACMK, BDNL, CEOM, FHRP, GISQ, HJTR, KMWU, LNXV and MOYW i.e. 9.
The squares composed of nine simple squares are ADSP, BETQ, FIXU and GJYV i.e. 4.
AEYU is the only square composed of sixteen simple squares.
There are 16 + 9 + 4 + 1 = 30 squares in the figure.
How many triangles are there in the figure given below:
- (a)
16
- (b)
22
- (c)
28
- (d)
32
The figure may be labelled as shown below:
How many parallelograms are there in the following figure?
- (a)
12
The figure may be labelled as shown.
The simplest 11 gms are ABML, BCNM, CDON, DEFO, OFGH, NOHI, MNIJ and LMJK i.e. 8.
The 11 gms composed of two simple ones are ACLN, BDOM, CEFN, LNIK, MOHJ, NFGI, ABJK, BCIJ, CDHI and DEGH i.e. 10.
The 11 gms composed of three simple 11 gms each, are ADOL, BEFM, LOHK and MFGJ i.e. 4.
The 11 gms composed of four simple 11 gms each, are AEFL, LFGK, ACIK, BDHJ and CEGI i.e. 5.
The 11 gms composed of six simple 11 gms each, are ADHK and BEGJ i.e. 2.
AEGK is the only 11 gm composed of eight 11 gms.
Total number of parallelograms in the figure = 8 + 10 + 4 + 5 + 2 + 1 = 30.
Determine the number of parallelograms in the following figure:
- (a)
39
- (b)
36
- (c)
28
- (d)
20
The figure is labelled as shown
The 11 gms composed of two triangles each, are ADME, DFNM, EMOG, FHJN, MNKO, GOLl, DEGM, FMON, MGIO, HNKJ, NOLK, OICL, DEMF, MGON, FMNH, OILK, NOKJ and HNJB i.e. 18.
The 11 gms composed of four triangles each, are AGOO, EILM, OOKF, AFNE, OHJM, ENKG, NICK, HOLJ, FGIN, HOKB, NILJ and FGOH i.e. 12.
The 11 gms composed of six triangles each, are HICJ, HILB, OECL, AOLl, AEJH and OEJB i.e. 6.
The 11 gms composed of eight triangles each, are FGCK, FGKB and AGKF i.e. 3.
Total number of parallelograms in the figure = 18 + 12 + 6 + 3 = 39.
In the following figure, if the centres of all the circles are joined by horizontal and vertical and lines, then find the number of squares that can be formed
- (a)
6
- (b)
7
- (c)
8
- (d)
10
The centres of all the circles are joined and all the vertices are labelled as shown:
The simplest squares are ABKJ, BCOK, JKLI, KOEL, ILGH and LEFG i.e. 6.
The squares composed of four simple squares each, are ACEI & JOFH i.e. 2
Thus, in this way, 6 + 2 = 8 squares will be formed.
Count the number of rectangles in the following figure:
- (a)
8
- (b)
17
- (c)
18
- (d)
20
The figure may be labelled as shown:
The simplest rectangles are ABOP, PONO, BCON, NOEM, MEFL, LFJK, FGHR and RHIJ i.e. 8.
The rectangles composed of two components each, are ABNO, BCEM, NDFL, MEJK and FGIJ i.e. 5.
The rectangles composed of three components each, are ACDO, BCFL. NDJK and LGIK i.e. 4.
The only rectangle composed of four components is BCJK.
Total number of rectangles in the given figure = 8 + 5 + 4 + 1 = 18.
Count the number of triangles in the following figure:
- (a)
12
- (b)
18
- (c)
22
- (d)
26
The figure is labelled as follows:
The simplest triangles are ABH, BJC, GHI, IJE, JCE, GIE, COE and GEF i.e. 8.
The triangles composed of two components each, are ICE, GJE, HBE, HEG and BCE i.e. 5.
The triangles composed of three components each, are BED, HEF and GCE i.e. 3.
The only triangle composed of four components is AGC.
The only triangle composed of nine components is AFO.
Thus, there are 8 + 5 + 3 + 1 + 1 = 18 triangles in the given figure.
Count the number of pentagons in the following figure:
- (a)
16
- (b)
14
- (c)
12
- (d)
10
The figure is labelled as shown:
The pentagons in the figure are ABDFH, ABDFG, ACDFH, ACDFG, CDFHB, CEFHB, CEFHA, EFHBD, EGHBD, EGHBC, GHBDF and GABDE.
Clearly, these are twelve in number.
Determine the number of rectangles and hexagons in the following figure:
- (a)
8 triangles, 3 hexagons
- (b)
15 triangles, 3 hexagons
- (c)
24 triangles, 5 hexagons
- (d)
30 triangles, 5 hexagons
The figure is labelled as shown:
The simplest rectangles are CVSR, VETS, STKW and RSWM i.e. 4.
The rectangles having two components each. are CETR, RTKM, CVWM and VEKW i.e. 4.
The rectangles having three components each. are ACRP, EGHT, THIK and PRMO i.e. 4.
The rectangles having four components each, are AVSP, VGHS, SHIW, PSWO and CEKM i.e. 5.
The rectangles having five components each, are AETP, CGHR, RHIM and PTKO i.e.4.
The rectangles having six con;ponents each, are ACMO and EGIK i.e. 2.
The rectangles having eight components each, are AGHP, PHIO, AVWO and VGIW i.e. 4.
The rectangles having ten components each, are AEKO and CGIM i.e. 2.
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.
Also, the hexagons in the given figure are CDEKLM, CEUKMQ, CFHJMQ, BEUKNP, and BFHJNP.
There are 5 hexagons in the given figure.
How many circles are there in the figure below?
- (a)
11
- (b)
12
- (c)
13
- (d)
14
There are 13 circles in the given figure. This is clear from the following figure in which all the circles have been numbered from 1 to 13.