Practice Counting figures - non verbal reasoning Online Quiz (set-2) For All Competitive Exams
Q-1)
(a)
(b)
(c)
(d)
The figure may be labelled as shown
The Simplest triangles are GLK, DLJ, DJM, HMN, QRE, IRA, IPA and FPO i.e., 8 in number.
The triangles having two components each are BDO, CDQ, DLM, PRA, KFI, NEI, HJI, GJI, DKI and DNI i.e., 10 in number.
The triangles having four components each are DIE, DFI, DOA, DQA and GHI i.e., 5 in number.
The triangles having six components each are DCA and DBA i.e., 2 in number.
DEF is the only one triangle having eight components.
ABC is the only one triangle having twelve components.
Thus, there are 8 + 10 + 5 + 2 + 1 + 1 = 27. triangles in the given figure.
Q-2)
(a)
(b)
(c)
(d)
The figure may be labelled as shown
Triangles
The Simplest triangles are BGM, GHM, HAM, ABM, GIN, IJN, JHN, HGN, IKO, KLO, LJO, JIO, KDP, DEP, ELP, LKP, BCD and AFE i.e.,18 in number.
The triangles composed of two components each are ABG, BGH, GHA, HAB, HGI, GIJ, IJH, JHG, JIK, IKL, KLJ, LJI, LKD, KDE, DEL and ELK i.e.,16 in number.
The triangles composed of four components each are BHI, GJK, ILD, AGJ, HIL and JKE i.e.,6 in number.
Thus, there are 18 + 16 + 6 = 40. triangles in the given figure.
Squares
The squares composed of two components each are MGNH, NIOJ and OKPL i.e.,3 in number.
The squares composed of four components each are BGHA, GIJH, IKLJ and KDEL i.e.,4 in number.
Thus, there are 3 + 4 = 7 squares in the given figure.
Q-3)
(a)
(b)
(c)
(d)
We may the label the figure as shown
The Simplest triangles are AFB, FEB, EBC, DEC, DFE and AFD i.e., 6 in number.
The triangles composed of two components each are AEB, FBC, DFC, ADE, DBE and ABD i.e., 6 in number.
The triangles composed of three components each are ADC and ABC i.e., 2 in number.
There is only one triangle i.e., DBC which is composed of four components.
Thus, there are 6 + 6 + 2 + 1 = 15 triangles in the given figure.
Q-4)
(a)
(b)
(c)
(d)
The figure may be labelled as shown
The Simplest triangles are ABJ, ACJ, BDH, DHF, CIE and GIE i.e.,6 in number.
The triangles composed of two components each are ABC, BDF, CEG, BHJ, JHK, JKI and CJI i.e.,7 in number.
There is only one triangle JHI which is composed of four components.
Thus, there are 6 + 7 + 1 = 14 triangles in the given figure.
Q-5)
(a)
(b)
(c)
(d)
The figure may be labelled as shown
The Simplest triangles are IJO, BCJ, CDK, KQL, MLQ, GFM, GHN and NIO i.e.,8 in number.
The triangles composed of two components each are ABO, AHO, NIJ, IGP, ICP, DEQ, FEQ, KLM, LCP and LGP i.e.,10 in number.
The triangles composed of four components each are HAB, DEF, LGI, GIC, ICL and CLG i.e.,6 in number.
Thus, there are 8 + 10 + 6 = 24. triangles in the given figure.
Q-6)
(a)
(b)
(c)
(d)
Q-7)
(a)
(b)
(c)
(d)
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.
Q-8)
(a)
(b)
(c)
(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
Q-9)
(a)
(b)
(c)
(d)
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.
Q-10)
(a)
(b)
(c)
(d)
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
Q-11)
(a)
(b)
(c)
(d)
We may the label the figure as shown
The Simplest triangles are AEI, AIH, BEJ, BJF, CFK, CKG, DGL, DLH, EOJ, FOJ, FOG, LOG, HOL and HOE i.e.,14 in number.
The triangles composed of two components each are EAH, FBE, BEO, EOF, BFO, FCG, GDH, HOD, HOG and GOD i.e.,10 in number.
The triangles composed of three components each are EFH, EHG, FGH and EFG i.e.,4 in number.
Thus, there are 14 + 10 + 4 = 28. triangles in the given figure.
Q-12)
(a)
(b)
(c)
(d)
Naming the figure
Names of the squares are
| □ABA'X, | □DEFB', | □C'D'T'S', | □D'V'E'T', |
| □WYP'V, | □S'T'W'Q', | □T'E'U'W', | □G'GHH', |
| □TO'RS, | □M'L'OP, | □L'K'NO, | □I'JKL, |
| □ACT'W, | □CEGT' | □WT'OS, | □T'GKO, |
| □AEKS, | □C'V'U'Q', | □WZN'U. | □ZT'R'N' |
| □T'F'J'R', | □F'GIJ', | □UN'QS, | □N'R'OQ |
| □R'J'MO, | □J'IKM, | □ZF'MQ, |
Hence, there are 27 squares in this figure.
Q-13)
(a)
(b)
(c)
(d)
Horizontal lines = AB, EF, GH, CD, LM, PQ, ON = 7
Vertical lines = AC, EG, FH, BD, LO, MN = 6
∴ Total number of straight lines = 7 + 6 = 13
Q-14)
(a)
(b)
(c)
(d)
The figure may be labelled as shown
The horizontal lines are DF and BC i.e., 2 in number
The vertical lines are DG, AH and FI i.e., 3 in number
The slanting lines are AB, AC, BF and DC i.e., 4 in number
Thus, there are 2 + 3 + 4 = 9 straight lines in the figure.
Now, we shall count the number of triangles in the figure.
The Simplest triangles are ADE, AEF, DEK, EFK, DJK, FLK, DJB, FLC, BJG and LIC i.e.,10 in number.
The triangles composed of two components each are ADF, AFK, DFK, ADK, DKB, FCK, BKH, KHC, DGB and FIC i.e.,10 in number.
The triangles composed of three components each are DFJ and DFL i.e.,2 in number.
The triangles composed of four components each are ABK, ACK, BFI, CDG, DFB, DFC and BKC i.e.,7 in number.
The triangles composed of six components each are ABH, ACH, ABF, ACD, BFC and CDB i.e.,6 in number.
There is only one triangle i.e., ABC composed of twelve components.
Thus, there are 10 + 10 + 2 + 7 + 6 +1 = 36 triangles in the given figure.
Q-15)
(a)
(b)
(c)
(d)
Smallest hexagons = KBCMHI, LCDNGH = 2
Largest hexagons = KBDNGI = 1
∴ Total hexagons = 2 + 1 = 3
Q-16)
(a)
(b)
(c)
(d)
The figure, in question may be labelled as shown in following figure.
There are a total of 27 rectangles in the figure, namely
| ▭AEKI, | ▭EGJK, | ▭AGJI, | ▭IKOL, |
| ▭KJMO, | ▭IJML, | ▭LORP, | ▭OMQR, |
| ▭LMQP, | ▭PRFD, | ▭RQHF, | ▭PQHD = 12 |
| ▭AGML, | ▭EBNO, | ▭ABNL, | ▭IJQP, |
| ▭LMHD, | ▭ONCF, | ▭LNCD = 7, | |
| ▭APRE, | ▭IKFD, | ▭AEFD, | ▭ERQG, |
| ▭KFHJ, | ▭EFHG, | ▭GBCH = 7 |
and there is 1 more rectangle ▭ ABCD.
Hence there are a total of 27 rectangles.
Q-17)
(a)
(b)
(c)
(d)
The above figure has following six parallelograms
▱ ABDC,▱ ABFE, ▱ BCED, ▱ BCGF, ▱ CDFE and ▱ DEGF.
Q-18)
(a)
(b)
(c)
(d)
Q-19)
(a)
(b)
(c)
(d)
Smallest and single rectangles
= ▭ABFE, ▭EFIH, ▭BCGF, ▭FGJI = 4
Rectangles formed with two rectangles
= ▭ABIH, ▭AEGC, ▭EGJH, ▭BCJI = 4
Largest rectangle = ▭ACJH = 1
∴ Total number of Rectangles = 4 + 4 + 1 = 9
Q-20)
(a)
(b)
(c)
(d)
We shall label the figure as shown
The Simplest triangles are AFJ, FJK, FKB, BKG, JKG, JGC, HJC, HIJ, DIH, DEI, EIJ and AEJ i.e., 12 in number.
The triangles composed of two components each are JFB, FBG, BJG, JFG, DEJ, EJH, DJH and DEH i.e., 8 in number.
The triangles composed of three components each are AJB, JBC, DJC and ADJ i.e., 4 in number.
The triangles composed of six components each are DAB, ABC, BCD and ADC i.e., 4 in number.
Thus, there are 12 + 8 + 4 + 4 = 28 triangles in the given figure.