Question 1
Find the minimum number of straight lines needed to draw the figure given below.

figure for analytical reasoning question 1
A
8✓✗
B
10✓✗
C
12✓✗
D
14✓✗
Explanation
The figure may be labelled as shown in the solution image. The horizontal lines are BD, GI, EF, i.e. 3 in number. The vertical lines are DI, BG, AH, i.e. 3 in number. The slanting lines are AB, AD, CG, CI, i.e. 4 in number. Thus, there are 3 + 3 + 4 = 10 straight lines in the figure.


labelled solution figure for analytical reasoning question 1
Question 2
What is the least number of straight lines required to construct the figure shown below?

figure for analytical reasoning question 2
A
5✓✗
B
7✓✗
C
9✓✗
D
11✓✗
Explanation
The figure may be labelled as shown in the solution image. The horizontal lines are BF, GI, i.e. 2 in number. The vertical lines are FI, BG, DH, i.e. 3 in number. The slanting lines are BH, DG, DI, FH, AC, AE, i.e. 6 in number. Thus, there are 2 + 3 + 6 = 11 straight lines in the figure.


labelled solution figure for analytical reasoning question 2
Question 3
Determine the minimum number of straight lines required to make up the figure below.

figure for analytical reasoning question 3
A
17✓✗
B
19✓✗
C
20✓✗
D
22✓✗
Explanation
The figure may be labelled as shown in the solution image. The horizontal lines are AC, DE, HJ, KL, i.e. 4 in number. The vertical lines are DK, EL, FH, BI, GJ, i.e. 5 in number. The slanting lines are AF, BF, BG, CG, FK, HK, GL, JL, i.e. 8 in number. Thus, there are 4 + 5 + 8 = 17 straight lines in the figure.


labelled solution figure for analytical reasoning question 3
Question 4
Study the figure given below and find the total number of triangles it contains.

figure for analytical reasoning question 4
A
9✓✗
B
11✓✗
C
13✓✗
D
16✓✗
Explanation
The figure may be labelled as shown in the solution image. The triangles are: AEG, AEF, AGF, ABD, ABF, ABC, ADF, ADC, EBF, GDF, BDF, BFC, DFC. Thus, there are 13 triangles in the figure.


labelled solution figure for analytical reasoning question 4
Question 5
Examine the figure carefully and count the total number of triangles present in it.

figure for analytical reasoning question 5
A
8✓✗
B
10✓✗
C
12✓✗
D
15✓✗
Explanation
The figure may be labelled as shown in the solution image. The triangles are: AFI, AFG, AFH, AIG, AIH, AGH, ABE, ABC, ABD, AEC, AED, ACD. Thus, there are 12 triangles in the figure.


labelled solution figure for analytical reasoning question 5
Question 6
In the figure given below, find out how many triangles it contains in total.

figure for analytical reasoning question 6
A
16✓✗
B
18✓✗
C
19✓✗
D
21✓✗
Explanation
The figure may be labelled as shown in the solution image. The triangles are: AHJ, AHI, AJI, AEG, AEI, AEF, AGI, AGF, ABD, ABC, ADC, HEI, JGI, EGI, EIF, GIF. Thus, there are 16 triangles in the figure.


labelled solution figure for analytical reasoning question 6
Question 7
Look at the figure below and determine the total number of triangles formed in it.

figure for analytical reasoning question 7
A
14✓✗
B
16✓✗
C
18✓✗
D
20✓✗
Explanation
The figure may be labelled as shown in the solution image. The triangles are: ACM, ACK, ACG, AMK, AKG, ABF, ABD, AFD, CMK, CMG, CBH, CBE, CHE, MKG, MHL, MHJ, MLJ, KLF, KLI, KFI. Thus, there are 20 triangles in the figure.


labelled solution figure for analytical reasoning question 7
Question 8
The figure below is divided by several lines. Find the total number of triangles in it.

figure for analytical reasoning question 8
A
14✓✗
B
16✓✗
C
18✓✗
D
20✓✗
Explanation
The figure may be labelled as shown in the solution image. The triangles are: ABI, ABH, ABE, AIH, AHE, BIH, BIE, IHE, CDG, CDF, CDE, CGF, CFE, DGF, DGE, GFE. Thus, there are 16 triangles in the figure.


labelled solution figure for analytical reasoning question 8
Question 9
Carefully observe the given figure and count the number of triangles present.

figure for analytical reasoning question 9
A
8✓✗
B
10✓✗
C
12✓✗
D
14✓✗
Explanation
The figure may be labelled as shown in the solution image. The triangles are: ABI, AIG, BED, ICH, ICD, IHD, IHF, IDF, GJH, CEK, CKJ, CHD, CHF, CDF. Thus, there are 14 triangles in the figure.


labelled solution figure for analytical reasoning question 9
Question 10
How many triangles can be counted in the figure given below?

figure for analytical reasoning question 10
A
15✓✗
B
17✓✗
C
19✓✗
D
21✓✗
Explanation
The figure may be labelled as shown in the solution image. The triangles are: BDH, BDF, BDA, BDE, BHF, BFE, BAC, BAE, BCE, DHF, DHE, DAC, DAE, DCE, HFE, HGE, FGE. Thus, there are 17 triangles in the figure.


labelled solution figure for analytical reasoning question 10
Question 11
Analyse the figure below and find the total number of triangles it contains.

figure for analytical reasoning question 11
A
9✓✗
B
11✓✗
C
13✓✗
D
16✓✗
Explanation
The figure may be labelled as shown in the solution image. The triangles are: BLC, FNE, NLA, NAM, NKJ, LAM, LGH, ACE, ACD, AED, AHJ, AHI, AJI. Thus, there are 13 triangles in the figure.


labelled solution figure for analytical reasoning question 11
Question 12
Work out the total number of triangles present in the figure shown below.

figure for analytical reasoning question 12
A
13✓✗
B
15✓✗
C
16✓✗
D
18✓✗
Explanation
The figure may be labelled as shown in the solution image. The triangles are: BGC, FIE, LJH, LIH, LKH, JGH, JKH, AGI, AGH, AIH, ACE, ACD, AED. Thus, there are 13 triangles in the figure.


labelled solution figure for analytical reasoning question 12
Question 13
Count the minimum number of straight lines that must be drawn to form the figure given below.

figure for analytical reasoning question 13
A
9✓✗
B
11✓✗
C
12✓✗
D
14✓✗
Explanation
The figure may be labelled as shown in the solution image. The horizontal lines are BC, DE, FI, i.e. 3 in number. The slanting lines are AF, AI, CG, BH, EH, DG, i.e. 6 in number. Thus, there are 3 + 6 = 9 straight lines in the figure.


labelled solution figure for analytical reasoning question 13
Question 14
Work out the least possible number of straight lines used to draw the figure below.

figure for analytical reasoning question 14
A
9✓✗
B
11✓✗
C
13✓✗
D
16✓✗
Explanation
The figure may be labelled as shown in the solution image. The horizontal lines are BC, DE, FG, HL, i.e. 4 in number. The vertical lines are AJ, i.e. 1 in number. The slanting lines are AH, AL, CI, BK, EJ, DJ, GK, FI, i.e. 8 in number. Thus, there are 4 + 1 + 8 = 13 straight lines in the figure.


labelled solution figure for analytical reasoning question 14
Question 15
Find the minimum number of straight lines that make up the figure shown below.

figure for analytical reasoning question 15
A
8✓✗
B
10✓✗
C
12✓✗
D
14✓✗
Explanation
The figure may be labelled as shown in the solution image. The horizontal lines are AD, IL, EF, GH, i.e. 4 in number. The vertical lines are DL, AI, BJ, CK, i.e. 4 in number. The slanting lines are AL, DI, i.e. 2 in number. Thus, there are 4 + 4 + 2 = 10 straight lines in the figure.


labelled solution figure for analytical reasoning question 15
Question 16
The given figure below is made up of several intersecting lines. Count the total number of triangles in it.

figure for analytical reasoning question 16
A
5✓✗
B
7✓✗
C
9✓✗
D
11✓✗
Explanation
The figure may be labelled as shown in the solution image. The triangles are: AFH, AFD, AFE, AHD, ADE, FHD, FHE, HDE, DCB, DCG, CBG. Thus, there are 11 triangles in the figure.


labelled solution figure for analytical reasoning question 16
Question 17
Count all the triangles, of every size, present in the figure given below.

figure for analytical reasoning question 17
A
22✓✗
B
24✓✗
C
26✓✗
D
28✓✗
Explanation
The figure may be labelled as shown in the solution image. The triangles are: AHF, AHG, AHB, AHE, AFG, AFD, AFE, ABD, ABC, ABE, ADC, ADE, HFB, HFD, HFE, HGE, HBD, HDE, FGE, FBD, FBE, BDE, BCE, DCE. Thus, there are 24 triangles in the figure.


labelled solution figure for analytical reasoning question 17
Question 18
Find out the exact number of triangles contained in the figure shown below.

figure for analytical reasoning question 18
A
20✓✗
B
22✓✗
C
23✓✗
D
25✓✗
Explanation
The figure may be labelled as shown in the solution image. The triangles are: ACK, ACI, ACF, AKI, AIF, ABF, CKI, CKF, CBG, CBF, CBD, CGD, KIF, KJF, IJE, IJF, IJH, IEH, BFD, JFH. Thus, there are 20 triangles in the figure.


labelled solution figure for analytical reasoning question 18
Question 19
In the figure shown below, determine the total count of triangles.

figure for analytical reasoning question 19
A
12✓✗
B
14✓✗
C
16✓✗
D
18✓✗
Explanation
The figure may be labelled as shown in the solution image. The triangles are: AIM, AIK, AMK, ANG, ANH, ACE, ACD, AED, IGJ, MLH, NBF, NBD, NFD, NJL, NJK, NLK, BGC, FEH. Thus, there are 18 triangles in the figure.


labelled solution figure for analytical reasoning question 19
Question 20
Observe the figure below closely and find the number of triangles it is made up of.

figure for analytical reasoning question 20
A
11✓✗
B
13✓✗
C
15✓✗
D
18✓✗
Explanation
The figure may be labelled as shown in the solution image. The triangles are: ACK, AKB, ABD, CKB, CBE, KBE, KBD, KIG, KIH, KGH, BFJ, BFH, BJH, FDG, JIE. Thus, there are 15 triangles in the figure.


labelled solution figure for analytical reasoning question 20
Question 21
Study the given figure and work out the total number of triangles present in it.

figure for analytical reasoning question 21
A
9✓✗
B
11✓✗
C
13✓✗
D
16✓✗
Explanation
The figure may be labelled as shown in the solution image. The triangles are: AJM, ACD, ABD, AEH, MKD, MLD, CKN, CBD, CFI, KLD, DHF, DHG, DFG. Thus, there are 13 triangles in the figure.


labelled solution figure for analytical reasoning question 21
Question 22
Count the total number of squares, of every size, in the figure given below.

figure for analytical reasoning question 22
A
8✓✗
B
10✓✗
C
12✓✗
D
14✓✗
Explanation
The figure may be labelled as shown in the solution image. Squares of size 1 (smallest first): ABFE, DCGH, POKL, MNJI, BCGF, NOKJ, EIJF, HLKG, FJKG, i.e. 9 in number. Squares of size 2 (smallest first): ACKI, DBJL, PNFH, MOGE, i.e. 4 in number. Squares of size 3 (smallest first): ADPM, i.e. 1 in number. Total number of squares = 9 + 4 + 1 = 14.


labelled solution figure for analytical reasoning question 22
Question 23
Study the figure below and find the total number of squares it contains.

figure for analytical reasoning question 23
A
10✓✗
B
12✓✗
C
13✓✗
D
15✓✗
Explanation
The figure may be labelled as shown in the solution image. Squares of size 1 (smallest first): DEIH, FEIJ, NMIJ, LMIH, i.e. 4 in number. Squares of size 2 (smallest first): ABIG, CBIK, QPIK, OPIG, DFNL, i.e. 5 in number. Squares of size 3 (smallest first): ACQO, i.e. 1 in number. Total number of squares = 4 + 5 + 1 = 10.


labelled solution figure for analytical reasoning question 23
Question 24
How many squares, of any size, are there in the figure given below?

figure for analytical reasoning question 24
A
9✓✗
B
11✓✗
C
13✓✗
D
15✓✗
Explanation
The figure may be labelled as shown in the solution image. Squares of size 1 (smallest first): DEIH, FEIJ, NJIM, LMIH, i.e. 4 in number. Squares of size 2 (smallest first): ABIG, CBIK, QKIP, OPIG, DFNL, i.e. 5 in number. Squares of size 3 (smallest first): BKPG, i.e. 1 in number. Squares of size 4 (smallest first): ACQO, i.e. 1 in number. Total number of squares = 4 + 5 + 1 + 1 = 11.


labelled solution figure for analytical reasoning question 24
Question 25
Study the figure given below and find the total number of triangles and squares it contains.

figure for analytical reasoning question 25
A
24 triangles, 7 squares✓✗
B
26 triangles, 5 squares✓✗
C
28 triangles, 7 squares✓✗
D
30 triangles, 5 squares✓✗
Explanation
The figure may be labelled as shown in the solution image. Triangles: BEA, BIC, BIJ, BIF, BCJ, BCF, BJD, ELD, ELK, ELH, ECK, EDK, EDH, ILM, ICJ, ICK, IJF, LJD, LDK, LKH, CJD, CJK, CJF, CJG, CDK, CDG, JDK, JKG, DKG, DKH, i.e. 30 in number. Squares: BIJC, ELKD, CJKD, CFJG, DGKH, i.e. 5 in number. So there are 30 triangles and 5 squares.


labelled solution figure for analytical reasoning question 25
Question 26
Count the number of triangles as well as squares present in the figure shown below.

figure for analytical reasoning question 26
A
16 triangles, 3 squares✓✗
B
18 triangles, 5 squares✓✗
C
20 triangles, 3 squares✓✗
D
22 triangles, 5 squares✓✗
Explanation
The figure may be labelled as shown in the solution image. Triangles: BDH, BDA, BGC, BGH, BGE, BCH, BCE, DIC, DIH, DIF, DCH, DCF, GIC, GIJ, GCH, GHE, ICH, IHF, CHE, CHF, i.e. 20 in number. Squares: BGHC, DIHC, CEHF, i.e. 3 in number. So there are 20 triangles and 3 squares.


labelled solution figure for analytical reasoning question 26
Question 27
Examine the figure below and determine the total number of triangles and squares in it.

figure for analytical reasoning question 27
A
37 triangles, 9 squares✓✗
B
39 triangles, 7 squares✓✗
C
41 triangles, 9 squares✓✗
D
43 triangles, 7 squares✓✗
Explanation
The figure may be labelled as shown in the solution image. Triangles: BFA, BKC, BKL, BKG, BCL, BCG, BLD, FOE, FON, FOJ, FDN, FEN, FEJ, KCL, KCM, KLG, OME, OEN, ONJ, CLD, CLM, CLG, CLH, CDM, CDH, CME, LDM, LDN, LMH, DME, DMN, DMH, DMI, DEN, DEI, MEN, MNI, ENI, ENJ, i.e. 39 in number. Squares: BKLC, FONE, CLMD, CGLH, DMNE, DHMI, EINJ, i.e. 7 in number. So there are 39 triangles and 7 squares.


labelled solution figure for analytical reasoning question 27
Question 28
Examine the figure shown below and count the number of squares present in it.

figure for analytical reasoning question 28
A
9✓✗
B
11✓✗
C
12✓✗
D
14✓✗
Explanation
The figure may be labelled as shown in the solution image. Squares of size 1 (smallest first): DFML, HFMN, VTMN, RTML, i.e. 4 in number. Squares of size 2 (smallest first): AEJC, BIKG, PWYU, OSXQ, i.e. 4 in number. Squares of size 3 (smallest first): DHVR, i.e. 1 in number. Total number of squares = 4 + 4 + 1 = 9.


labelled solution figure for analytical reasoning question 28
Question 29
Work out the total number of squares (of all sizes) in the figure given below.

figure for analytical reasoning question 29
A
7✓✗
B
9✓✗
C
10✓✗
D
12✓✗
Explanation
The figure may be labelled as shown in the solution image. Squares of size 1 (smallest first): BCGF, DCGH, LHGK, JKGF, i.e. 4 in number. Squares of size 2 (smallest first): CHKF, i.e. 1 in number. Squares of size 3 (smallest first): BDLJ, i.e. 1 in number. Squares of size 4 (smallest first): AIME, i.e. 1 in number. Total number of squares = 4 + 1 + 1 + 1 = 7.


labelled solution figure for analytical reasoning question 29
Question 30
Find the exact number of squares contained in the figure shown below.

figure for analytical reasoning question 30
A
8✓✗
B
10✓✗
C
12✓✗
D
14✓✗
Explanation
The figure may be labelled as shown in the solution image. Squares of size 1 (smallest first): EDHI, EFJI, HLMI, JNMI, i.e. 4 in number. Squares of size 2 (smallest first): AEHC, EHMJ, EBGJ, HMPK, JOQM, i.e. 5 in number. Squares of size 3 (smallest first): DFNL, i.e. 1 in number. Total number of squares = 4 + 5 + 1 = 10.


labelled solution figure for analytical reasoning question 30
Question 31
How many circles are there in the figure given below?

figure for analytical reasoning question 31
A
7✓✗
B
9✓✗
C
11✓✗
D
13✓✗
Explanation
The figure may be labelled as shown in the solution image. There are 13 circles. This is clear from the solution figure, in which the circles have been numbered 1 to 13.


labelled solution figure for analytical reasoning question 31
Question 32
Count the total number of circles present in the figure shown below.

figure for analytical reasoning question 32
A
6✓✗
B
8✓✗
C
10✓✗
D
13✓✗
Explanation
The figure may be labelled as shown in the solution image. There are 10 circles. This is clear from the solution figure, in which the circles have been numbered 1 to 10.


labelled solution figure for analytical reasoning question 32
Question 33
Study the figure below and find out how many circles it contains.

figure for analytical reasoning question 33
A
11✓✗
B
13✓✗
C
15✓✗
D
17✓✗
Explanation
The figure may be labelled as shown in the solution image. There are 13 circles. This is clear from the solution figure, in which the circles have been numbered 1 to 13.


labelled solution figure for analytical reasoning question 33
Question 34
Determine the total number of rectangles and hexagons present in the figure given below.

figure for analytical reasoning question 34
A
24 rectangles, 11 hexagons✓✗
B
26 rectangles, 9 hexagons✓✗
C
28 rectangles, 11 hexagons✓✗
D
30 rectangles, 9 hexagons✓✗
Explanation
The figure may be labelled as shown in the solution image. Rectangles (squares count as rectangles): AEOK, AEJF, AKLB, AKMC, AKND, AFGB, AFHC, AFID, EOLB, EOMC, EOND, EJGB, EJHC, EJID, OKFJ, OJGL, OJHM, OJIN, KFGL, KFHM, KFIN, BLMC, BLND, BCHG, BDIG, LMHG, LNIG, CMND, CDIH, MNIH, i.e. 30 in number. Hexagons: AEJNLF, ADJOLF, ADJNLF, EJNKFB, EJNLFB, OKFBDJ, OLFBDJ, KFBDJN, FBDJNL, i.e. 9 in number. So there are 30 rectangles and 9 hexagons.


labelled solution figure for analytical reasoning question 34
Question 35
Study the figure shown below and find the number of rectangles as well as hexagons it contains.

figure for analytical reasoning question 35
A
26 rectangles, 1 hexagons✓✗
B
28 rectangles, 3 hexagons✓✗
C
30 rectangles, 1 hexagons✓✗
D
32 rectangles, 3 hexagons✓✗
Explanation
The figure may be labelled as shown in the solution image. Rectangles (squares count as rectangles): BFPL, BFKG, BLMC, BLOE, BLND, BGHC, BGJE, BGID, FPMC, FPOE, FPND, FKHC, FKJE, FKID, PLGK, PKHM, PKJO, PKIN, LGHM, LGJO, LGIN, CMOE, CMND, CEJH, CDIH, MOJH, MNIH, EOND, EDIJ, ONIJ, i.e. 30 in number. Hexagons: AEOQMC, i.e. 1 in number. So there are 30 rectangles and 1 hexagons.


labelled solution figure for analytical reasoning question 35
Question 36
Count the total number of rectangles and hexagons in the figure given below.

figure for analytical reasoning question 36
A
10 rectangles, 13 hexagons✓✗
B
12 rectangles, 15 hexagons✓✗
C
14 rectangles, 13 hexagons✓✗
D
16 rectangles, 15 hexagons✓✗
Explanation
The figure may be labelled as shown in the solution image. Rectangles (squares count as rectangles): AEMI, AIJB, AIKC, AILD, EMJB, EMKC, EMLD, BJKC, BJLD, CKLD, i.e. 10 in number. Hexagons: AEHLJF, ABGKJF, ADHMJF, ADHLJF, EHLIFB, EHLJFB, EHLKGD, MIFBDH, MJFBDH, MLGCDH, IFBCGJ, IFBDHL, BDHLJF, i.e. 13 in number. So there are 10 rectangles and 13 hexagons.


labelled solution figure for analytical reasoning question 36
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