Analytical solving

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Directions: In the following questions, find the correct number of hidden figures which is embedded as whole one figure. You can also review your choices by clicking into answer section.


1. Find the minimum number of straight lines required to make the given figure.

1.

A. 9        

B.11

C.15      

D.16


Answer

                  Ans: Option B

       Explanation:       

      The figure may be labeled as shown.

                      2

       The horizontal lines are DE, FH, IL and BC i.e. 4 in number.

       The slanting lines are AC, DO, FN, IM, AB, EM and HN i.e. 7 in number.

       Thus, there are 4 + 7 = 11 straight lines in the figure.


2. Find the number of triangles in the given figure.

3.

A.16      

B.18

C.14      

D.15


Answer

                  Ans: Option B

       Explanation:

       The figure may be labeled as shown.

            4

      The simplest triangles are BFG, CGH, EFM, FMG, GMN, GHN, HNI, LMK, MNK and KNJ i.e. 10 in number.

      The triangles composed of three components each are FAK and HKD i.e. 2 in number.

      The triangles composed of four components each are BEN, CMI, GLJ and FHK i.e. 4 in number.

      The triangles composed of eight components each are BAJ and OLD i.e. 2 in number.

      Thus, there are 10 + 2 + 4 + 2 = 18 triangles in the given figure.


3. Count the number of squares in the given figure.

5

A. 32      

B. 30

C. 29      

D. 28


Answer

                  Ans: Option B

       Explanation:

       The figure may be labeled as shown.

            6

       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.


4. Count the number of rectangles in the given figure.

7

A. 20     

B. 18

C. 16     

D. 15


Answer

                  Ans: Option A

       Explanation:

       The figure may be labeled as shown.

            8

       The rectangles composed of two components each are HIJE, EKJ,F, FMNG, GPQH, AEOH, EBFO, OFCG and HOGD i.e. 8 in number.

       The rectangles composed of four components each are ABFH, BCGE, CDHF, DAEG and EFGH i.e. 5 in number.

       The rectangles composed of six components each are IJFG, KLGH, MNHE and PQEF i.e. 4 in number.

       The rectangles composed of eight components each are IJMN, KLPQ and ABCD i.e. 3 in number.

       Thus, there are 8 + 5 + 4 + 3 = 20 rectangles in the given figure.

       (Here note that the squares are also counted amongst rectangles)


5. Count the number of parallelogram in the given figure.

9

A. 8       

B. 11

C. 12     

D. 15


Answer

                  Ans: Option D

       Explanation:

       The figure may be labeled as shown.

            10

      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.


6. Find the number of triangles in the given figure.

11

A. 11     

B. 13

C. 15     

D. 17


Answer

                  Ans: Option C

       Explanation:

       The figure may be labeled as shown.

            12

      The simplest triangles are AKI, AIL, EKD, LFB, DJC, BJC, DHC and BCG i.e. 8 in number.

      The triangles composed of two components each are AKL, ADJ, AJB and DBC i.e. 4 in number.

      The triangles composed of the three components each are ADC and ABC i.e. 2 in number.

      There is only one triangle i.e. ADB composed of four components.

      Thus, there are 8+ 4 + 2 + 1= 15 triangles in the figure.


7. Find the number of quadrilaterals in the given figure.

13

A. 6       

B. 7

C. 9        

D. 11


Answer

                  Ans: Option D

       Explanation:

       The figure may be labeled as shown.

             14

        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.


8. In the adjoining figure, if the centers of all the circles are joined by horizontal and vertical lines, then find the number of squares that can be formed.

15

A. 6       

B. 7

C. 8        

D. 1


Answer

                  Ans: Option C

       Explanation:

       The figure may be labeled as shown.

            16

       We shall join the centers 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.


9. Find the minimum number of straight lines required to make the given figure.

17

A. 11     

B. 14

C. 16     

D. 17


Answer

                  Ans: Option B

       Explanation:

       The figure may be labeled as shown.

             22

        The horizontal lines are AK, BJ, CI, DH and EG i.e. 5 in number.

        The vertical lines are AE, LF and KG i.e. 3 in number.

        The slanting lines are LC, CF, FI, LI, EK and AG i.e. 6 in number.

        Thus, there are 5 + 3 + 6 = 14 straight lines in the figure.


10. Find the number of triangles in the given figure.

19

A. 12     

B. 18

C. 22     

D. 26


Answer

                  Ans: Option B

       Explanation:

       The figure may be labeled as shown.

            20

      The simplest triangles are AHB, GHI, BJC, GFE, GIE, IJE, CEJ and CDE i.e. 8 in number.

      The triangles composed of two components each are HEG, BEC, HBE, JGE and ICE i.e. 5 in number.

      The triangles composed of three components each are FHE, GCE and BED i.e. 3 in number.

      There is only one triangle i.e. AGC composed of four components.

      There is only one triangle i.e. AFD composed of nine components.

      Thus, there are 8 + 5 + 3 + 1 + 1 = 18 triangles in the given figure.


11. Count the number of squares in the given figure.

21

A. 8       

B. 12

C. 15     

D. 18


Answer

                  Ans: Option C

       Explanation:

Answer: Option C

Explanation:

     22

The figure may be labeled 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.


 

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