SSC CGL Exam Tier-I: Reasoning: Figure Puzzle Quiz!

1. How many triangles are there in the figure PQRS?

16

12

10

8

First of all label the given diagram:

∆PED; ∆PEA; ∆AEQ; ∆QEB; ∆BER; ∆CER; ∆CES; ∆DES; ∆PES; ∆SER; ∆REQ; ∆PEQ; ∆PSR; ∆QRS; ∆PQR; ∆PQS

Thus, there are 16 triangles.

Explanation

First of all label the given diagram:

∆PED; ∆PEA; ∆AEQ; ∆QEB; ∆BER; ∆CER; ∆CES; ∆DES; ∆PES; ∆SER; ∆REQ; ∆PEQ; ∆PSR; ∆QRS; ∆PQR; ∆PQS

Thus, there are 16 triangles.

2. How many triangles are there in the given figure?

16

8

14

12

∆AIH; ∆AIE; ∆EIB; ∆BFI; ∆IHC; ∆IGC; ∆IGD; ∆DFI; ∆IAB; ∆IBD; ∆ICD; ∆IAC; ∆BAC; ∆ACD; ∆BDC; ∆BDA

Explanation

∆AIH; ∆AIE; ∆EIB; ∆BFI; ∆IHC; ∆IGC; ∆IGD; ∆DFI; ∆IAB; ∆IBD; ∆ICD; ∆IAC; ∆BAC; ∆ACD; ∆BDC; ∆BDA

3. How many rectangles are there in the given diagram?

4

7

9

18

The rectangles are:

ABKJ; JKHI; BCLK; KLGH; CDML; LMFG; ACGI; ACLJ; JLGI; BDFH; BDMK; KMFH; ADFI; ADMJ; JMFI

ABHI, BCGH and CDFG are squares.

We know that every square is a rectangle. But its reverse is not always true.

Explanation

The rectangles are:

ABKJ; JKHI; BCLK; KLGH; CDML; LMFG; ACGI; ACLJ; JLGI; BDFH; BDMK; KMFH; ADFI; ADMJ; JMFI

ABHI, BCGH and CDFG are squares.

We know that every square is a rectangle. But its reverse is not always true.

4. How many squares are there in the square figure ABCD?

16

17

26

30

The squares are:

ABCD, AFUO, FBIU, OULD, UICL, EGVT, TVKM, PRXN, RHJX, QSYW, AEQP, PQTO, OTWN, NWMD, EFRQ, QRUT, TUXW, WXLM, FGSR, RSVU, UVYX, XYKL, GBHS, SHIV, VIJY, YJCK, AGYN, EBJW, PSKD, QHCM.

Thus, there are 30 squares.

Explanation

The squares are:

ABCD, AFUO, FBIU, OULD, UICL, EGVT, TVKM, PRXN, RHJX, QSYW, AEQP, PQTO, OTWN, NWMD, EFRQ, QRUT, TUXW, WXLM, FGSR, RSVU, UVYX, XYKL, GBHS, SHIV, VIJY, YJCK, AGYN, EBJW, PSKD, QHCM.

Thus, there are 30 squares.

5. How many triangles are there in the given figure?

18

28

20

24

The triangles are:

∆EAB; ∆FBC; ∆GCD; ∆HAD; ∆ADC; ∆BCD; ∆ABC; ∆ABD; ∆MAB; ∆MBC; ∆MCD; ∆MAD; ∆EAI; ∆EBI; ∆BFJ; ∆FCJ; ∆GCK; ∆GDK; ∆HDL; ∆HAL; ∆AHM; ∆DHM; ∆BFM; ∆CFM; ∆ALM; ∆MLD; ∆BMJ; ∆MCJ

There are 28 triangles.

Explanation

The triangles are:

∆EAB; ∆FBC; ∆GCD; ∆HAD; ∆ADC; ∆BCD; ∆ABC; ∆ABD; ∆MAB; ∆MBC; ∆MCD; ∆MAD; ∆EAI; ∆EBI; ∆BFJ; ∆FCJ; ∆GCK; ∆GDK; ∆HDL; ∆HAL; ∆AHM; ∆DHM; ∆BFM; ∆CFM; ∆ALM; ∆MLD; ∆BMJ; ∆MCJ

There are 28 triangles.

6. How many triangles are there in the following figures?

29

27

23

30

The triangles are:

∆ABC; ∆ADE; ∆AFH; ∆AIL; ∆DFG; ∆DIK; ∆DBO; ∆GDE; ∆EGH; ∆EJL ; ∆EMC ; ∆FIJ; ∆FBN; ∆JFG; ∆GJK; ∆KGH; ∆HKL; ∆HNC; ∆NFH; ∆GMO; ∆IBM; ∆MIJ; ∆JMN; ∆NJK; ∆KNO; ∆OKL; ∆LOC;

Explanation

The triangles are:

∆ABC; ∆ADE; ∆AFH; ∆AIL; ∆DFG; ∆DIK; ∆DBO; ∆GDE; ∆EGH; ∆EJL ; ∆EMC ; ∆FIJ; ∆FBN; ∆JFG; ∆GJK; ∆KGH; ∆HKL; ∆HNC; ∆NFH; ∆GMO; ∆IBM; ∆MIJ; ∆JMN; ∆NJK; ∆KNO; ∆OKL; ∆LOC;

7. How many triangles are there in the following figure?

11

13

9

15

The triangles are:

∆ABC ; ∆ABD ; ∆ADC ; ∆AFC ; ∆FDC ; ∆AFB ; ∆FDB ; ∆FBC ; ∆GBD ; ∆ADE ; ∆GBE ; ∆FDG ; ∆DBE ;

Explanation

The triangles are:

∆ABC ; ∆ABD ; ∆ADC ; ∆AFC ; ∆FDC ; ∆AFB ; ∆FDB ; ∆FBC ; ∆GBD ; ∆ADE ; ∆GBE ; ∆FDG ; ∆DBE ;

8. Six toys are quite identical to look at, but only one of them is less in weight. It is to be identified using the balance minimum number of times. What is that minimum number of using the balance?

Once

2 times

3 times

More than 3 times

First of all, put three toys each on both the pans of the balance. Then, pick up the toys from a lighter pan. Now put one toy each on both the pans. If both the pans weigh equal, then the remaining toy is lighter. If one pan weighs less then that is the lighter toy.

Explanation

First of all, put three toys each on both the pans of the balance. Then, pick up the toys from a lighter pan. Now put one toy each on both the pans. If both the pans weigh equal, then the remaining toy is lighter. If one pan weighs less then that is the lighter toy.

9. Directions: In the following questions, select the related letters/word/number/figure from the given alternatives. How many triangles are there in the following figure?

16

13

9

7

The triangles are: ∆ABC; ∆ABE; ∆ACE; ∆ABD; ∆ACF; ∆ABD; ∆BCD; ∆AFG; ∆ADG; ∆BFG; ∆BEG; ∆CEG; ∆CDG; ∆ACG; ∆ABG; ∆BCG

Thus, there are altogether 16 triangles

Explanation

The triangles are: ∆ABC; ∆ABE; ∆ACE; ∆ABD; ∆ACF; ∆ABD; ∆BCD; ∆AFG; ∆ADG; ∆BFG; ∆BEG; ∆CEG; ∆CDG; ∆ACG; ∆ABG; ∆BCG

Thus, there are altogether 16 triangles

10. How many triangles are there in the following figure?

20

24

28

32

The triangles are:

∆FEB ; ∆CBD ; ∆FAG ; ∆FEG ; ∆BCI ; ∆CDI ; ∆AFI ; ∆EFI ; ∆BGC ; ∆DCG ; ∆AGI ; ∆BIH ; ∆AGB ; ∆ABI ; ∆HAB; ∆HBI ; ∆HGI ; ∆HAG ; ∆GEI ; ∆GED ; ∆IDE ; ∆IDG ; ∆JGI ; ∆JDI ; ∆JGE ; ∆JDE ; ∆AIE ; ∆BGD ;

Thus, there are 28 triangles.

Explanation

The triangles are:

∆FEB ; ∆CBD ; ∆FAG ; ∆FEG ; ∆BCI ; ∆CDI ; ∆AFI ; ∆EFI ; ∆BGC ; ∆DCG ; ∆AGI ; ∆BIH ; ∆AGB ; ∆ABI ; ∆HAB; ∆HBI ; ∆HGI ; ∆HAG ; ∆GEI ; ∆GED ; ∆IDE ; ∆IDG ; ∆JGI ; ∆JDI ; ∆JGE ; ∆JDE ; ∆AIE ; ∆BGD ;

Thus, there are 28 triangles.

11. How many rectangles are there in the figure given?

8

9

10

11

The rectangles are: ABCD, AEJK, AFIK, ABGK, EFIJ, EBGJ, FBGI, FBCH, IGCH, AFHD, KIHD

Explanation

The rectangles are: ABCD, AEJK, AFIK, ABGK, EFIJ, EBGJ, FBGI, FBCH, IGCH, AFHD, KIHD

12. How many triangles are there in the given figure?

29

38

40

35

The simplest triangles are:

∆PNO; ∆PNM; ∆MPQ; ∆MQR; ∆AQP; ∆AQR; ∆BRA; ∆BRC; ∆SRC; ∆SCD; ∆SGR; ∆SGD; ∆DFG; ∆DFE; ∆TLM; ∆TJK; ∆TLK; ∆TIH;

The triangles composed of two components are:

∆PON; ∆PMA; ∆APR; ∆RAM; ∆RAC; ∆RGC; ∆DGC; ∆DGE; ∆MPR; ∆GRD; ∆DCR; ∆TMK; ∆TKI; ∆TIG

The triangles composed of four components are:

∆AMO; ∆AMC; ∆CAG; ∆CGE; ∆MKI; ∆GIK;

Other triangles are: ∆SPI; ∆DQK

Total number of triangles

18 + 14 + 6 + 2 = 40

Explanation

The simplest triangles are:

∆PNO; ∆PNM; ∆MPQ; ∆MQR; ∆AQP; ∆AQR; ∆BRA; ∆BRC; ∆SRC; ∆SCD; ∆SGR; ∆SGD; ∆DFG; ∆DFE; ∆TLM; ∆TJK; ∆TLK; ∆TIH;

The triangles composed of two components are:

∆PON; ∆PMA; ∆APR; ∆RAM; ∆RAC; ∆RGC; ∆DGC; ∆DGE; ∆MPR; ∆GRD; ∆DCR; ∆TMK; ∆TKI; ∆TIG

The triangles composed of four components are:

∆AMO; ∆AMC; ∆CAG; ∆CGE; ∆MKI; ∆GIK;

Other triangles are: ∆SPI; ∆DQK

Total number of triangles

18 + 14 + 6 + 2 = 40

13. How many rectangles are there in the given figure?

24

16

21

14

The rectangles, are: AEML, LMOK, AEOK, KNJD, NOIJ, KOID, AEID, LMID, EFPO, FBGP, EBGO, OGHQ, QHCI, OGCI, EBHQ, EBCI, AFPK, ABGK. NGCJ, KGCD, ABCD.

Thus, there are 21 rectangles.

Explanation

The rectangles, are: AEML, LMOK, AEOK, KNJD, NOIJ, KOID, AEID, LMID, EFPO, FBGP, EBGO, OGHQ, QHCI, OGCI, EBHQ, EBCI, AFPK, ABGK. NGCJ, KGCD, ABCD.

Thus, there are 21 rectangles.