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Reasoning
» Analytical Reasoning
1
How many triangles are there in the following figure. (R.R.B. 2004)
A) 6
B) 10
C) 11
D) 12
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1
How many triangles are there in the following figure. (R.R.B. 2004)
Answer:
A) 6
B) 10
C) 11
D)
12
Explanation:
The figure may be labelled as shown below:
The simplest triangles are ABE, BEF, EFC, CDE and AED i.e. 5 in number.
The triangles composed of two components each are ABF, BCE, ACE and ABD i.e. 4 in number.
The triangles composed of three components each are AFC and BCD i.e. 2 in number.
There is only one triangle ABC composed of five components
Thus, there are 5 + 4 + 2 + 1 = 12 triangles in the figure.
2
How many triangles are there in the following figure. (R.R.B. 2003)
A) 4
B) 5
C) 6
D) 7
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2
How many triangles are there in the following figure. (R.R.B. 2003)
Answer:
A) 4
B)
5
C) 6
D) 7
Explanation:
We may label the figure as shown.
The simplest triangles are ADE, BDF, DEF and EFC i.e., 4 in number
There is only one triangle ABC composed of four components
Thus, there are 4 + 1 = 5 triangles in the given figure.
3
How many triangles are there in the following figure. (S.S.C. 2004)
A) 16
B) 13
C) 9
D) 7
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3
How many triangles are there in the following figure. (S.S.C. 2004)
Answer:
A)
16
B) 13
C) 9
D) 7
Explanation:
The figure may be labelled as shown.
The simplest triangles are AGE, EGC, GFC, BGF, DGB and ADG i.e. 6 in number
The triangles composed of two components each are AGC, BGC and ABG i.e. 3 in number
The triangles composed of three components each are AFC, BEC, BDC, ABF, ABE and DAC i.e. 6 in number
There is only one triangle i.e. ABC composed of six components.
Thus, there are 6 + 3 + 6 + 1 = 16 triangles in the given figure.
4
How many triangles are there in the following figure. (A.A.O. 2005)
A) 16
B) 22
C) 28
D) 32
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4
How many triangles are there in the following figure. (A.A.O. 2005)
Answer:
A) 16
B) 22
C)
28
D) 32
Explanation:
We shall lablel 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 figure.
5
How many triangles are there in the following figure. (R.R.B. 2006)
A) 16
B) 18
C) 14
D) 15
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5
How many triangles are there in the following figure. (R.R.B. 2006)
Answer:
A) 16
B)
18
C) 14
D) 15
Explanation:
We may label the figure as shown.
The simplest triangles are BFG, CGH, EFM, FMG, GMN, GHN, HNI, LMK, MNK and KNJ i.e. 10 in number.
The triangles composed o 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 CLD i.e. 2 in number.
Thus, there are 10 + 2 + 4 + 2 = 18 triangles in the given figure.
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