Missing Numbers :
Missing numbers in the figures : In these type of
questions certain numbers are given in
(a)
figure or figures with a blank space. The numbers given in the figures have
certain relationship among them. Identify the relationship among the given
numbers and find the missing number(s) in the figure. Let us discuss the
concept with the following examples.
Worked out Examples :
Example 1.
Find the missing number numbers in the figure.
|
3
|
5
|
8
|
12
|
|
11
|
13
|
16
|
20
|
|
9
|
?
|
14
|
18
|
(a) 12
(b) 11
(c) 10
(d) 16
Solution.
The logic in the first row is = 3+2, 5+3,
8+4, 12.
The logic in the second row is = 11+2, 13+3,
16+4, 20.
Similarly the logic in the third row is = 9+1,
11+3, 14+4, 18.
The
missing number in the figure is 11.
Example 2.
Find the missing number in the given figure.
Solution.
The given logic is as shown below.
Similarly
The
missing number in the figure is 27. Choice (a)
Counting Triangles :
Counting
Triangles : Though it is named as counting triangles the questions may be based
on the counting triangles squares, rectangles etc. In these questions a
geometrical figure is given (which may be regular or irregular in shape) and
asked to count the number of regular geometrical figures (triangles, squares
etc.) hidden in the given figure.
Let us discuss the concept with the following examples.
Example 3.
Find
the number of triangles in the given figure.
(a) 5
(b) 6
(c) 7
(d) 8
Solution.
Let
us represents the vertices in the given Geometrical figures with the alphabet
as shown below.
In the Ale ABC, we have the smaller triangles,
i.e., ADE.
CDF, BEF and DEF.
The
total number of triangles are 5.
Choice (a)
Example 4.
Find the number of squares in the given figure.
(a) 12
(b) 9
(c) 10
(d) 11
Solution.
Let us represent the vertices in the given Geometrical
figure with the alphabet as shown below.
The
squares in the given figure are ABCD, AEQH, EQBF. QFCG, HQGD, IJKL, IMQP, MJNQ,
QNKO and QOLP .
The
total number of squares are 10.
Example 5.
Find the number of triangles in the given figure.
(a) 18
(b) 19
(c) 20
(d) 21
Solution.
Let
us represent the given vertices on the given Geometrical figure with the
alphabet as shown below.
The
triangles in the given figure are – ABC, DEF, GHI, AGJ, DKH, ADL, JKL, MLN,
GKE, JBH, GCE, LEB, HBF, GOP, HQR, PME, NQB, EBI, PQI, AON and DMR.
The
total number of triangles are 21.
Choice (d)
