Notes - Inserting Number Test
Category : 11th Class
Learning Objectives
Inserting the Missing Number
In this chapter questions contain a figure, a set of figures, an arrangement or a matrix, each of which bears certain characters, be it numbers, letters or group/combination of letters numbers which follow a particular pattern. You are required to identify and decipher this pattern and accordingly find the missing character in the figure.
Direction: Find the missing character from among the given alternatives.
1. 
(a) 45 (b) 35
(c) 25 (d) 15
(e) None of these
Ans. (c)
Explanation: The pattern is
\[\to {{(16-6)}^{2}}+{{(5-2)}^{2}}=100+9=109\]
\[\to {{(22-15)}^{2}}+{{(21+19)}^{2}}=49+4=53\]
\[\to {{(17-13)}^{2}}+{{(51-48)}^{2}}=16+9=\]
2. 
(a) 63 (b) 60
(c) 50 (d) 45
(e) None of these
Ans. (a)
Explanation: Moving clockwise direction, the numbers are
\[{{1}^{3}}-1=0,\,\,{{2}^{3}}-1=7,\,\,{{3}^{3}}-1=26\,\,and\,\,{{4}^{3}}-1=63\]
3. 
(a) 4 (b) 9
(c) 24 (d) 27
(e) None of these
Ans. (b)
Explanation: Starting from 3 and moving clockwise, the number in each quadrant is the square of that in the previous quadrant. So, the missing number \[={{3}^{2}}=9.\]
4. 
(a) 50 (b) 39
(c) 26 (d) 1
(e) None of these
Ans. (b)
Explanation: The pattern is \[3\times 2-1=5\]
\[\to 5\times 2-2=8\]
\[\to 8\times 2-3=13\]
\[\to 13\times 2-4=22\]
So, \[22\times 2-5=39\]
5. 
(a) 35 (b) 32
(c) 22 (d) 19
(e) None of these
Ans. (d)
Explanation: Starting from 27 and moving clockwise, the number in alternate segments from the series - 27, 30, 33, 36. The number in remaining segments moving anti clockwise, may from the series - \[,\text{ }21,\text{ }23,\text{ }25,\] or \[21,\text{ }23,\text{ }25\text{ }.\]
So, the missing number is either 19 or 27.
6. 
(a) 0 (b) 25
(c) 125 (d) 216
(e) None of these
Ans. (d)
Explanation: The pattern is
\[{{(5-4)}^{3}}=1\]
\[{{(7-3)}^{3}}=64\]
\[{{(11-8)}^{3}}=27\]
So, the missing number \[={{\left( 8-2 \right)}^{3}}=216.\]
7. 
(a) 18
(b) 36
(c) 135
(d) 175
(e) None of these
Ans. (c)
Explanation: The pattern is
\[15\times 2=30\]
\[2\times 7=63\]
So, the missing number is \[9\times 15=135.\]
Commonly Asked Questions
Direction: In each of the following questions a set of figures carrying certain characters, is given. Assuming that the characters in each set follow a similar pattern, find the missing character in each case.
1. 
(a) 21 (b) 25
(c) 35 (d) 45
(e) None of these
Ans. (b)
Explanation: We have \[\sqrt{4}\times \sqrt{9}=2\times 3=6\]
\[\sqrt{9}\times \sqrt{16}=3\times 4=12\]
Let the missing number be x. Then
\[\sqrt{16}\times \sqrt{x}=20\]
\[\sqrt{x}=\frac{20}{\sqrt{16}}=\frac{20}{4}=5\]
\[\Rightarrow x={{(5)}^{2}}=25\]
2. 
(a) 35 (b) 24
(c) 21 (d) 12
(e) None of these
Ans. (c)
The pattern is \[\frac{27+54}{9}=\frac{81}{9}=9\]
\[\frac{42+84}{14}=\frac{126}{14}=9\]
Let the missing number be x. Then
\[\frac{x+42}{7}=9\to x=63-42=21\]
\[\to \,\,\]
Direction: Find the missing character from among the given alternatives.
3. 
(a) 860
(b) 1140
(c) 2880
(d) 3240
(e) None of these
Ans. (c)
Explanation: Clearly, moving clockwise, we observe the following pattern:
\[4\times 1=4;\text{ }4\times 2=8;\text{ }8\times 3=24;\text{ }24\times 4\text{ }=\text{ }96;\text{ }96\times 5=480\]
So required number \[=\text{ (480}\times \text{6)}=2880\]
Hence, the answer is (c).
4. 
(a) M (b) P
(c) Q (d) S
(e) None of these
Ans. (b)
Explanation: Putting \[A=1,\text{ }B=2,\text{ }C=3,\text{ }D=4,..............\text{ }X=24,\text{ }Y=25,\text{ }Z=26,\]we have:
\[F+P=6+16=22;\text{ }G+N=7+14\text{ }=21;\text{ }J+E=10+5=15\]
Since K = 11, so value corresponding to missing letter \[=\left( 27-11 \right)=16\]
So, the missing letter is the 16th letter of the English alphabet, which is P.
Hence, the answer is (b).
5. 
(a) 22 (b) 30
(c) 32 (d) 42
(e) None of these
Ans. (c)
Explanation: Clearly, we have: \[\frac{5\times 6\times 4}{10}=12;\,\,\frac{6\times 7\times 5}{10}=21;\]
So, missing number = \[\frac{4\times 8\times 10}{10}=32\]
Hence, the answer is (c).
6. 
(a) 15 (b) 25
(c) 45 (d) 55
(e) None of these
Ans. (b)
Explanation: We have: \[\left( 56+15 \right)-\left( 22+8 \right)=41,\text{ }\left( 46+9 \right)-\left( 10+6 \right)=39\]
So, missing number \[=\left( 34+11 \right)-\left( 14+6 \right)=25\]
Hence, the answer is (b).
|
1 |
2 |
3 |
|
4 |
5 |
6 |
|
7 |
8 |
9 |
|
27 |
38 |
? |
(a) 47 (b) 49
(c) 51 (d) 52
(e) None of these
Ans. (c)
Explanation: In the first column, \[\left( 4\times 7 \right)-1=27\]
In the second column, \[(5\times 8)-2=38\]
So, missing number \[=\left( 6\times 9 \right)-3=\left( 54-3 \right)=51\]
Hence, the answer is (c).
|
18 |
24 |
32 |
|
12 |
14 |
16 |
|
3 |
? |
4 |
|
72 |
112 |
128 |
(a) 5 (b) 4
(c) 3 (d) 2
(e) None of these
Ans. (c)
Explanation: In the first column, \[12\times \left( 18\div 3 \right)=72\]
In the third column, \[16\times \left( 32\div 4 \right)=128\]
Let the missing number be x Then, in the second column, we have
\[14\times \left( 24\div x \right)=112\Rightarrow 24\div x=8\Rightarrow x=3\]
Hence, the answer is (c).
|
F |
I |
O |
|
A |
J |
K |
|
E |
M |
? |
(a) P (b) R
(c) S (d) V
(e) None of these
Ans. (b).
Explanation: Putting A = 1, B = 2, C = 3,.......... M = 13, …….., X = 24, Y – 25, Z = 26, we have:
In the first row, F + I = 6 + 9 = 15 = 0
In the second row, A + J = 1 + 10 = 11 = K
So, in the third row, missing letter = E + M = 5 + 13 = 18 = R
Hence, the answer is (b)
Direction: Find the missing character in each of the following:
1. 
(a) 13 (b) 5
(c) 17 (d) 19
(e) None of these
Ans. (b)
Explanation: The sum of the two number in the upper part is 7 times the number in the lower part. So, missing number \[=\left( 89+16 \right)\div 7=15.\]
2. 
(a) 6 (b) 9
(c) 12 (d) 18
(e) None of these
Ans. (c)
Explanation: We have: \[\left( 27\div 3 \right)+\left( 16\div 4 \right)=13;\text{ }\left( 42\div 7 \right)+\left( 65\div 13 \right)=11\]
So, missing number \[=\left( 27\div 9 \right)+\left( 72\div 8 \right)=\left( 3+9 \right)=12.\]
3. 
(a) 84 (b) 195
(c) 240 (d) 180
(e) None of these
Ans. (b)
Explanation: We have: \[{{(2+6+2+3)}^{3}}-1=168;\,\,{{(3+5+2+1)}^{2}}-1=120\]
So, missing number \[={{\left( 2+3+5+4 \right)}^{2}}-1=\left( 196-1 \right)=195.\]
|
1 |
4 |
9 |
? |
|
1 |
2 |
3 |
4 |
|
2 |
4 |
6 |
? |
(a) 16, 8 (b) 25, 5
(c) 36, 4 (d) 49, 7
(e) None of these
Ans. (a)
Explanation: Let x represent a number in the second row. Then, corresponding number in the first row is represented by \[{{x}^{2}}\] and that in the third row by \[2x\]
So, missing number in the first row \[=42=16\]
And, missing number in the third row \[=2\times 4=8.\]
|
5 |
4 |
9 |
|
6 |
3 |
? |
|
7 |
2 |
4 |
|
65 |
20 |
45 |
(a) 1 (b) 2
(c) 3 (d) 4
(e) None of these
Ans. (a)
Explanation: In the first column, \[(6+7)\times 5=65\]
In the second column, \[(3+2)\times 4=20\]
Let the missing number be x. Then,\[(4+x)\times 9=45\Rightarrow 4+x=5\,\,x=1.\]
|
2 |
5 |
10 |
|
17 |
? |
37 |
|
50 |
65 |
82 |
(a) 15 (b) 26
(c) 27 (d) 42
(e) None of these
Ans. (d)
Explanation: We have: \[2+3=5,\text{ }5+5-10,\text{ }10+7=17,\text{ }37+13=50,\text{ }50+15-65,\,\,65+17=82.\]
\[\therefore \] Missing number \[=17+9=26.\]
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