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Worked Examples Type-I

One of the terms in the following number series is wrong. Identify the wrong term (odd man).
 
Example-1
3 7 16 33 74 153 312
  1. 7
  2. 33
  3. 74
  4. 153
  5. 312
Solution
First, we shall identify the pattern followed by the terms of the above number series.
 
3 × 2 + 1 = 7.
 
7 × 2 + 2 = 16.
 
16 × 2 + 3 = 35 ≠ 33.
 
35 × 2 + 4 = 74.
 
74 × 2 + 5 = 153.
 
153 × 2 + 6 = 312.
 
So, 33 is the wrong number in the series.
 
Answer: (2)
 
 
Example-2
20 24 40 76 150 240
  1. 20
  2. 40
  3. 76
  4. 150
  5. 240
Solution
20 + 22 = 20 + 4 = 24.
 
24 + 42 = 24 + 16 = 40.
 
40 + 62 = 40 + 36 = 76.
 
76 + 82 = 76 + 64 = 140 ≠ 150.
 
140 + 102 = 140 + 100 = 240.
 
Answer: (4)
 
 
Example-3
3 15 25 100 110 324 330 660 664
  1. 15
  2. 100
  3. 110
  4. 330
  5. 660
Solution
3 × 5 = 15.
 
15 + 10 = 25.
 
25 × 4 = 100.
 
100 + 8 = 108 ≠ 110.
 
108 × 3 = 324.
 
324 + 6 = 330.
 
330 × 2 = 660.
 
660 + 4 = 664.
 
Answer: (3)
 
 
Example-4
26 34 41 46 56 68 80 88
  1. 26
  2. 41
  3. 56
  4. 68
  5. 88
Solution
On carefully observing each term of the series, we notice that the sum of the digits of a term is added to the same term to get the next term.
 
26 + (2 + 6) = 34.
 
34 + (3 + 4) = 41.
 
41 + (4 + 1) = 46.
 
46 + (4 + 6) = 56.
 
56 + (5 + 6) = 67 ≠ 68.
 
67 + (6 + 7) = 80.
 
80 + (8 + 0) = 88.
 
Answer: (4)
 
 
Example-5
16 22 26 38 62 74 100
  1. 16
  2. 26
  3. 62
  4. 74
  5. 100
Solution
In this example, the product of digits of a term is added to the same term to get the next term.
 
16 + (1 × 6) = 16 + 16 = 22.
 
22 + (2 × 2) = 22 + 4 = 26.
 
26 + (2 × 6) = 26 + 12 = 38.
 
38 + (3 × 8) = 38 + 24 = 62.
 
62 + (6 × 2) = 62 + 12 = 74.
 
74 + (7 × 4) = 74 + 28 = 102 ≠ 100.
 
Answer: (5)
 
 
Example-6
6 13 24 51 98 201 408
  1. 6
  2. 13
  3. 51
  4. 201
  5. 408
Solution
6 × 2 + 1 = 13.
 
13 × 2 - 2 = 24.
 
24 × 2 + 3 = 51.
 
51 × 2 - 4 = 98.
 
98 × 2 + 5 = 201.
 
201 × 2 - 6 = 396 ≠ 408.
 
Answer: (5)
 
 
Example-7
696 340 168 80 36 14 3
  1. 168
  2. 36
  3. 696
  4. 340
  5. 696
Solution
Observe the difference between the consecutive terms.
 
In this illustration, let us analyse the pattern from the right end of the series.
 
3 + 11 = 14.
 
14 + 22 = 36.
 
36 + 44 = 80.
 
80 + 88 = 168.
 
168 + 176 = 344 ≠ 340.
 
344 + 352 = 696.
 
Alternate method:
 
3 × 2 + 8 = 14.
 
14 × 2 + 8 = 36.
 
36 × 2 + 8 = 80.
 
80 × 2 + 8 = 168.
 
168 × 2 + 8 = 344 ≠ 340.
 
344 × 2 + 8 = 696.
 
So, 340 is the wrong term.
 
Answer: (4)
 
 
Example-8
2 3 4 6 12 12 48 24 250
  1. 4
  2. 6
  3. 48
  4. 24
  5. 250
Solution
In this example, two series are combined together.
 
First, consider the terms only at the odd positions and find out the pattern.
 
2 4 12 48 250
 
2 × 2 = 4.
 
4 × 3 = 12.
 
12 × 4 = 48.
 
48 × 5 = 240 ≠ 250.
 
Now, consider the terms at the even positions and find the pattern.
 
3 6 12 24
 
3 × 2 = 6.
 
6 × 2 = 12.
 
12 × 2 = 24.
 
All the terms follow the same pattern.
 
So, 250 is the wrong term.
 
Answer: (5)
 
 
Example-9
3 11 31 68 131 223
  1. 131
  2. 68
  3. 223
  4. 31
  5. 11
Solution
13 + 2 = 3.
 
23 + 3 = 11.
 
33 + 4 = 31.
 
43 + 5 = 69 ≠ 68.
 
53 + 6 = 131.
 
63 + 7 = 223.
 
Answer: (2)
 
 
Example-10
1112 1314 1516 1718 1921 2122 2324
  1. 1112
  2. 1516
  3. 1921
  4. 2122
  5. 2324
Solution
Two consecutive two-digit numbers are written side-by-side, in each of the term except in 1921.
 
Hence, 1921 is the wrong term.
 
Answer: (3)
 





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