Chapter 9 Exercise 9A CA foundation maths solutions
Number series Coding Decoding and Odd Man out Series chapter 9 exercise 9A CA foundation maths solutions are given.
You must study the textbook lesson Number series Coding Decoding and Odd Man out Series very well.
You should practice all examples which are given in the textbook.
You can observe the solutions given below and try them in your own way.
Number series, Coding Decoding and Odd Man out Series CA foundation maths solutions
CA foundation maths solutions
Chapter 9
Number series Coding Decoding and Odd Man out Series
Exercise 9A
Questions and solutions
1) 6, 11, 21, 36, 56 ?
Solution:
6, 11, 21, 36, 56 ?
The difference between two consecutive terms are 5, 10, 15, 20.
It increased by 5 so the next difference must be 25
Therefore, the next term = 56 + 25 = 81
So, the required number is 81.
2) 10, 100, 200, 310 ?
Solution:
10, 100, 200, 310 ?
The difference between two consecutive terms are 90, 100, 110.
It increased by 10, so the next difference must be 20.
Therefore, the next term = 300 + 120 = 430
So, the required number is 430.
3) 11, 13, 17, 19, 23, 25, 29 ?
Solution:
11, 13, 17, 19, 23, 25, 29 ?
The difference between the numbers are 2, 4, 2, 4, 2, 4.
From this pattern the numbers after 29 should be 31. [ 29 + 2]
Therefore, the required number is 31.
4) 6, 12, 21, 33 ?
Solution:
6, 12, 21, 33 ?
The difference between two consecutive terms are 6, 9, 12.
It increased by 3, so the next difference must be 15.
Therefore, the next term = 33 + 15 = 48.
So, the required number is 48.
5) 2, 5, 9, 14, ?, 27
Solution:
2, 5, 9, 14, ?, 27
The difference between two consecutive terms are 3, 4, 5.
It increased by 1, so the next difference must be 6.
Therefore, the next term = 14 + 6 = 20.
Again the next difference become 7.
The next term 20 + 7 = 27.
Therefore, the required number is 20.
6) 6, 11, 21, ?, 56, 81
Solution:
6, 11, 21, ?, 56, 81
The difference between two consecutive terms are 5, 10, 25.
It increased by 5, so the next difference must be 15.
Therefore, the next term = 21 + 15 = 36
So, the required number is 36.
7) 10, 18, 28, 40, 54, ?, 88
Solution:
10, 18, 28, 40, 54, ?, 88
Difference between two consecutive terms are 8, 10, 12, 14.
It increased by 2, so the next difference must be 16.
Therefore, the next term = 54 + 16 = 70.
Again the next term = 70 + 18 = 88.
So, the required number is 70.
8) 120, 99, ?, 63, 48, 35
Solution:
120, 99, ?, 63, 48, 35
The difference between first and second term is 21.
The difference between 4th and 5th term is 15.
The difference between 5th and 6th is 13.
So the difference decreased by 2.
Therefore, the difference between second and third term must be 19.
So the required term = 99 – 19 = 80.
The difference between next terms 80 – 63 =17
9) 22, 24, 28, 36, ?, 84
Solution:
22, 24, 28, 36, ?, 84
They difference between two consecutive terms are 2, 4, 8.
It is double of the previous one. From this pattern the next differences must be 16, 32.
First term = 22
Second term = 22 + 2 = 24
Third term = 24 + 4 = 28
4th term = 28 + 8 = 36
5th term = 36 + 16 = 52.
6th term = 52 + 32 = 84.
Therefore, the required number is 52.
10) 4832, 5840, 6848, 7856 ?
Solution:
4832, 5840, 6848, 7856 ?
The difference between the numbers is 1008.
Therefore, the next number or the required number = 7856 + 1008 = 8864.
11) 10, 100, 200, 310, 430,?
Solution:
10, 100, 200, 310, 430 ?
The difference between consecutive terms are 90, 100, 110, 120.
From this pattern the next difference must be 130.
Therefore, the next term or the required term = 430 + 130 = 560.
12) 28, 33, 31, 36, 34, ?
Solution:
28, 33, 31, 36, 34, ?
The difference between the terms are 5, – 2, 5, – 2.
From this pattern the next difference must be 5.
Therefore, the required number = 34 + 5 = 39
13) 120, 80, 40, 45, ?, 15
Solution:
120, 80, 40, 45, ?, 15
Let the first group 120, 80, 40.
The average of first and third number is second number.
From this pattern second number must be average of first and third number.
Second group 45, ?, 15.
Therefore, the required number = (45 + 15) / 2 = 60\2 = 30.
14) 2, 15, 41, 80, 132, ?
Solution:
2, 15, 41, 80, 132, ?
The difference between the terms are 13, 26, 39, 52.
From this pattern the next difference must be 65.
Therefore, the next term or the required number = 132 + 65 = 197
15) 6, 17, 39, ?, 116
Solution:
6, 17, 39, ?, 116
The difference between the terms are 11, 22.
From this pattern the difference between the next terms must be 33, 44.
The next term = 39 + 33 = 72
Or 116 – 44 = 72.
Therefore, the required number is 72.
16) 1, 4, 10, 22, ?, 94
Solution:
1, 4, 10, 22, ?, 94
The difference between the terms are 3, 6, 12.
From this pattern the difference between the next terms must be 24, 48
Therefore, the next term = 22 + 24 = 46
Or 94 – 48 = 46.
Therefore, the required number is 46.
17) 4, 9, 25, 49, ?, 169, 289, 361
Solution:
4, 9, 25, 49, ?, 169, 289, 361
The given all the numbers are squares of prime numbers.
Therefore, the required number = 11 × 11 = 121
18) 4, 12, 36, ?, 324
Solution:
4, 12, 36, ?, 324
The number is 3 times of the previous number.
From this pattern,
4th term or the required term = 3 × 36 = 108
19) 1, 1, 4, 8, 9, ?, 16, 64
Solution:
1, 1, 4, 8, 9, ?, 16, 64
20) 5760, 960, 192, ?, 16, 8
Solution:
5760, 960, 192, ?, 16, 8
We observed that 5760 /960 = 6
960/192 = 5, 16/8 = 2
Let the required number be x
From this pattern 192/x = 4 and x/ 16 = 3.
Solve this we get x = 48
Therefore, the required number is 48.
21) 1, 2, 6, 7, 21, 22, 66, ?, 201
Solution:
1, 2, 6, 7, 21, 22, 66, ?, 201
The required number be x.
The first two numbers are consecutive numbers.
Third number is three times of second number.
4th number is consecutive of third number.
From this pattern x is equal to 67.
Therefore, the required number is 67.
22) 48, 24, 96, ?, 192
Solution:
48, 24, 96, ?, 192
The first number is 48.
Second number = (first number) 48 / 2 = 24
Third number = (Second number) 24 × 4 = 96
From this pattern
4th number = (Third number) 96/ 2 96 = 48.
5th number = (4th number) 48 × 4 = 192.
Therefore, the required number = 48
23) 165, 195, 255, 285, ?, 375
Solution:
165, 195, 255, 285, ?, 375
Solution:
The difference between the numbers are 30, 60, 30.
From this pattern, the next difference must be 60.
So, the required number = 285 + 60 = 345
Next number = 345 + 30 = 375.
Therefore, the required number = 345
24) 2, 3, 3, 5, 10, 13, 39, ?, 172, 177
Solution:
2, 3, 3, 5, 10, 13, 39, ?, 172, 177
First number = 2.
Second number = First number +1 = 2 + 1 = 3
Third number = Second number × 1 = 3 × 1 = 3.
4th number = Third number + 2 = 3 + 2 = 5
5th number = 4th number × 2 = 5 × 2 = 10
6th number = 5th number + 3 = 10 + 3 = 13
7th number = 6th number × 3 = 39
8th number = 7th number + 4 = 39 + 4 = 43
Therefore, the required number = 43.
25) 7, 26, 63, 214, 215, ?, 511
Solution:
7, 26, 63, 214, 215, ?, 511
26) 3, 7, 15, 31, ?, 127
Solution;
3, 7, 15, 31, ?, 127
27) 8, 28, 116, 584, ?
Solution
8, 28, 116, 584, ?
The relation is in this pattern.
First term is 8
Second term = (1st term × 3) + 4 = 8 × 3 + 4 = 28
Third term = (Second term × 4) + 4 = 28 × 4 + 4 = 116
4th term = (Third term × 5) + 4 = 116 × 5 + 4 = 584
5th term = (4th term × 6) + 4 = 584 × 6 + 4 = 3508
Therefore, the required number or 5th term = 3508
28) 6, 13, 28, 59, ?
Solution:
6, 13, 28, 59, ?
The relation is in this pattern.
The first term is 6.
Second term = (First term × 2) + 1 = 6 × 2 + 1 = 13
Third term = (Second term × 2) + 2 = 13 × 2 + 2 =28
4th term = (Third term × 2) + 3 = 28 × 2 + 3 = 59.
5th term = (4th term × 2) + 4 = 59 × 2 + 4 = 122
Therefore, the required number or 5th term = 122
29) 2, 7, 27, 107, 427, ?
Solution:
2, 7, 27, 107, 427, ?
The relation is in this pattern.
The first term is 2.
Second term = (First term × 4) – 1 = 2 × 4 – 1 = 7
Third term = (Second term × 4) – 1 = 7 × 4 – 1 =27
4th term = (Third term × 4) – 1 = 27 × 4 – 1 = 107
5th term = (4th term × 4) – 1 = 107 × 4 – 1 = 427
6th term = (5th term × 4) – 1 = 427 × 4 – 1 = 1707.
Therefore, the required number or 6th term = 1707.
30) 5, 2, 7, 9, 16, 25, 41, ?
Solution:
5, 2, 7, 9, 16, 25, 41, ?
The relation is in this pattern. The term is addition of previous two terms
Third term = 5 + 2 = 7
4th term = 2 + 5 = 9
5th term = 7 + 9 = 16.
6th term = 9 + 16 = 25
7th term = 16 + 25 = 41
8th term = 25 + 41 = 66
Therefore, the required number or 8th term is 66.
Solutions Chapter 9 Exercise 9A CA foundation maths solutions
31) In a certain language MADRAS is coded NBESBT, how DELHI is coded in that code?
Solution:
In a certain language MADRAS is coded NBESBT
In the code language, every alphabet is written by next alphabet.
Therefore, DELHI will be written as EFMIJ
32) If RAMAN is written as 12325 and DINESH as 675489 how HAMAM is written ?
Solution:
If RAMAN is written as 12325 and DINESH as 675489
From this we can write alphabet as number, we get
R = 1, A = 2, M = 3, N = 5, D = 6, I = 7, E = 4, S = 8, H = 9.
From this given information, we can write HAMAM as 92323
33) If RED is coded as 6720 then GREEN would be coded as
Solution:
RED is coded as 6720.
R is 18th alphabet, E is 5th alphabet, D is 4th alphabet.
If we interchange position of RED as DER 4518
Comparing with number 6720 we get,
D = 4 + 2 = 6, E = 5 + 2 = 7, R = 18 + 2 = 20.
Therefore, RED = DER = 6720
Thus GREEN interchange the position as NEERG
N is 14th alphabet = 14 + 2 = 16
E is 5th alphabet = 5 + 2 = 7
R is 18th alphabet = 18 + 2 = 20
G is 7th alphabet = 7 + 2 = 9
Therefore, GREEN = NEERG = 1677209
34) If A = 1, FAT = 27, FAITH = ?
Solution:
A = 1, FAT = 27
A is 1st alphabet, F is 6th alphabet, T is 20th alphabet, H is 8th alphabet.
Therefore, FAT = 6 + 1 + 20 = 27
FAITH = 6 + 1 + 9 + 20 + 8 = 44
35) If BROTHER is coded 2456784, SISTER coded as 919684 what is coded for BORBERS ?
Solution:
If BROTHER is coded 2456784, SISTER coded as 919684.
B = 2, R = 4, O = 5, T = 6, H = 7, E = 8, S = 9
Therefore, BORBERS = 2542829
36) If DELHI is coded 73541 and CALCUTTA as 82589662. How can CALICUT be coded ?
Solution:
If DELHI is coded 73541 and CALCUTTA as 82589662.
D = 7, E = 3, l = 5, H = 4, I = 1, c C = 8, A = 2, U = 9, T = 6
Therefore, CALICUT is coded as 8251896.
37) If CLOCK is coded 34235 and TIME is 8679, what will be code of MOTEL ?
Solution:
If CLOCK is coded 34235 and TIME is 8679.
C = 3, L = 4, O = 2, K = 5, T = 8, I = 6, M = 7, E = 9
Therefore, MOTEL can be coded as 72894
38) If PALE is coded as 2134 and EARTH is coded as 41590, how is PEARL is coded ?
Solution:
If PALE is coded as 2134 and EARTH is coded as 41590
P = 2, A = 1, L = 3, E = 4, R = 5, T = 9, H = 0.
Therefore, PEARL can be coded as 24153.
39) If LOSE is coded as 1357 and GAIN is coded as 2468, what do figure 82146 stands for ?
Solution:
If LOSE is coded as 1357 and GAIN is coded as 2468.
L = 1, O = 3, S = 5, E = 7, G = 2, A = 4, I = 6, N = 8.
Therefore, NGLAI can be coded as 82146.
40) If MEKLE is coded as 91782 and LLLJK as 88867, how can IHJED is coded as ?
Solution:
If MEKLE is coded as 91782 and LLLJK as 88867.
M = 9, E = 1, K = 7, L = 8, F = 2, J = 4.
If we arrange alphabet from D to M we get,
D = 0, E = 1, F = 2, G = 3, H = 4, I = 5, J = 6, K = 7, L = 8, M = 9.
Therefore, IHJED can be coded as 54610.
41) If in a certain code language NAME is written as 4258 then what is coded as MEAN ?
Solution:
If in a certain code language NAME is written as 4258.
N = 4, A = 2, M = 5, E = 8
Therefore, MEAN can be coded as 5824.
42) If GOLD is written as IQNF, how WIND can be written as code ?
Solution:
If GOLD is written as IQNF.
From this we can observe that instead of G it is written as I.
Alphabet next to next alphabet is written.
Therefore, WIND can be coded as YKPE.
43) If ROSE is written as TQUG, how BISCUIT can be written in that code ?
Solution:
If ROSE is written as TQUG.
From this we can observe that instead of R it is written as T.
Thus alphabet next to next alphabet is written.
Therefore, BISCUIT can be coded as DKUEWKV.
Problems
Letter : C Z N V R S W F D
Code digit : 8 6 4 7 2 9 3 5 1
44. Then the code of ZDRCVF
Solution:
Letter : C Z N V R S W F D
Code digit : 8 6 4 7 2 9 3 5 1
Therefore, ZDRCVF can be coded as 612875
45) The code of WNCSZV
Solution:
Letter : C Z N V R S W F D
Code digit : 8 6 4 7 2 9 3 5 1
Therefore, WNCSZV can be coded as 348967.
46) The code of RDNFVS
Solution:
Letter : C Z N V R S W F D
Code digit : 8 6 4 7 2 9 3 5 1
Therefore, RDNFVS can be coded as 214579.
47) If DELHI is coded as CCIDD, how would you encode BOMBAY ?
Solution:
If DELHI is coded as CCIDD
We can observe that instead of the D it is written C, that is previous alphabet.
E is replaced by C, two alphabets before.
L is replaced by I, 3rd previous alphabet, and so on.
From this pattern we can write BOMBOY as AMJXVS.
48) In a certain code RIPPLE is written as 6133 82 and LIFE is written as 8192. How is PILLER written in that code ?
Solution:
In a certain code RIPPLE is written as 6133 82 and LIFE is written as 8192.
R = 6, I = 1, P = 3, L = 8, F = 9.
Therefore, PILLER can be coded as 318826.
49) If PALAM could be given the code number 43, what code number can be given to SANTACRUZ ?
Solution:
If PALAM could be given the code number 43.
PALAM = 16 + 1 + 12 + 1 + 13 = 43.
If they have added the position of alphabet to get the code.
Therefore, the code of SANTACRUZ = 19 + 1 + 14 + 20 + 1 + 3 + 18 + 21 + 26 = 123.
Problem 50.
Directions : The number in each question below is to be codified in the following code :
Digit 7 2 1 5 3 9 8 6 4
Letter. W L M S I N D J B
50) the code of 184632
From the given information we get
the code of 184632 = MDBJIL.
51) In a certain code ‘256’ means ‘you are good’, ‘637’ means ‘we are bad’ and ‘358’ means ‘good and bad’, Which of the following represents ‘and’ in that code ?
Solution:
In a certain code ‘256’ means ‘you are good’, ‘637’ means ‘we are bad ‘and’ 358′ means ‘good and bad’,
The word ‘good’ is used in two phrases, The common number in these two is 5.
It indicates ‘good’ = 5.
In like manner, ‘bad’ is used in second and third statement. The common number is 3.
It indicates ‘bad’ = 3.
The number left from third statement is 8.
Therefore, it indicates ‘and’.
Therefore, 8 represents ‘and ‘ in that code.
Problem : Directions : Find odd man out of the following
52) 3, 5, 7, 15, 17, 19
Solution:
3, 5, 7, 15, 17, 19
From this information we get, except 15 others are prime numbers.
Therefore, 15 is odd man out.
53). Find the odd man out of the 10, 14, 16, 18, 23, 24, 26.
Solution:
10, 14, 16, 18, 23, 24, 26
From this information we get, except 23 others all are even numbers.
Therefore, 23 is odd man out.
54) Find the odd man out of the 1, 4, 9, 16, 24, 25, 26.
Solution:
1, 4, 9, 16, 24, 25, 26
From this information we get, except 24 others all are square numbers.
Therefore, 24 is odd man out.
55) Find the odd man out of the 41, 43, 47, 53, 61, 71, 83, 75.
Solution:
41, 43, 47, 53, 61, 71, 83, 75
From this information we get, except 75 others all are prime numbers.
Therefore, 75 is odd man out.
56) Find the odd man out of the 16, 25, 36, 73, 144, 196, 225
Solution:
16, 25, 36, 73, 144, 196, 225
From this information we get, except 73 others all are square numbers.
Therefore, 73 is odd man out.
57) Find the odd man out of the 1, 4, 9, 16, 19, 36, 49.
Solution:
1, 4, 9, 16, 19, 36, 49
From this information we get, except 19 others all are square numbers.
Therefore, 19 is odd man out.
58) Find the odd man out of the 1, 5, 14, 30, 49, 55, 91
Solution:
1, 5, 14, 30, 49, 55, 91
Therefore, 49 is odd man out.
59. Find the odd man out of the 835, 734, 642, 751, 853, 981, 532.
Solution:
835, 734, 642, 751, 853, 981, 532
From this information we get, except 751 others numbers are such that the sum of digits of the number is even number.
Therefore, 751 is odd man out.
60) Find the odd man out of the 4, 5, 7, 10, 14, 18, 25, 32
Solution:
4, 5, 7, 10, 14, 18, 25, 32
The difference between first two terms is 1.
The difference between second and third is 2.
The difference between to third and 4th is 3
The difference between 4th and 5th term is 4 and so on.
The number next to 14 should be 19.
Therefore, 18 is odd man out.
61) Find the odd man out of the 52, 51, 48, 43, 34, 27, 16
Solution:
52, 51, 48, 43, 34, 27, 16
The difference between the numbers are 1, 3, 5.
The next difference should be 7.
The next number after 43 should be 36.
Therefore, 34 is odd man out.
Note : You can observe the solutions and try them in your own method.