MCQs' Number Series, Coding and Decoding and Odd Man Out - Quantitative Aptitude

Q1: Find the next number in the series:
2, 5, 11, 23, 47, …
(a) 84
(b) 95
(c) 98
(d) 105
Ans: (b)

Sol:
Given Series: 2, 5, 11, 23, 47, … 
On analysing the pattern, we get 
2 + 3 = 5 
5 + 6 = 11 
11 + 12 = 23 
23 + 24 = 47 
47 + 48 = 95 
Therefore the next term is 95.

Q2: In the following series, which number will replace the question mark?
23, 29, 31, 37, 41, 43, ?
(a) 45
(b) 54
(c) 47
(d) 49
Ans: (c)

Sol:
Given series: 23, 29, 31, 37, 41, 43, ? 
We analyse that, 
The given series is the series of prime numbers. 
Therefore the next term is 47.

Q3: The number in place of question mark in: 7, 26, 63, 124, 215, ?, 511 is
(a) 342
(b) 443
(c) 441
(d) 421
Ans: (a)

Sol:
Given series: 7, 26, 63, 124, 215, ?, 511 
Here, the pattern followed is: 7 = 2³ – 1 
26 = 3³ – 1 
63 = 4³ – 1 
124 = 5³ – 1 
215 = 6³ – 1 
342 = 7³ – 1 
511 = 8³ – 1 
Therefore 342 is the required missing term.

Q4: Find the missing term of the series 2, 3, 3, 5, 10, 13, ?, 43, 172, 177
(a) 23 
(b) 38 
(c) 39 
(d) 40
Ans: (c)

Sol: Given series: 2, 3, 3, 5, 10, 13, ?, 43, 172, 177

Here, the pattern alternates between two operations:

Add that same number and then multiply by a number.

Let's trace through:

• 2 × 1 + 1 = 3 (add 1)
• 3 × 1 = 3 (multiply by 1)
• 3 + 2 = 5 (add 2)
• 5 × 2 = 10 (multiply by 2)
• 10 + 3 = 13 (add 3)
• 13 × 3 = 39 (multiply by 3) ← Missing term
• 39 + 4 = 43 (add 4)
• 43 × 4 = 172 (multiply by 4)
• 172 + 5 = 177 (add 5)

Pattern Summary: The operations alternate and increase incrementally:

×1, +1, ×1, +2, ×2, +3, ×3, +4, ×4, +5

Therefore the missing term is 39.

Q5:  2, 3, 8, ………, 3968
(a) 65
(b) 63
(c) 70
(d) 80
Ans: (b)

Sol:
Given series: 2, 3, 8, ……… , 3968 
Here, the pattern followed is: 
2² – 1 = 3 
3² – 1 = 8 
8² – 1 = 63 
63² – 1 = 3968
Therefore, 63 is the required number.

Q6: Find the next term of the series: 1, 3, 4, 8, 15, 27, ?
(a) 37
(b) 44
(c) 50
(d) 55
Ans: (c)

Sol:

Given series: 1, 3, 4, 8, 15, 27, ?

Here, the pattern follows is: 
Adding the three consecutive numbers to get the next number i.e.,

• 1 + 3 + 4 = 8
• 3 + 4 + 8 = 15
• 4 + 8 + 15 = 27
• 8 + 15 + 27 = 50

Therefore, the next term of series is 50.

Q7: Find the next term of the series: 1, 5, 14, 30, 55, 91, ?
(a) 130
(b) 140
(c) 150
(d) 160
Ans: (b)

Sol:
Given series: 1, 5, 14, 30, 55, 91, ? 
Here, the pattern is
1 + 2² = 5 
5 + 3² = 14 
14 + 4² = 30 
30 + 5² = 55
55 + 6² = 91 
91 + 7² = 140
 Therefore, the next term is 140.

Q8: In a certain code language, if TOUR is written as 1234, CLEAR is written as 56784, and SPARE is written as 90847. Find the code for TEARS. 
(a) 17947 
(b) 17846
(c) 17947
(d) 17849
Ans: (d)

Sol:
Given, TOUR is written as 1234, CLEAR is written as 56784 and SPAR is written as 90847 
Thus, the codes for the letters of TEARS is follow: 
T → 1 
E → 7 
A → 8 
R → 4 
S → 9 
Therefore, the code for TEARS is 17849.

Q9: In a certain code, RIPPLE is written as 613382 and LIFE is written as 8192. How is PILLER written in that code? 
(a) 318827
(b) 318826 
(c) 618826
 (d) 338816
Ans: (a)

Sol:
We have, 
Word RIPPLE is coded as 613382

Word LIFE is coded as 8192

Therefore, we can directly examine the code for each letter. Thus, the word PILLER can be coded as:

• P → 3
• I → 1
• L → 8
• L → 8
• E → 2
• R → 6

Hence, PILLER is coded as 318826.

Q10: In a certain code, TEACHER is written as VGCEJGT. How is CHILDREN written in that code? 
(a) EJFNEGTP 
(b) EGKNIETP 
(c) EJGNEGTP 
(d) EJKNFTGP
Ans: (d)

Sol:
Given, TEACHER is written as VGCEJGT i.e, 
T + 2 = V
 E + 2 = G 
A + 2 = C 
C + 2 = E 
H + 2 = J 
E + 2 = G 
R + 2 = T
 Similarly, CHILDREN will be written as; 
C + 2 = E
H + 2 = J
l + 2 = K
L + 2 = N
D + 2 = F
R + 2 = T
E + 2 = G
N + 2 = P
Hence, CHILDREN will be coded as EJKNFTGP

Q11. In a certain code, “CHAIR” is written as “GCLMY”. How is “INSTRUCT” written in that code? 
(a) MRWXVYGX
(b) MQWUVYGX
(c) MRWXVZGX
(d) MQXWVYGX
Ans: (a)

Sol:
Given, “CHAIR” is written as ”GLMVV”

Each letter is shifted +4.

C → G
H → L
A → E
I → M
R → V

Similarly:
I → M
N → R
S → W
T → X
R → V
U → Y
C → G
T → X

So, INSTRUCT → MRWXVYGX

Q12: If HEALTH is coded as GSKZDG, then how will NORTH be written in that code? 
(a) OPSUI 
(b) GSQNM
(c) FRMPJ 
(d) USPO
Ans: (b)

Sol:
Given HEALTH is coded as GSKZDG i.e.,
H – 1 = G
E – 1 = D
A – 1 = Z
L – 1 = K
T – 1 = S
H – 1 = G
Thus, on reversing the code will be GSKZDG.
Similarly, for NORTH;
N – 1 = M
O – 1 = N
R – 1 = Q
T – 1 = S
H – 1 = G
Now, on reversing we get the code as GSQNM. 
Hence, the code for NORTH is GSQNM.

Q13: If HONEY is coded as JQPGA, which word is coded as VTIGVU? 
(a) CARPETS 
(b) TRAPETS 
(c) TARGETS 
(d) UMBRELU
Ans: (c)

Sol:
Given: HONEY is coded as JQPGA i.e.,
H + 2 = J
O + 2 = Q
N + 2 = P
E + 2 = G
Y + 2 = A

Each letter is shifted +2.

V − 2 = T
C − 2 = A
T − 2 = R
I − 2 = G
G − 2 = E
V − 2 = T
U − 2 = S

So, the word is TARGETS.

Q14: In a certain code, ‘493’ means ‘Friendship is Sweet’, ‘167’ means ‘Friendship Examines Exam’, and ‘178’ means ‘Exam believable subject’; then which digit is used for ‘believable’? 
(a) 7 or 8 
(b) 7 or 9 
(c) 8 
(d) 8 or 1
Ans: (a)

Sol:

Given: '493' means 'Friendship is Sweet', '961' means 'Friendship Examines Exam'

Thus, the common word and number in above mentioned codes is Friendship and either 4, 9, or 6 and 9, or 1 respectively.

Comparing '493' and '961': Common word is 'Friendship' and common digit could be 9. ⇒ Friendship → 9 (most likely)

Now, '961' means 'Friendship Examines Exam' and '178' means 'Exam believable subject'

Thus, the common word in above codes is Exam and the common digit must be 1. ⇒ Exam → 1

From '178' which means 'Exam believable subject':

• Since Exam → 1
• The remaining digits 7 and 8 correspond to 'believable' and 'subject'
• We cannot determine which is which

Hence, the code for believable can be either 7 or 8.

Q15: 16, 25, 36, 72, 144, 196, 225, find the odd one out.
(a) 36 
(b) 72 
(c) 196
(d) 225 
Ans: (b)

Sol:

Given series: 16, 25, 36, 72, 144, 196, 225 Here, the pattern followed is; 
4² = 16 
5² = 25 
6² = 36 
12² = 144 
14² = 196 
15² = 225 
Therefore, 72 is odd one out.

Q16: Out of the following; 41, 43, 47, 53, 61, 71, 83, 95, the odd man out shall be; 
(a) 95 
(b) 81 
(c) 71 
(d) 53 
Ans: (a)

Sol:

Given series: 41, 43, 47, 53, 61, 71, 83, 95 
Clearly, all the numbers except 95 is prime. Therefore, 95 is odd man out.

Q17: Find wrong number of the series; 1, 5, 5, 9, 7, 11, 11, 15, 12, 17
(a) 11 
(b) 12 
(c) 17 
(d) 15
Ans: (b)

Sol:
Given series: 1, 5, 5, 9,7,11,11,15,12,17

Here, there are two alternating series such that:

1 + 4 = 5

5 + 2 = 7

7 + 4 = 11

11 + 2 = 13 ≠ 12

The another series is:

5 + 4 = 9

9 + 2 = 11

11 + 4 = 15

15 + 2 = 17

Clearly, 12 is wrong term in the series.

Q18: Find the odd man out of the following series; 7, 23, 47, 119, 171, 287
(a) 119 
(b) 171 
(c) 287
(d) 7

Ans: (b)

Sol:
On analysing the pattern, we get

3² – 2 = 7

5² – 2 = 23

7² – 2 = 47

11² – 2 = 119

13² – 2 = 167 ≠ 171

17² – 2 = 287

Therefore, 171 is odd one out.

Q19: Find the odd man out in the following series; 190, 145, 136, 352, 460, 324, 631, 244.
(a) 136
(b) 244 
(c) 460 
(d) 324 
Ans: (d)

Sol:
Given series; 190, 145, 136, 352, 460, 324, 631, 244
Here, the pattern followed is;

1 + 9 + 0 = 10

1 + 4 + 5 = 10

1 + 3 + 6 = 10

3 + 5 + 2 = 10

4 + 6 + 0 = 10

3 + 2 + 4 = 9 ≠ 10

6 + 3 + 1 = 10

2 + 4 + 4 = 10

Therefore, 324 is odd one out of the series

Q20: Which of the following is the odd one out?
 (a) CEHL 
(b) KMPT 
(c) OQTX 
(d) NPSV 
Ans: (d)

Sol:
Here, we have

CEHL → C + 2 = E, E + 3 = H, H + 4 = L ✓
KMPT → K + 2 = M, M + 3 = P, P + 4 = T ✓
OQTX → O + 2 = Q, Q + 3 = T, T + 4 = X ✓
NPSV → N + 2 = P, P + 3 = S, S + 3 = V ✗
Therefore, NPSV is odd one out.