Examkin

Number and Alphabet Series

49 questions

All types49Multiple choice26Numeric13Fill in the blank10
Question 21Question →
Which of the following terms logically completes the given alphanumeric series: E3V,H7S,K15P,N31M,…E3V, H7S, K15P, N31M, \dots?
Show answer & explanation

Answer: Q63JQ63J

Answer

Q63JQ63J
The correct term is obtained by shifting the first letter forward by 3 positions (N→QN \rightarrow Q), applying the numerical rule nk+1=2nk+1n_{k+1} = 2n_k + 1 (31→6331 \rightarrow 63), and shifting the last letter backward by 3 positions (M→JM \rightarrow J).

Step-by-Step Solution

1
Analyze the pattern of the first letter in each term.
The sequence of first letters is E(5),H(8),K(11),N(14)E (5), H (8), K (11), N (14). The pattern adds 33 to the alphabetical position each time. The next letter is 14+3=1714 + 3 = 17, which corresponds to QQ.
To establish the progressive forward positional shift rule.
2
Analyze the numerical pattern in the middle of each term.
The numerical sequence is 3,7,15,313, 7, 15, 31. Each term is obtained by multiplying the previous term by 22 and adding 11 (3×2+1=73 \times 2 + 1 = 7; 7×2+1=157 \times 2 + 1 = 15; 15×2+1=3115 \times 2 + 1 = 31). The next number is 31×2+1=6331 \times 2 + 1 = 63.
To identify the arithmetic progression operating on the numeric component.
3
Analyze the pattern of the last letter in each term.
The sequence of last letters is V(22),S(19),P(16),M(13)V (22), S (19), P (16), M (13). The pattern subtracts 33 from the alphabetical position each time. The next letter is 13−3=1013 - 3 = 10, which corresponds to JJ.
To establish the progressive reverse positional shift rule.
4
Combine the results from all three components.
Combining QQ, 6363, and JJ yields the next term Q63JQ63J.
To form the complete missing term.

Key Concept

Alphanumeric Series Completion with Simultaneous Positional Shifts and Operation Patterns
Question 22Question →

Complete the given alphanumeric series by identifying the missing term that logically follows the established rules.

Fill in the blanks below

In the series A4Z,C9X,F16U,J25Q,…A4Z, C9X, F16U, J25Q, \dots, the missing fifth term is .
Show answer & explanation

Answer

The correct missing term is O36L.
The term O36L correctly completes the series because the first letter advances by increasing forward steps (+2, +3, +4, +5 to reach O), the middle number follows the sequence of consecutive squares (22,32,42,52,62=362^2, 3^2, 4^2, 5^2, 6^2 = 36), and the last letter retreats by increasing backward steps (-2, -3, -4, -5 to reach L).

Step-by-Step Solution

1
Analyze the first letter pattern
The positional values in the forward alphabetical order are: A(1)→+2C(3)→+3F(6)→+4J(10)A(1) \xrightarrow{+2} C(3) \xrightarrow{+3} F(6) \xrightarrow{+4} J(10). The next increment must be +5+5, giving position 10+5=1510 + 5 = 15, which corresponds to the letter OO.
The forward position shift increases by +1+1 at each step.
2
Analyze the numerical middle term pattern
The numerical terms are perfect squares of consecutive integers starting from 22: 22=42^2 = 4, 32=93^2 = 9, 42=164^2 = 16, 52=255^2 = 25. The next term is 62=366^2 = 36.
The numerical sequence represents consecutive integer squares (n2n^2 for n=2,3,4,5,6n = 2, 3, 4, 5, 6)....
3
Analyze the last letter pattern
The positional values in reverse alphabetical order decrease as follows: Z(26)→−2X(24)→−3U(21)→−4Q(17)Z(26) \xrightarrow{-2} X(24) \xrightarrow{-3} U(21) \xrightarrow{-4} Q(17). The next decrement must be −5-5, giving position 17−5=1217 - 5 = 12, which corresponds to the letter LL.
The backward position shift increases by −1-1 at each step.
4
Combine the components
Combining the calculated parts yields the complete term: O+36+L=O36LO + 36 + L = O36L.
Joining the first letter, middle number, and last letter produces the complete missing term.

Key Concept

Alphanumeric Series with Multi-layered Incremental Positional Shifts and Perfect Squares
Estimated Time:1m 30s
Question 23Question →
Which term logically completes the following alphanumeric series?
B26,G20,L15,Q11,?,A6B26, G20, L15, Q11, ?, A6
Show answer & explanation

Answer: V8

Answer

V8
The correct term is V8 because the letter sequence follows a +5 positional shift rule (B→G→L→Q→V→AB \to G \to L \to Q \to V \to A) and the numerical sequence follows a decreasing step pattern subtractive rule (−6,−5,−4,−3,−2-6, -5, -4, -3, -2).

Step-by-Step Solution

1
Analyze the pattern for the letter positions.
The alphabetical positions advance by +5 at each step: B (2) -> G (7) -> L (12) -> Q (17). Adding 5 to Q (17) gives 22, which corresponds to the letter V. Verifying the next term: V (22) + 5 = 27, which wraps around to A (1).
Establishing the consistent forward positional shift of the alphabetical components.
2
Analyze the pattern for the numerical components.
The numbers decrease by successive decrements: 26 - 6 = 20, 20 - 5 = 15, 15 - 4 = 11. The next subtraction must be -3, giving 11 - 3 = 8. Verifying the subsequent step: 8 - 2 = 6, which matches the final term.
Determining the decreasing difference sequence for the numerical values.
3
Combine the letter and numerical results.
Combining the 5th letter V with the number 8 yields V8.
Forming the complete term for the missing position.

Key Concept

Dual-pattern alphanumeric series featuring constant letter positional increment and consecutive integer decrement
Estimated Time:1m 0s
Question 24Question →

A transportation company schedules its daily long-distance routes by increasing the total daily mileage according to a specific mathematical progression. Over the first five days of a new expansion phase, the daily total route distances recorded are 55, 1212, 2626, 4949, and 8383 miles respectively.

If this pattern continues strictly, what will be the total route distance in miles for the sixth day?

Show answer & explanation

Answer: 130

Answer

130
The sequence follows a double-difference pattern where the second-level differences form a simple arithmetic progression increasing by 22. By extending this pattern, the next addition to the sequence is 4747, which yields exactly 130130 when added to the fifth term.

Step-by-Step Solution

1
Calculate the differences between consecutive terms in the given sequence.
12−5=712 - 5 = 7; 26−12=1426 - 12 = 14; 49−26=2349 - 26 = 23; 83−49=3483 - 49 = 34.
Finding the first-level differences is the standard approach to identify hidden polynomial sequences.
2
Calculate the differences of the first-level differences (second-level differences).
14−7=714 - 7 = 7; 23−14=923 - 14 = 9; 34−23=1134 - 23 = 11.
The first-level differences do not form a constant sequence, but measuring their rate of change reveals an underlying arithmetic progression.
3
Identify the pattern in the second-level differences and extrapolate the next value.
The second-level differences (77, 99, 1111) increase by 22 each time. The next second-level difference will be 11+2=1311 + 2 = 13.
Establishing the core constant pattern allows for accurate forward prediction.
4
Calculate the next first-level difference and the final 6th term.
Next first-level difference = 34+13=4734 + 13 = 47. Sixth term = 83+47=13083 + 47 = 130.
Applying the extrapolated differences forward up the chain yields the final required value.

Key Concept

Double Difference Number Series
Question 25Question →

During an audit of a warehouse, a supervisor notices that the serial numbers on a batch of secured containers follow a specific alphanumeric progression. The first four container tags are recorded as B3M, E7P, I12T, and N18Y. Based on this established progression, what should be the serial number on the fifth container?

Show answer & explanation

Answer: T25E

Answer

T25E
The progression operates on three separate tracks. The first letter shifts by +3, +4, +5, and subsequently +6 (N to T). The central number increases by +4, +5, +6, and subsequently +7 (18 to 25). The last letter shifts by +3, +4, +5, and subsequently +6, which requires wrapping past Z (Y + 6 = E). Combining these three components yields T25E.

Step-by-Step Solution

1
Analyze the pattern of the first letter in each term.
B to E is +3; E to I is +4; I to N is +5.
To identify the rule governing the first alphabetical component.
2
Apply the established rule to find the first letter of the fifth term.
The next shift must be +6. N (14th letter) + 6 = 20th letter, which is T.
To determine the starting character of the missing serial number.
3
Analyze the pattern of the numerical portion in each term.
3 to 7 is +4; 7 to 12 is +5; 12 to 18 is +6.
To identify the rule governing the central numbers.
4
Apply the numerical rule to find the central number of the fifth term.
The next addition must be +7. 18 + 7 = 25.
To determine the numerical component of the missing serial number.
5
Analyze the pattern of the final letter in each term.
M to P is +3; P to T is +4; T to Y is +5.
To identify the rule governing the last alphabetical component.
6
Apply the rule to find the final letter of the fifth term, accounting for the end of the alphabet.
The next shift must be +6. Y (25th letter) + 6 = 31. Since the alphabet has 26 letters, 31 - 26 = 5th letter, which is E.
To determine the final character of the missing serial number by wrapping around the alphabet.

Key Concept

Progressive Alphanumeric Series and Alphabetical Wrapping
Question 26Question →

Consider the following numerical sequence: 11,14,23,44,83,…11, 14, 23, 44, 83, \dots What is the next term in this sequence?

Show answer & explanation

Answer: 146

Answer

The next term in the sequence is 146.
The sequence follows a double-difference pattern where the differences between consecutive terms (3,9,21,393, 9, 21, 39) themselves differ by an arithmetic progression of multiples of 6 (6,12,186, 12, 18). Adding the next increment of 24 to 39 gives a term difference of 63. Adding 63 to the last term 83 results in 146.

Step-by-Step Solution

1
Find the first difference between consecutive terms
The differences are 3, 9, 21, and 39.
Analyzing differences helps reveal underlying polynomial or double-difference patterns.
2
Find the second difference (difference of differences)
The second differences are 6, 12, and 18.
The first differences do not form an obvious basic sequence, so taking second differences reveals the hidden pattern.
3
Determine the next first-difference value
Next second difference is 24, making the next first difference 39 + 24 = 63.
The second-level differences increase by 6 each step (multiples of 6).
4
Calculate the next term in the sequence
83 + 63 = 146
Adding the computed term difference to the latest term yields the next sequence number.

Key Concept

Double Difference Number Series
Estimated Time:1m 30s
Question 27Question →

Which of the following terms logically completes the given alphanumeric series?

A1,C4,E9,G16,…A1, C4, E9, G16, \dots
Show answer & explanation

Answer: I25I25

Answer

The term that logically completes the series is I25I25.
The correct term is formed by combining the two independent rules governing the series: the letter advances by 2 steps in standard forward alphabetical order (A→C→E→G→IA \to C \to E \to G \to I), and the number sequence follows consecutive perfect squares (12=1,22=4,32=9,42=16,52=251^2=1, 2^2=4, 3^2=9, 4^2=16, 5^2=25). Thus, the missing term is I25I25.

Step-by-Step Solution

1
Analyze the letter pattern
A→+2C→+2E→+2G→+2IA \xrightarrow{+2} C \xrightarrow{+2} E \xrightarrow{+2} G \xrightarrow{+2} I
Each letter moves forward by 2 positions in standard alphabetical order.
2
Analyze the number pattern
12=1,22=4,32=9,42=16,52=251^2 = 1, \quad 2^2 = 4, \quad 3^2 = 9, \quad 4^2 = 16, \quad 5^2 = 25
The numbers represent squares of consecutive positive integers starting from 1.
3
Combine the letter and number terms
Fifth term = I25I25
Combining the 5th letter (I) and the 5th square (25) completes the sequence.

Key Concept

Alphanumeric Series Completion
Question 28Question →

Complete the given alphanumeric series by determining the missing term.

Fill in the blanks below

In the series B2D,E6G,H12J,K20M,…B2D, E6G, H12J, K20M, \dots, the term that logically follows next is .
Show answer & explanation

Answer

The term that logically completes the series is N30P.
The series consists of three independent patterns: the first letter advances by +3+3 alphabetical positions (B→E→H→K→NB \rightarrow E \rightarrow H \rightarrow K \rightarrow N), the middle number follows a difference pattern of +4,+6,+8,+10+4, +6, +8, +10 (20+10=3020 + 10 = 30), and the third letter advances by +3+3 alphabetical positions (D→G→J→M→PD \rightarrow G \rightarrow J \rightarrow M \rightarrow P). Combining these results gives N30P.

Step-by-Step Solution

1
Analyze the pattern of the first letters in each term.
The first letters are B,E,H,KB, E, H, K. Their alphabetical positions are 2,5,8,112, 5, 8, 11, which increase by +3+3 each time (2+3=5,5+3=8,8+3=112+3=5, 5+3=8, 8+3=11). The next position is 11+3=1411 + 3 = 14, corresponding to letter NN.
To establish the positional shift pattern for the first component.
2
Analyze the pattern of the middle numerical values.
The sequence of numbers is 2,6,12,202, 6, 12, 20. The differences between consecutive terms are 6−2=46-2=4, 12−6=612-6=6, and 20−12=820-12=8. The differences increase by +2+2 each time (4,6,84, 6, 8). Therefore, the next difference must be 8+2=108 + 2 = 10. The next number is 20+10=3020 + 10 = 30.
To determine the double-difference rule governing the numerical values.
3
Analyze the pattern of the third letters in each term.
The third letters are D,G,J,MD, G, J, M. Their alphabetical positions are 4,7,10,134, 7, 10, 13, which increase by +3+3 each time (4+3=7,7+3=10,10+3=134+3=7, 7+3=10, 10+3=13). The next position is 13+3=1613 + 3 = 16, corresponding to letter PP.
To establish the positional shift pattern for the final component.
4
Combine the components to form the final term.
Combining the first letter (NN), the number (3030), and the last letter (PP) yields N30PN30P.
Synthesizing the three independent patterns into a single term.

Key Concept

Alphanumeric Series Pattern Analysis
Estimated Time:1m 0s
Question 29Question →
Determine the value of the missing term that logically continues the given numerical sequence:
6,13,28,59,122,?6, 13, 28, 59, 122, ?
Show answer & explanation

Answer: 249

Answer

The missing term in the sequence is 249.
The sequence follows the pattern Tn=Tn−1×2+(n−1)T_n = T_{n-1} \times 2 + (n-1) for n≥2n \ge 2. Thus, the 6th term is 122×2+5=249122 \times 2 + 5 = 249.

Step-by-Step Solution

1
Examine the transition between consecutive numbers in the series
From 6 to 13: 6×2+1=136 \times 2 + 1 = 13
From 13 to 28: 13×2+2=2813 \times 2 + 2 = 28
Establishing the basic recursive function pattern
2
Verify the pattern across remaining terms
From 28 to 59: 28×2+3=5928 \times 2 + 3 = 59
From 59 to 122: 59×2+4=12259 \times 2 + 4 = 122
Confirming that the multiplier is constant (2) while the added constant increments by 1 at each step
3
Apply the rule to find the missing term
122×2+5=244+5=249122 \times 2 + 5 = 244 + 5 = 249
Extending the pattern by adding 5 after doubling the previous term

Key Concept

Recursive series with constant multiplier and arithmetic additive offset
Estimated Time:1m 0s
Question 30Question →
Which of the following terms logically completes the given alphanumeric series?
D8W,F15U,I24R,M35O,?D8W, F15U, I24R, M35O, ?
Show answer & explanation

Answer: R48IR48I

Answer

The term that logically completes the series is R48IR48I.
The first letter moves forward with increasing shifts of +2, +3, +4, and +5 (M + 5 = R). The middle number increases by odd consecutive differences +7, +9, +11, and +13 (35+13=4835 + 13 = 48). The last letter is the complementary reverse alphabet pair summing to 27 (27−18=927 - 18 = 9, which is I). Combining these yields R48IR48I.

Step-by-Step Solution

1
Analyze the pattern of the first letter in each term
D (4) →+2\xrightarrow{+2} F (6) →+3\xrightarrow{+3} I (9) →+4\xrightarrow{+4} M (13). The next shift is +5+5, giving 13+5=1813 + 5 = 18, which corresponds to R.
The positional step increases by 1 at each term.
2
Analyze the pattern of the middle numerical value
The numbers are 8,15,24,358, 15, 24, 35. The differences between consecutive terms are 15−8=715-8=7, 24−15=924-15=9, 35−24=1135-24=11. The next difference is +13+13, making 35+13=4835 + 13 = 48 (or 72−1=487^2 - 1 = 48).
The consecutive difference increases by 2 each time.
3
Analyze the pattern of the second letter in each term
Each second letter is the reverse alphabetical pair of the first letter (sum of positions = 27): D(4)+W(23)=27, F(6)+U(21)=27, I(9)+R(18)=27, M(13)+O(14)=27. For R (18th letter), the complementary position is 27−18=927 - 18 = 9, which corresponds to I.
The second letter maintains a constant complementary sum of 27 with the first letter.

Key Concept

Alphanumeric Series Completion via Multi-Pattern Analysis
Question 31Question →
What is the next term that continues the pattern established in the following alphanumeric sequence?
Z2B,X6E,V12H,T20K,…Z2B, X6E, V12H, T20K, \dots
Show answer & explanation

Answer: R30NR30N

Answer

R30NR30N
The sequence consists of three parallel sub-patterns: the first letters decrease by 2 positions (Z→X→V→T→RZ \rightarrow X \rightarrow V \rightarrow T \rightarrow R), the middle numbers increase by expanding even differences +4,+6,+8,+10+4, +6, +8, +10 (2→6→12→20→302 \rightarrow 6 \rightarrow 12 \rightarrow 20 \rightarrow 30), and the trailing letters increase by 3 positions (B→E→H→K→NB \rightarrow E \rightarrow H \rightarrow K \rightarrow N). Combining these yields R30NR30N.

Step-by-Step Solution

1
Analyze the pattern of the first letter in each term
Z (26) -> X (24) -> V (22) -> T (20) -> R (18)
Each term's first letter shifts backward by 2 positions in alphabetical order.
2
Analyze the pattern of the middle number in each term
2, 6, 12, 20, 30
The difference between consecutive numbers increases by 2 each step (+4, +6, +8, +10).
3
Analyze the pattern of the last letter in each term
B (2) -> E (5) -> H (8) -> K (11) -> N (14)
Each term's last letter shifts forward by 3 positions in alphabetical order.
4
Combine the derived elements to form the next term
First letter: R, Middle number: 30, Last letter: N => R30N
Synthesizing all three independent rules yields the required term in the sequence.

Key Concept

Multi-pattern Alphanumeric Series
Estimated Time:1m 15s
Question 32Question →
Consider the following complex alphanumeric sequence:
C3F,E8I,H18L,L38O,Q78R,…C3F, E8I, H18L, L38O, Q78R, \dots

Which of the following terms logically completes the series?

Show answer & explanation

Answer: W158UW158U

Answer

W158UW158U
The term is obtained by breaking the alphanumeric code into three parallel streams: (1) First letter follows increasing step intervals (+2, +3, +4, +5, +6), bringing Q (17) to W (23). (2) Numerical component uses the rule 2x+22x + 2, converting 78 to 158. (3) Second letter has a constant increment of +3, moving R (18) to U (21). Combining these gives the complete term W158UW158U.

Step-by-Step Solution

1
Analyze the pattern of the first letter in each term
Positions in alphabet: C (3), E (5), H (8), L (12), Q (17). The positional increments are +2, +3, +4, +5. Following this pattern, the next increment must be +6. Adding 6 to Q (17) yields 23, which corresponds to the letter W.
The first element follows an increasing arithmetic step pattern.
2
Analyze the numerical progression in the terms
Sequence of numbers: 3, 8, 18, 38, 78. The recurrence relation is Nk=2×Nk−1+2N_k = 2 \times N_{k-1} + 2. Calculating the next value: 2×78+2=156+2=1582 \times 78 + 2 = 156 + 2 = 158.
Each number is formed by doubling the previous term and adding 2.
3
Analyze the pattern of the second letter in each term
Positions in alphabet: F (6), I (9), L (12), O (15), R (18). The positional increment is constant at +3. Adding 3 to R (18) yields 21, which corresponds to the letter U.
The third element follows a constant positional step pattern.
4
Synthesize the components to form the final term
Combining the calculated first letter (W), numerical middle value (158), and second letter (U) yields W158UW158U.
All three independent term rules must be combined.

Key Concept

Multi-Pattern Alphanumeric Series Completion
Estimated Time:2m 0s
Question 33Question →

Consider the following alphanumeric sequence:

B2D,E6H,J14N,Q30V,…B2D, E6H, J14N, Q30V, \dots

Which of the following terms correctly completes the given series?

Show answer & explanation

Answer: Z62F

Answer

The term that correctly completes the given alphanumeric series is Z62F.
The correct term is obtained by breaking down the alphanumeric pattern into three separate sub-series. The first letter advances by odd increments (+3, +5, +7, +9) from B to Z. The middle number doubles and adds 2 at each step (2×30+2=622 \times 30 + 2 = 62). The third letter advances by even increments (+4, +6, +8, +10) from D to F (with alphabet wrap-around). Combining these yields Z62F.

Step-by-Step Solution

1
Analyze the pattern of the first letter in each term.
The alphabetical positions of the first letters are B (2), E (5), J (10), Q (17). The differences between consecutive terms are +3+3, +5+5, and +7+7. The next difference must be +9+9. Adding +9+9 to Q (17) yields 17+9=2617 + 9 = 26, which corresponds to the letter Z.
The first letter follows an increasing sequence of consecutive odd integer positional shifts.
2
Analyze the numerical pattern in the middle of each term.
The numbers are 2, 6, 14, 30. The progression rule is nk+1=2×nk+2n_{k+1} = 2 \times n_k + 2. Applying this to the last known number: 2×30+2=622 \times 30 + 2 = 62.
Each number is generated by doubling the previous number and adding 2.
3
Analyze the pattern of the third letter in each term.
The alphabetical positions of the third letters are D (4), H (8), N (14), V (22). The positional shifts are +4+4, +6+6, +8+8. The next shift must be +10+10. Adding +10+10 to V (22) gives 22+10=3222 + 10 = 32. Modulo 26 alphabet cycle gives 32−26=632 - 26 = 6, which corresponds to the letter F.
The third letter follows an increasing sequence of consecutive even integer positional shifts with alphabetical wrap-around.
4
Combine the derived components into the final term.
Combining the first letter (Z), the number (62), and the third letter (F) gives Z62F.
The complete term must satisfy all three sub-patterns simultaneously.

Key Concept

Alphanumeric Series Completion with Multi-Pattern Positional Shifts and Arithmetic Operations
Estimated Time:2m 0s
Question 34Question →

Consider the following alphabetical sequence:

C,F,I,L,…C, F, I, L, \dots

Which letter completes the given series?

Show answer & explanation

Answer: O

Answer

The letter that completes the series is O.
Each letter advances by 3 positions in forward alphabetical order: C (3) → F (6) → I (9) → L (12). Adding 3 positions to 12 gives 15, which corresponds to the letter O.

Step-by-Step Solution

1
Determine the numerical positions of each letter in the standard alphabet.
C = 3, F = 6, I = 9, L = 12.
Translating letters to positional values simplifies pattern identification.
2
Identify the pattern of position shifts between consecutive terms.
6 - 3 = 3; 9 - 6 = 3; 12 - 9 = 3. Each term increases by +3 positions.
Finding the consistent rule enables calculating the next term.
3
Apply the rule (+3 positions) to the last given letter L (12).
12 + 3 = 15, which corresponds to the letter O.
Adding the common difference yields the next alphabetical term.

Key Concept

Alphabetical Positional Series with Constant Step Shift
Question 35Question →

Which of the following terms logically replaces the question mark (?) to complete the given alphanumeric series?

P3C,R7F,?,V27L,X43OP3C, \quad R7F, \quad ?, \quad V27L, \quad X43O
Show answer & explanation

Answer: T15I

Answer

T15I
The correct term is obtained by independently evaluating the three sub-series: first letters advance by +2+2 (P,R,T,V,XP, R, T, V, X), central numbers increment by expanding step differences of +4,+8,+12,+16+4, +8, +12, +16 (3,7,15,27,433, 7, 15, 27, 43), and third letters advance by +3+3 (C,F,I,L,OC, F, I, L, O). Unifying these components produces T15IT15I.

Step-by-Step Solution

1
Analyze the pattern of the first letter in each term
The first letters follow an increasing positional shift of +2+2: P(16)→+2R(18)→+2T(20)→+2V(22)→+2X(24)P(16) \xrightarrow{+2} R(18) \xrightarrow{+2} T(20) \xrightarrow{+2} V(22) \xrightarrow{+2} X(24). Thus, the missing first letter is TT.
Tracking alphabet positional values reveals a constant linear addition of 2 units.
2
Analyze the pattern of the central numerical values
The differences between consecutive numbers form a sequence of multiples of 44: 7−3=47 - 3 = 4, so the next difference is 4+4=84 + 4 = 8, giving 7+8=157 + 8 = 15. Verifying subsequent terms: 15+12=2715 + 12 = 27 and 27+16=4327 + 16 = 43. Thus, the missing number is 1515.
The number sequence follows an increasing double-difference pattern where each term's increment grows by +4+4.
3
Analyze the pattern of the third letter in each term
The third letters follow an increasing positional shift of +3+3: C(3)→+3F(6)→+3I(9)→+3L(12)→+3O(15)C(3) \xrightarrow{+3} F(6) \xrightarrow{+3} I(9) \xrightarrow{+3} L(12) \xrightarrow{+3} O(15). Thus, the missing third letter is II.
Tracking alphabet positional values reveals a constant shift of 3 steps forward.
4
Combine the results of all three components
Combining the first letter TT, middle number 1515, and third letter II yields the complete term T15IT15I.
Each element operates independently according to its own sub-rule.

Key Concept

Alphanumeric Series Completion with Multi-Pattern Positional Shifts
Estimated Time:1m 15s
Question 36Question →
Consider the following alphanumeric sequence:
C3Z,E7Y,H16V,M35Q,T74J,…C3Z, E7Y, H16V, M35Q, T74J, \dots
What is the next term in this sequence?
Show answer & explanation

Answer: E153AE153A

Answer

The next term in the sequence is E153AE153A.
The term E153AE153A is derived by combining three distinct concurrent rules: adding consecutive prime numbers (+2, +3, +5, +7, +11) to the first letter's position, applying the operations ×2+1,×2+2,…\times 2 + 1, \times 2 + 2, \dots to the numeric value, and subtracting consecutive odd numbers (-1, -3, -5, -7, -9) from the last letter's position.

Step-by-Step Solution

1
Analyze the pattern of the first letter in each term
The positional values of the first letters are C=3,E=5,H=8,M=13,T=20C=3, E=5, H=8, M=13, T=20. The differences between consecutive terms are +2,+3,+5,+7+2, +3, +5, +7. These differences are prime numbers. The next prime number to add is +11+11. T(20)+11=31T(20) + 11 = 31. Subtracting 26 for alphabetical wraparound gives 31−26=531 - 26 = 5, which corresponds to the letter EE.
To establish the rule governing the first component of each term.
2
Analyze the numerical pattern in the middle of each term
The numerical sequence is 3,7,16,35,743, 7, 16, 35, 74. The recurrence relation is Termk+1=Termk×2+k\text{Term}_{k+1} = \text{Term}_k \times 2 + k. Specifically: 3×2+1=73 \times 2 + 1 = 7, 7×2+2=167 \times 2 + 2 = 16, 16×2+3=3516 \times 2 + 3 = 35, 35×2+4=7435 \times 2 + 4 = 74. The next term is 74×2+5=148+5=15374 \times 2 + 5 = 148 + 5 = 153.
To identify the algebraic multiplier and incremental addition rule of the numeric component.
3
Analyze the pattern of the second letter in each term
The positional values of the second letters are Z=26,Y=25,V=22,Q=17,J=10Z=26, Y=25, V=22, Q=17, J=10. The differences between consecutive terms are −1,−3,−5,−7-1, -3, -5, -7. These subtractions follow consecutive odd numbers. The next odd number to subtract is −9-9. J(10)−9=1J(10) - 9 = 1, which corresponds to the letter AA.
To determine the positional shift pattern for the final letter element.
4
Combine the results from all three components
Combining the first letter (EE), the middle number (153153), and the second letter (AA) yields E153AE153A.
To form the complete missing term of the alphanumeric sequence.

Key Concept

Alphanumeric Series Completion with Interdependent Prime, Odd, and Linear Operations
Question 37Question →

Consider the following numerical series: 4,7,12,19,28,…4, 7, 12, 19, 28, \dots. What is the next number in this series?

Show answer & explanation

Answer: 39

Answer

The next number in the series is 3939.
The difference between consecutive terms increases by 2 each time (+3,+5,+7,+9+3, +5, +7, +9). The next difference to add is +11+11, yielding 28+11=3928 + 11 = 39.

Step-by-Step Solution

1
Calculate the difference between each pair of consecutive terms.
The differences are 3,5,7,93, 5, 7, 9.
Identifying the first-order difference sequence reveals the pattern of progression.
2
Find the next value in the difference sequence.
The next odd number after 99 is 1111.
The pattern of differences consists of consecutive prime/odd increments (specifically, odd numbers +2+2 each step).
3
Add the calculated difference to the final given term of the series.
28+11=3928 + 11 = 39
Applying the pattern to find the subsequent term.

Key Concept

Number series completion using a sequence of increasing odd differences.
Question 38Question →

Consider the following alphanumeric series:
Z1A,X2C,V6E,T24G,R120I,…Z1A, X2C, V6E, T24G, R120I, \dots

What is the next term in this series?

Show answer & explanation

Answer: P720K

Answer

The correct next term is P720K.
The term P720K correctly combines all three independent patterns: the first letter decreases by 2 positional steps in the alphabet (Z -> X -> V -> T -> R -> P), the central numerical term multiplies by increasing integers (1×21 \times 2, 2×32 \times 3, 6×46 \times 4, 24×524 \times 5, 120×6=720120 \times 6 = 720), and the last letter increases by 2 positional steps (A -> C -> E -> G -> I -> K).

Step-by-Step Solution

1
Analyze the first letter sequence
Alphabetical positions: Z(26),X(24),V(22),T(20),R(18)Z (26), X (24), V (22), T (20), R (18). The pattern is a step shift of −2-2. The next letter position is 18−2=1618 - 2 = 16, which corresponds to PP.
Determine the rule governing the initial letter of each term.
2
Analyze the middle numerical sequence
The sequence is 1,2,6,24,1201, 2, 6, 24, 120. The multipliers increase sequentially: 1×2=21 \times 2 = 2, 2×3=62 \times 3 = 6, 6×4=246 \times 4 = 24, 24×5=12024 \times 5 = 120. The next multiplier is 66, so 120×6=720120 \times 6 = 720.
Identify the multiplication progression for the numerical components.
3
Analyze the final letter sequence
Alphabetical positions: A(1),C(3),E(5),G(7),I(9)A (1), C (3), E (5), G (7), I (9). The pattern is a step shift of +2+2. The next letter position is 9+2=119 + 2 = 11, which corresponds to KK.
Determine the rule governing the trailing letter of each term.
4
Combine the components
Combining the first letter (PP), middle number (720720), and last letter (KK) yields P720KP720K.
Assemble the complete final term of the series.

Key Concept

Multi-component alphanumeric series pattern recognition combining arithmetic step shifts and factorial multiplication.
Estimated Time:1m 0s
Question 39Question →
Which of the following letter pairs logically completes the given sequence?
ZA,YC,XF,WJ,…ZA, YC, XF, WJ, \dots
Show answer & explanation

Answer: VOVO

Answer

VOVO
The sequence consists of two independent letter patterns. The first letter decreases monotonically by 1 position (Z -> Y -> X -> W -> V). The second letter follows an increasing difference series (+2, +3, +4, +5), advancing J (10th position) to O (15th position). Combining these yields VO.

Step-by-Step Solution

1
Analyze the pattern of the first letter in each pair
Z (26), Y (25), X (24), W (23). The letters move backward by 1 step continuously. The next letter is V (22).
Determines the first letter of the missing term.
2
Analyze the pattern of the second letter in each pair
A (1) to C (3) is +2; C (3) to F (6) is +3; F (6) to J (10) is +4. The increment increases by 1 at each term. Adding 5 to J (10) gives 15, which corresponds to the letter O.
Determines the second letter of the missing term.
3
Combine both components to form the final term
Combining V and O gives VO.
Completes the sequence.

Key Concept

Dual-Pattern Alphabet Series with Positional Shifts
Question 40Question →
Consider the following multi-pattern alphanumeric series:
B3Y,E5W,I13T,N49P,T241K,…B3Y, E5W, I13T, N49P, T241K, \dots
Which of the following alphanumeric terms correctly completes the given sequence?
Show answer & explanation

Answer: A1441E

Answer

A1441E
The correct term is determined by combining three distinct concurrent rules: the first letter shifts forward by incrementally larger intervals (+3, +4, +5, +6, +7) wrapping from T to A; the middle number follows the operational recurrence relation (Previous × n) - (n - 1) yielding (241 × 6) - 5 = 1441; and the third letter shifts backward by expanding steps (-2, -3, -4, -5, -6) moving from K to E.

Step-by-Step Solution

1
Analyze the pattern of the first letters in the terms: B, E, I, N, T
Positions in alphabet: B(2) → (+3) → E(5) → (+4) → I(9) → (+5) → N(14) → (+6) → T(20). The next shift must be +7. T(20) + 7 = 27, which wraps around to A(1).
The forward positional shift increases by +1 at each successive step.
2
Analyze the pattern of the middle numerical sequence: 3, 5, 13, 49, 241
Step 1 to 2 (n=2): (3 × 2) - 1 = 5. Step 2 to 3 (n=3): (5 × 3) - 2 = 13. Step 3 to 4 (n=4): (13 × 4) - 3 = 49. Step 4 to 5 (n=5): (49 × 5) - 4 = 241. Step 5 to 6 (n=6): (241 × 6) - 5 = 1446 - 5 = 1441.
The operational formula for the nth transition is Term_n = (Term_{n-1} × n) - (n - 1).
3
Analyze the pattern of the third letters in the terms: Y, W, T, P, K
Positions in alphabet: Y(25) → (-2) → W(23) → (-3) → T(20) → (-4) → P(16) → (-5) → K(11). The next shift must be -6. K(11) - 6 = 5, which corresponds to E.
The backward positional shift magnitude increases by 1 step sequentially.
4
Combine the results of the three independent sub-patterns
First letter: A, Middle number: 1441, Last letter: E. Combined term: A1441E.
Formulating the final composite term completing the series.

Key Concept

Multi-layered Alphanumeric Series Completion
PreviousPage 2 / 3Next
Number and Alphabet Series Practice Questions — State PSC Exam — Page 2 | Examkin