Number and Letter Series for CUET General Aptitude

AnswerA · 32

1. Differences: $12 - 7 = 5$, $17 - 12 = 5$, $22 - 17 = 5$, $27 - 22 = 5$.

2. The difference is always 5, so the next term is $27 + 5 = 32$.

AnswerC · 405

1. The differences 10, 30, 90 are not constant, so try ratios: $15 \div 5 = 3$, $45 \div 15 = 3$, $135 \div 45 = 3$.

2. Each term is 3 times the one before, so the next term is $135 \times 3 = 405$.

AnswerC · 56

1. Differences: 3, 6, 9, 12. They go up by 3 each time.

2. The next difference is 15, so the next term is $41 + 15 = 56$.

AnswerD · 39

1. Differences: 3, 5, 7, 9, rising by 2, so the next difference is 11.

2. Next term $= 28 + 11 = 39$. Check: the terms are $1^2 + 3, 2^2 + 3, 3^2 + 3, 4^2 + 3, 5^2 + 3$, and $6^2 + 3 = 39$.

AnswerB · 17

1. The terms are the prime numbers in order: 2, 3, 5, 7, 11, 13.

2. The next prime after 13 is 17 (14, 15 and 16 all have factors).

AnswerB · 24

1. Differences: $6 - 4 = 2$, $9 - 6 = 3$, $13 - 9 = 4$, $18 - 13 = 5$.

2. Each difference is one more than the last, so add 6: $18 + 6 = 24$.

AnswerD · 240

1. Ratios: $2 \div 2 = 1$, $4 \div 2 = 2$, $12 \div 4 = 3$, $48 \div 12 = 4$.

2. The multiplier rises by 1 each step, so the next is $48 \times 5 = 240$.

AnswerB · 169

1. The terms are $2^2, 3^2, 5^2, 7^2, 11^2$: squares of the prime numbers.

2. The next prime is 13, so the next term is $13^2 = 169$.

AnswerC · 127

1. Test the gaps first: 4, 8, 16, 32. They are doubling, which suggests a multiplicative rule.

2. Check it: each term is double the one before it, plus one. $3 \times 2 + 1 = 7$, $7 \times 2 + 1 = 15$, $15 \times 2 + 1 = 31$, $31 \times 2 + 1 = 63$.

3. So the next term is $63 \times 2 + 1 = 127$.

AnswerC · 42

1. The differences between consecutive terms are 4, 6, 8 and 10 — rising by 2 each time.

2. The next difference is therefore 12, giving $30 + 12 = 42$.

3. The rule can also be written directly: the terms are $1 \times 2$, $2 \times 3$, $3 \times 4$, $4 \times 5$, $5 \times 6$, so the next is $6 \times 7 = 42$.

AnswerC · 65

1. Differences: 2, 4, 8, 16. They double, so the next difference is 32.

2. Next term $= 33 + 32 = 65$.

3. The same rule in one line: each term is $2 \times (\text{previous}) - 1$, and $33 \times 2 - 1 = 65$.

AnswerB · 365

1. Test $\times 3$: $2 \times 3 = 6$, but the next term is 5, one less.

2. So the rule is $\times 3 - 1$: $5 \times 3 - 1 = 14$, $14 \times 3 - 1 = 41$, $41 \times 3 - 1 = 122$.

3. Next term $= 122 \times 3 - 1 = 365$.

AnswerD · 217

1. Each term is one more than a cube: $1^3 + 1 = 2$, $2^3 + 1 = 9$, $3^3 + 1 = 28$, $4^3 + 1 = 65$, $5^3 + 1 = 126$.

2. Next term $= 6^3 + 1 = 216 + 1 = 217$.

AnswerA · 19

1. The terms jump up and down, so split them into two series.

2. 1st, 3rd, 5th terms: 4, 9, 14 (add 5). 2nd, 4th, 6th terms: 30, 27, 24 (subtract 3).

3. The 7th term belongs to the first series: $14 + 5 = 19$.

AnswerC · 47

1. Differences 1, 3, 4, 7, 11 do not follow an obvious pattern, but notice $3 + 4 = 7$, $4 + 7 = 11$, $7 + 11 = 18$, $11 + 18 = 29$.

2. Each term is the sum of the two before it, so the next is $18 + 29 = 47$.

AnswerD · 57

1. Differences: 1, 4, 9, 16. These are $1^2, 2^2, 3^2, 4^2$.

2. The next difference is $5^2 = 25$, so the next term is $32 + 25 = 57$.

AnswerA · 100

1. Differences: 3, 6, 12, 24. They double each time.

2. Next difference $= 48$, so the next term is $52 + 48 = 100$.

3. Check with the rule $\times 2 - 4$: $52 \times 2 - 4 = 100$.

AnswerB · 35

1. Differences: 21, 19, 17, 15, falling by 2, so the next difference is 13 and $48 - 13 = 35$.

2. Check: the terms are $11^2 - 1, 10^2 - 1, 9^2 - 1, 8^2 - 1, 7^2 - 1$, so the next is $6^2 - 1 = 35$.

AnswerC · 445

1. Try a changing multiplier with a matching addition: $1 \times 1 + 1 = 2$, $2 \times 2 + 2 = 6$, $6 \times 3 + 3 = 21$, $21 \times 4 + 4 = 88$.

2. The next step is $\times 5 + 5$: $88 \times 5 + 5 = 440 + 5 = 445$.

AnswerA · 35

1. Compare each term with a square: $2 = 1^2 + 1$, $3 = 2^2 - 1$, $10 = 3^2 + 1$, $15 = 4^2 - 1$, $26 = 5^2 + 1$.

2. The +1 and −1 alternate, so the 6th term is $6^2 - 1 = 35$.

AnswerC · 27

1. The terms go down, up, down, up, so look at the operations: $8 \div 2 = 4$, $4 \times 3 = 12$, $12 \div 2 = 6$, $6 \times 3 = 18$, $18 \div 2 = 9$.

2. The operations alternate $\div 2$ and $\times 3$. The next is $\times 3$: $9 \times 3 = 27$.

AnswerB · 252

1. Split each term into a square times the next number: $2 = 1^2 \times 2$, $12 = 2^2 \times 3$, $36 = 3^2 \times 4$, $80 = 4^2 \times 5$, $150 = 5^2 \times 6$.

2. So the 6th term is $6^2 \times 7 = 36 \times 7 = 252$.

3. Check with differences: 10, 24, 44, 70 have differences 14, 20, 26 (rising by 6), so the next difference is $70 + 32 = 102$, and $150 + 102 = 252$.

AnswerA · Q

1. Positions: B = 2, E = 5, H = 8, K = 11, N = 14.

2. Each letter is 3 places after the one before, so the next is $14 + 3 = 17$, which is Q.

AnswerD · P

1. Positions: Z = 26, X = 24, V = 22, T = 20, R = 18.

2. Each step goes back 2 places, so the next is $18 - 2 = 16$, which is P.

AnswerD · T

1. Positions: D = 4, H = 8, L = 12, P = 16, the multiples of 4.

2. Next position $= 16 + 4 = 20$, which is T. (EJOTY: T is the 20th letter.)

AnswerB · EV

1. First letters: A, B, C, D, moving forward one place, so the next is E.

2. Second letters: Z, Y, X, W, moving back one place, so the next is V.

3. Each pair is a letter with its opposite (the two positions add to 27). The next pair is EV.

AnswerC · QPO

1. The alphabet is being written backwards in blocks of three: ZYX, then WVU, then TSR.

2. The next three letters going backwards after R are Q, P, O, so the group is QPO.

AnswerA · D

1. The moves are +2, −1, +2, −1, +2 (A to C, C to B, B to D, D to C, C to E).

2. The next move is −1, so the letter after E is D.

3. Equivalently, the odd places read A, B, C and the next one is D.

AnswerC · U

1. Count the steps through the alphabet between consecutive letters: A to C is 2, C to F is 3, F to J is 4, J to O is 5.

2. The steps are growing by one each time, so the next step is 6.

3. O is the 15th letter, and $15 + 6 = 21$, which is U.

AnswerD · P

1. Positions: A = 1, B = 2, D = 4, H = 8.

2. Each position doubles (the jumps are 1, 2, 4), so the next position is 16, which is P.

AnswerB · E

1. Positions: Y = 25, W = 23, T = 20, P = 16, K = 11.

2. The backward jumps are 2, 3, 4, 5, growing by one, so the next jump is 6.

3. $11 - 6 = 5$, which is E.

AnswerB · TVX

1. Inside each group the letters skip one: B, D, F; H, J, L; N, P, R.

2. The groups start at B = 2, H = 8, N = 14, jumping 6 each time, so the next starts at 20, which is T.

3. Skipping one letter each time from T gives T, V, X.

AnswerA · G

1. Split the series: 1st, 3rd, 5th letters are A, C, E (forward by 2); 2nd, 4th, 6th are Z, X, V (backward by 2).

2. The 7th letter continues the first series: after E comes G.

AnswerD · Y

1. Positions: A = 1, D = 4, I = 9, P = 16. These are $1^2, 2^2, 3^2, 4^2$.

2. The next position is $5^2 = 25$, which is Y.

AnswerB · M

1. Positions: B = 2, C = 3, E = 5, G = 7, K = 11. These are the prime numbers.

2. The next prime is 13, which is M.

AnswerA · L

1. Positions: C = 3, D = 4, F = 6, G = 7, I = 9, J = 10.

2. The jumps alternate +1, +2, +1, +2, +1, so the next jump is +2: $10 + 2 = 12$, which is L.

AnswerD · OL

1. First letters: A = 1, C = 3, F = 6, J = 10. The jumps are 2, 3, 4, so the next jump is 5, giving 15, which is O.

2. Second letters: Z, X, U, Q are the opposites of A, C, F, J (each pair of positions adds to 27).

3. The opposite of O is $27 - 15 = 12$, which is L. The next pair is OL.

AnswerC · OT

1. First letters: A, C, F, J (positions 1, 3, 6, 10), jumps 2, 3, 4. Next jump 5 gives O (15).

2. Inside each pair the gap grows: A to B is 1, C to E is 2, F to I is 3, J to N is 4.

3. So the second letter is 5 after O: $15 + 5 = 20$, which is T. The pair is OT.

AnswerB · DTP

1. Read each column separately. First letters A, B, C move forward 1: next D.

2. Second letters Z, X, V move back 2: next T.

3. Third letters Y, V, S move back 3: next P. The group is DTP.

AnswerC · I9

1. Letters: A, C, E, G skip one letter each time, so the next is I.

2. Numbers: 1, 3, 5, 7 go up by 2, so the next is 9. Each number is the position of its letter.

3. The next term is I9.

AnswerA · 10J

1. Numbers: 2, 4, 6, 8, so the next is 10.

2. Letters: B, D, F, H are the 2nd, 4th, 6th and 8th letters, so the next is the 10th letter, J.

3. The next term is 10J.

AnswerA · bbcc

1. Look for a block that repeats. The visible letters fit the block abc: a_c | a_c | ab_ | ab_.

2. Fill each block as abc: the blanks are b, b, c, c.

3. The complete pattern is abcabcabcabc.

AnswerC · 3

1. Look at each digit and the element just to its right: 7 @, 3 E, 9 M, 2 %, 6 A, 4 =.

2. The digit is followed by a symbol in 7 @, 2 % and 4 =, so the count is 3.

AnswerD · R25

1. Letters: Z, X, V, T go back 2 each time, so the next is R.

2. Numbers: 1, 4, 9, 16 are $1^2, 2^2, 3^2, 4^2$, so the next is $5^2 = 25$.

3. The next term is R25.

AnswerB · O30

1. Letters: C, F, I, L are positions 3, 6, 9, 12, so the next is 15, which is O.

2. Numbers: 6, 12, 18, 24 go up by 6 (each is twice its letter's position), so the next is 30.

3. The next term is O30.

AnswerC · H48

1. Letters: P, N, L, J go back 2 each time (16, 14, 12, 10), so the next is 8, which is H.

2. Numbers: 3, 6, 12, 24 double each time, so the next is 48.

3. The next term is H48.

AnswerD · babab

1. The pattern has 12 places. Try blocks of 4: aa_b | a_b_ | _ab_.

2. The block aabb fits all the letters that are shown.

3. Filling each block as aabb gives the blanks b, a, b, a, b, and the pattern aabbaabbaabb.

AnswerC · bcac

1. Try blocks of 4: _aa_ | ba_c | baa_ read against the shown letters.

2. The block baac fits: the first block needs b and c, the second needs a, the third needs c.

3. So the blanks are b, c, a, c, and the pattern is baacbaacbaac.

AnswerD · 6

1. The 9th element from the left is M.

2. 5th to the right of the 9th is the $9 + 5 = 14$th element from the left.

3. Counting: K 7 @ R 3 E # 9 M U 2 % B 6, so the 14th element is 6.

AnswerA · rprp

1. The shown letters p q _ r q p suggest a block of 6 that reads the same backwards: pqrrqp.

2. Check the second block: _ q r _ q _ must be p q r r q p, so its blanks are p, r, p.

3. The blanks in order are r (first block), then p, r, p, giving rprp.

AnswerB · 2

1. First find the letters preceded by a digit: E (after 3), M (after 9), A (after 6).

2. Now check what follows each: E is followed by #, M by U, A by &.

3. E and A satisfy both conditions, so the count is 2.

AnswerA · B

1. Removing @, #, %, & and = leaves: K 7 R 3 E 9 M U 2 B 6 A T 4 H.

2. Counting from the right: H (1st), 4 (2nd), T (3rd), A (4th), 6 (5th), B (6th).

3. So the 6th element from the right is B.

AnswerC · 46

1. Each term looks like double the one before: $3 \times 2 = 6$, $6 \times 2 = 12$, $12 \times 2 = 24$.

2. Then $24 \times 2 = 48$, not 46, and $48 \times 2 = 96$ matches the last term.

3. So 46 is wrong; it should be 48.

AnswerD · 30

1. Differences: 6, 6, 6, 7, 5. The pattern is +6, broken at the fifth term.

2. $23 + 6 = 29$, and $29 + 6 = 35$ fits the last term, so 30 is wrong (it should be 29).

AnswerA · 16

1. Test the ratio: $8 \div 4 = 2$ and $64 \div 32 = 2$.

2. So each term doubles: the missing term is $8 \times 2 = 16$, and $16 \times 2 = 32$ checks.

AnswerD · 18

1. Use the complete end of the series: $38 - 27 = 11$, $51 - 38 = 13$. The differences rise by 2.

2. Working back, the differences are 5, 7, 9, 11, 13, so the missing term is $11 + 7 = 18$.

3. Check: $18 + 9 = 27$.

AnswerA · 7

1. The last three differences are 5, 6, 7 (10 to 15, 15 to 21, 21 to 28): they rise by one each time.

2. The full pattern is +2, +3, +4, +5, +6, +7, so the third term is $3 + 3 = 6$, not 7.

3. With 6 in place: 1, 3, 6, 10, 15, 21, 28.

AnswerC · P

1. Positions: C = 3, F = 6, I = 9, L = 12, P = 16, R = 18.

2. The jump is 3 each time, so after L (12) should come O (15), and then R (18) fits.

3. P (16) is the wrong letter; it should be O.

AnswerD · 124

1. 1, 8, 27, 64 and 216 are the cubes $1^3, 2^3, 3^3, 4^3, 6^3$.

2. The fifth term should be $5^3 = 125$, so 124 is wrong.

AnswerD · 38

1. The terms are one more than squares: $1^2 + 1, 2^2 + 1, 3^2 + 1, 4^2 + 1, 5^2 + 1$, and the last is $7^2 + 1 = 50$.

2. The sixth term should be $6^2 + 1 = 37$, so 38 is wrong.

AnswerB · 40

1. Test $\times 2 + 1$: $4 \times 2 + 1 = 9$, $9 \times 2 + 1 = 19$.

2. Next should be $19 \times 2 + 1 = 39$, not 40; then $39 \times 2 + 1 = 79$ and $79 \times 2 + 1 = 159$ both fit.

3. So 40 is the wrong term.