Series Set - 3





Q. Find the next number in the series: (āĻĒā§ā§°āĻļā§āĻ¨āĻƒ āĻļā§ƒāĻ‚āĻ–āĻ˛āĻžāĻŸā§‹ā§° āĻĒā§°ā§ąā§°ā§āĻ¤ā§€ āĻ¸āĻ‚āĻ–ā§āĻ¯āĻžāĻŸā§‹ āĻ¨āĻŋā§°ā§āĻŖāĻ¯āĻŧ āĻ•ā§°āĻ•āĨ¤) 0, 8, 24, 48, ?


Options / āĻŦāĻŋāĻ•āĻ˛ā§āĻĒāĻ¸āĻŽā§‚āĻš: A) 80  B) 96  C) 120  D) 144


Trick


Pattern: 0 + (8*1) = 8, 8 +(8*2) = 24, 24 +(8*3) = 48, 48 + (8*4) = 80


The numbers added are: +8, +16, +24, +32 (increase by 8 each time)


Number = 80


Ans: A) 80


Q) Find the missing term in the series: 10, 100, 200, 310, ?


Options: A) 400  B) 410  C) 420  D) 430


Soln


Find the differences: 100 − 10 = 90, 200 − 100 = 100, 310 − 200 = 110


The differences increase by 10 each time: 90, 100, 110, 120


So next term: 310 + 120 = 430


Ans: D) 430


Q.  A   G  ?    K   I
      E   C  ?    G  M  


Option: a. G/H  b. H/D  c. E/I,  d. J/E


The pattern is: A → G = +6 letters, E → C = −2 letters


Apply the same pattern to the next pair: i. ? → K = +6 ⇒ ? = E,  ii. ? → G = −2 ⇒ ? = I


So the missing letters are: E / I


An: (C) E / I


Check: A + 6 = G / E − 2 = C / E + 6 = K / I − 2 = G


Therefore, Option (C) E / I is correct.


Diagonal Trick: Look diagonally: A → C ⇒ Middle letter = B, E → G ⇒ Middle letter = F, Similarly, G → I ⇒ Middle letter = H, C → E ⇒ Middle letter = D, So the missing pair is:E/I


Ans: (C) E / I






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Q. Find the missing series ?

ac_a_c_a_cca

Options: (a) acac  (b) caac  (c) caca  (d) acca

Soln

Fill the blanks with caca: a c c a a c c a a c c a

⇒ acca acca acca

The pattern "acca" repeats 3 times.

Ans: (c) caca

Shortcut: After filling caca, the series becomes: ACCA | ACCA | ACCA (Perfect repeating pattern)

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Q. Find the next number in the series: 325, 200, 136, 109, 101, ?

Options: A. 101  B. 900  C. 102  D. 100

Soln: 325 - 53 = 325 - 125 = 200 / 200 - 43 = 200 - 64 = 136 / 136 - 33 = 136 - 27 = 109 / 109 - 23 = 109 - 8 = 101 / 101 - 13 = 101 – 1 = 100

Ans: D. 100

Short Trick: Subtract consecutive cubes in descending order: −5³, −4³, −3³, −2³, −1³ ⇒ 325, 200, 136, 109, 101, 100.

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Q. Find the next number in the series: 65, 40, 24, 15, 11, ?

Options: A. 12  B. 09  C. 10   D. 6

Soln:

Observe the pattern: 65 – 25 = 40 (25 = 52) / 40 – 16 = 24 (16 = 42) /' 24 – 9 = 15 (9 = 32) / 15 – 4 = 11 (4 = 22) Next, 11 – 1 = 10 (1 = 12)

Pattern: Subtract consecutive squares: −52, −42, −32, −22, −12 

Therefore, 11- 1 = 10

Ans: C. 10

Short Trick

Series: 19, 20, 28, 55, 119, ?

Look at the differences: 20 − 19 = 1 = 1³  / 28 − 20 = 8 = 2³  / 55 − 28 = 27 = 3³  / 119 − 55 = 64 = 4³

So next difference: 5³ = 125 

Therefore,  119 + 125 = 244

Ans: C. 244

One-line Trick: Add consecutive cubes: +1³, +2³, +3³, +4³, +5³.

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Q. Find the missing number: 64, 32, 28, 14, 10, 5, ?


Options: A. 1  B. 2  C. 3  D. 0


Trick: 64 ÷ 2 = 32 → 32 − 4 = 28 → 28 ÷ 2 = 14 → 14 − 4 = 10 → 10 ÷ 2 = 5 → 5 − 4 = 1


Pattern: ÷2, −4, ÷2, −4, ÷2, −4


Ans: A. 1


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Q. Series: 81 : 101 :: 121 :  ? 


Option: A) 141  B) 143  C) 145  D) 170


Trick


Notice that: 81 = 92 , 121 = 112

Apply the pattern: n2 → (n+1)2 + 1


Check with the first pair:


81 = 92  


(9 + 1)2 + 1 = 102 + 1 = 100 + 1 = 101


Pattern is correct.


Apply to 121:


121 = 112 


(11+1)2 + 1= 122 + 1= 144 + 1 = 145


Ans: C) 145


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Q. Find the missing number in the series: 0, 4, 18, 48, ?, 180


Options: (a) 58  (b) 68  (c) 84  (d) 100


Solution | āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨


Look at each number:



  • 0 = 0 × 12

  • 4 = 1 × 22

  • 18= 2 × 32

  • 48 = 3 × 42

  • ? = 4 × 52 = 4 × 25 = 100

  • 180 = 5 × 62 = 5 × 36 = 180


So the pattern is: 0×12, 1×22, 2×32, 3×42, 4×52, 5×62


Therefore,


Ans: (d) 100










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