CA Foundation P3 · Chapter 9

Number Series, Coding and Decoding and Odd Man Out MCQs with Answers

9 multiple-choice questions on Number Series, Coding and Decoding and Odd Man Out for CA Foundation P3 Quantitative Aptitude. Try each one before revealing the answer and explanation.

1. Question 1

   Find the next term: 3, 7, 15, 31, 63, ?

   • A) 126
   • B) 127
   • C) 95
   • D) 125
   Show answer & explanation

   Answer: B) 127

   Each term is twice the previous term plus 1: 3 x 2 + 1 = 7, 7 x 2 + 1 = 15, and so on. Next term = 63 x 2 + 1 = 127. Equivalently the terms are 2ⁿ − 1.

2. Question 2

   Find the next term: 2, 6, 12, 20, 30, ?

   • A) 40
   • B) 36
   • C) 44
   • D) 42
   Show answer & explanation

   Answer: D) 42

   The terms are n(n + 1): 1x2, 2x3, 3x4, 4x5, 5x6. The next is 6 x 7 = 42. Alternatively the differences 4, 6, 8, 10 increase by 2, so the next difference is 12 and 30 + 12 = 42.

3. Question 3

   Find the next term: 2, 3, 10, 15, 26, 35, ?

   • A) 48
   • B) 49
   • C) 50
   • D) 45
   Show answer & explanation

   Answer: C) 50

   The terms follow n² + 1 for odd n and n² − 1 for even n: 1+1 = 2, 4−1 = 3, 9+1 = 10, 16−1 = 15, 25+1 = 26, 36−1 = 35. The 7th term is 49 + 1 = 50. Answering 49 forgets the alternating +1/−1.

4. Question 4

   Find the wrong number in the series: 1, 8, 27, 64, 124, 216

   • A) 124
   • B) 27
   • C) 64
   • D) 216
   Show answer & explanation

   Answer: A) 124

   The series is of cubes: 1³, 2³, 3³, 4³, 5³, 6³. The fifth term should be 5³ = 125, so 124 is wrong.

5. Question 5

   In a certain code, MONEY is written as NPOFZ. How is LEDGER written in that code?

   • A) KDCFDQ
   • B) MFEHFS
   • C) MFEHFR
   • D) NGFIGT
   Show answer & explanation

   Answer: B) MFEHFS

   Each letter is replaced by the next letter of the alphabet (M→N, O→P, N→O, E→F, Y→Z). Applying +1 to LEDGER: L→M, E→F, D→E, G→H, E→F, R→S, giving MFEHFS. KDCFDQ applies −1 and NGFIGT applies +2.

6. Question 6

   In a certain code, CASH is written as XZHS. How is BANK written in that code?

   • A) YZNP
   • B) ZYMP
   • C) YAMP
   • D) YZMP
   Show answer & explanation

   Answer: D) YZMP

   Each letter is replaced by its mirror letter in the reversed alphabet (position p becomes 27 − p): C(3)→X(24), A(1)→Z(26), S(19)→H(8), H(8)→S(19). For BANK: B(2)→Y(25), A(1)→Z(26), N(14)→M(13), K(11)→P(16), giving YZMP.

7. Question 7

   If TEN is coded as 39 by adding the alphabetical positions of its letters, then SIX will be coded as:

   • A) 51
   • B) 53
   • C) 52
   • D) 48
   Show answer & explanation

   Answer: C) 52

   TEN = T(20) + E(5) + N(14) = 39, confirming the rule. SIX = S(19) + I(9) + X(24) = 52.

8. Question 8

   Find the odd one out: 27, 64, 144, 216

   • A) 144
   • B) 27
   • C) 64
   • D) 216
   Show answer & explanation

   Answer: A) 144

   27 = 3³, 64 = 4³ and 216 = 6³ are perfect cubes. 144 = 12² is a perfect square but not a perfect cube, so it is the odd one out.

9. Question 9

   Find the odd one out: 29, 37, 51, 61

   • A) 29
   • B) 37
   • C) 51
   • D) 61
   Show answer & explanation

   Answer: C) 51

   29, 37 and 61 are prime numbers. 51 = 3 x 17 is composite, so it is the odd one out.