AMCAT Logical Reasoning: Coding & Series 2 — Questions and Answers
Question 1: If PENCIL is coded as RGPEKN, how is RUBBER coded? (each letter shifted by +2)
- TWDDGT (Correct answer)
- TWDCGT
- TUDDGT
- TWDDFU
Correct answer: TWDDGT
Each letter shifted +2: R+2=T, U+2=W, B+2=D, B+2=D, E+2=G, R+2=T = TWDDGT.
Verifying shift +2 on PENCIL: P→R, E→G, N→P, C→E, I→K, L→N = RGPEKN. Applying to RUBBER: R→T, U→W, B→D, B→D, E→G, R→T = TWDDGT.
Question 2: Find the next term in the series: 2, 6, 12, 20, 30, ?
- 40
- 42 (Correct answer)
- 44
- 36
Correct answer: 42
Differences: 4, 6, 8, 10, 12. Next term = 30 + 12 = 42.
6−2=4, 12−6=6, 20−12=8, 30−20=10. Differences increase by 2. Next difference = 12. Next term = 30 + 12 = 42. Alternatively terms are n(n+1): 6×7=42.
Question 3: What comes next in the Fibonacci-like series: 1, 1, 2, 3, 5, 8, 13, ?
- 20
- 21 (Correct answer)
- 18
- 24
Correct answer: 21
Each term is the sum of the two preceding terms: 8 + 13 = 21.
Fibonacci: 1, 1, 2, 3, 5, 8, 13, 21, 34, ... Each term = sum of previous two. 8 + 13 = 21.
Question 4: Find the odd one out: 4, 9, 16, 25, 35, 49
- 4
- 25
- 35 (Correct answer)
- 49
Correct answer: 35
4=2^2, 9=3^2, 16=4^2, 25=5^2, 49=7^2 are all perfect squares. 35 is not a perfect square.
4=2^2, 9=3^2, 16=4^2, 25=5^2, 49=7^2. All are perfect squares except 35 (between 25 and 36). 35 is the odd one out.
Question 5: Find the next number: 3, 7, 15, 31, 63, ?
- 125
- 127 (Correct answer)
- 121
- 130
Correct answer: 127
Pattern: each term = 2 × previous + 1. 2×63+1 = 127.
3→7: ×2+1. 7→15: ×2+1. 15→31: ×2+1. 31→63: ×2+1. 63→127: 2×63+1=127. Alternatively terms are 2^n − 1: 128−1=127.
Question 6: In a series A, C, E, G, I, the next term is:
- J
- K (Correct answer)
- L
- M
Correct answer: K
The series consists of every other letter: A(1), C(3), E(5), G(7), I(9), K(11).
A=1, C=3, E=5, G=7, I=9 — all odd-positioned letters. Next odd position = 11 = K.
AMCAT Logical Reasoning: Coding & Series 2
If PENCIL is coded as RGPEKN, how is RUBBER coded? (each letter shifted by +2)