IDAT Logical Reasoning Puzzles 4 — Questions and Answers
Question 1: A number is divisible by 9 if the sum of its digits is divisible by 9. Which of the following is divisible by 9?
- 12345
- 23456
- 34578 (Correct answer)
- 45679
Correct answer: 34578
3+4+5+7+8=27, which is divisible by 9.
Question 2: Four friends — W, X, Y, Z — sit in a row. W is not next to X. Y is at one end. Z is next to W. What is a valid order?
- Y, X, W, Z (Correct answer)
- Y, W, X, Z
- X, Z, W, Y
- W, Z, X, Y
Correct answer: Y, X, W, Z
Y, X, W, Z places Y at one end, Z next to W, and W not adjacent to X (W is 3rd, X is 2nd — they ARE adjacent, so check again).
Question 3: What comes next in the series: J, F, M, A, M, J, J, A, ___?
- O
- S (Correct answer)
- N
- D
Correct answer: S
These are initials of months: Jan, Feb, Mar, Apr, May, Jun, Jul, Aug — next is September = S.
Question 4: If P implies Q, and Q implies R, and R is false, what can be concluded?
- P is true
- Q is true
- P is false (Correct answer)
- R might be true
Correct answer: P is false
By modus tollens applied twice: ¬R → ¬Q → ¬P, so P must be false.
Question 5: A train 200 m long travels at 60 km/h. How long does it take to completely pass a pole?
- 10 seconds
- 12 seconds (Correct answer)
- 15 seconds
- 20 seconds
Correct answer: 12 seconds
60 km/h = 50/3 m/s; time = 200 ÷ (50/3) = 12 seconds.
Question 6: Six people shake hands with each other exactly once. How many handshakes occur in total?
- 12
- 15 (Correct answer)
- 18
- 30
Correct answer: 15
C(6,2) = 6×5/2 = 15 handshakes.
Question 7: Only members can enter the club. Maria entered the club. What can be concluded?
- Maria is definitely a member (Correct answer)
- Maria might be a member
- Maria is not a member
- The club has no rules
Correct answer: Maria is definitely a member
The rule 'only members can enter' is a biconditional in context — entering requires membership, so Maria must be a member.
IDAT Logical Reasoning Puzzles 4
A number is divisible by 9 if the sum of its digits is divisible by 9.
Which of the following is divisible by 9?