Multiple choice general knowledge math & puzzles

Conditions:(i) A, B, C, D, E, F and G are seven members standing in a row (not necessarily in the same order) facing north.(ii) C and B have as many members between them as G and C have between them.(iii) D, who is 3rd from the extreme left, is 3rd to the left of E.(iv) A and D are neighbors and F and C are neighbors.Question 1 Which of the following statements may be false?

  1. A is the 3rd to the left of F

  2. D is 3rd to the left of E

  3. F is 3rd the right of A

  4. B is 3rd to the left of C
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Analyzing the positioning conditions: D is 3rd from left (position 2 in 0-indexed), and D is 3rd to the left of E (so E is at position 5). A is adjacent to D (positions 1 or 3), F is adjacent to C. The distance relationship between B and C must equal the distance relationship between G and C. Through analysis, the only arrangement satisfying all conditions places B at position 1 and C at position 3, making B two positions left of C. The statement 'B is 3rd to the left of C' uses directional language where '3rd to the left' means having two positions between them, which is false in this case (it's actually 2nd to the left).

AI explanation

Working through the clues: D is 3rd from the left, so D=3; D is 3rd to E's left, so E=6. A is D's neighbor, so A=2 or A=4. Testing condition (ii) — that C is equidistant from B and G — together with F and C being neighbors, the only self-consistent seating is A=2, D=3, C=4, F=5, E=6, with B and G occupying positions 1 and 7 in either order. Checking the four statements against this: 'A is 3rd left of F' (2→5) is always true; 'D is 3rd left of E' is given/always true; 'F is 3rd right of A' is always true. But 'B is 3rd to the left of C' only holds if B=1 (since C=4); if B=7 instead (with G=1), it's false. Since both B=1 and B=7 are valid arrangements, this statement is the one that 'may be false.'

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