Multiple choice

Directions: Read the following information and answer the question that follows.

There are six steps that lead from the first to the second floor. No two people can be on the same step. Mr. A is two steps below Mr. C. Mr. B is a step next to Mr. D. Only one step is vacant (no one is standing on that step). Denote the first step by step 1 and second step by step 2 and so on.

If Mr. E was on the third step and Mr. B was on a higher step than Mr. E, then which step must be vacant?

  1. Step 1

  2. Step 2

  3. Step 4

  4. Step 5

  5. Step 6

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Mr. E is on step 3, and Mr. B is on a higher step than Mr. E. Mr. A is two steps below Mr. C, and Mr. B is adjacent to Mr. D. Only one step is vacant. If E is on step 3, and B is higher than E (so B is on 4, 5, or 6), let's consider possibilities. If B is on step 4, D must be on step 3 or 5. Step 3 is occupied by E, so D is on step 5. A is two below C, so A and C could be on steps 1&3, 2&4, 3&5, or 4&6. But 3 is E, 4 is B, 5 is D. So A and C must be on 1&3 or 2&4 or 4&6. 3 is occupied, 4 is B. So A(1), C(3) or A(2), C(4) or A(4), C(6). But 3 is E, 4 is B. So only A(1), C(3) works, but 3 is E. Actually, A(2), C(4) doesn't work because 4 is B. A(4), C(6): 4 is B, so no. This seems to force A(1), C(3), but 3 is E. Let me reconsider: if B=5, D=4 or 6. If D=4, then A and C could be 1&3 or 2&4. 4 is D, so A(1), C(3). But 3 is E. So step 2 is vacant? Let me try B=6, D=5. Then A and C need to be on 1&3 or 2&4. A(1), C(3): 3 is E. A(2), C(4): This works! A is on 2, C is on 4, E is on 3, B is on 6, D is on 5. Vacant step is 1.