Question

The mean temperature of Monday to Wednesday was 37 degree Celsius and of Tuesday to Thursday was 34 degree. What was the temperature on Thursday?
I. The temperature on Thursday was that of Monday.
II. The mean temperature of Monday and Thursday was 40.5 degree Celsius.
III. The difference between the temperature on Monday and that on Thursday was 9 degree Celsius.

• A. I only
• B. Either I or II
• C. Either I or II or III
• D. None of these

Answer 1

The Correct Option is B

To solve the problem of determining the temperature on Thursday, let's analyze each piece of information:

• The mean temperature for Monday to Wednesday is 37°C. Let the temperatures be M (Monday), T (Tuesday), and W (Wednesday). Thus, we have:
  (M + T + W)/3 = 37
  ⟹ M + T + W = 111
• The mean temperature for Tuesday to Thursday is 34°C. Let the temperatures be T (Tuesday), W (Wednesday), and Th (Thursday). Thus, we have:
  (T + W + Th)/3 = 34
  ⟹ T + W + Th = 102

We wish to find Th. Now, consider the statements provided:

1. The temperature on Thursday was that of Monday. If Th = M, then using both equations:
   M + T + W = 111 and T + W + M = 102.
   Solving these equations gives M = Th.
2. The mean temperature of Monday and Thursday is 40.5°C. This implies:
   (M + Th)/2 = 40.5
   ⟹ M + Th = 81.
   Using equations
   M + T + W = 111 and T + W + Th = 102, by subtracting the second from the first, we have M - Th = 9°C.
   M + Th = 81.
   Solving M + Th = 81 and M - Th = 9 gives M = 45 and Th = 36.
3. The difference between the temperature on Monday and Thursday is 9°C:
   M - Th = 9.
   Using another derived equation, M + Th = 81, we solve these simultaneously and again deduce M = 45 and Th = 36.

Thus, statements I, II, and III solve for Th, but either I or II can independently determine it, as we've shown using either leads to consistent results. Therefore, the minimal sufficient answer is "Either I or II".