The average temperature for Monday, Tuesday, Wednesday and Thursday was 48°. The average temperature for Tuesday, Wednesday, Thursday and Friday was 52°. If the temperature on Monday was 42°, what was the temperature on Friday, in degrees?

Introduction / Context:
This question tests understanding of averages over overlapping groups of days and how to use them to recover an unknown value. We are given average temperatures over two overlapping four day periods in a week and the exact temperature for Monday. Using this information, we need to determine the temperature on Friday. The key idea is that the total temperature over each four day block can be written from the average and then compared.

Given Data / Assumptions:

• Average temperature for Monday, Tuesday, Wednesday and Thursday = 48°.
• Average temperature for Tuesday, Wednesday, Thursday and Friday = 52°.
• Temperature on Monday = 42°.
• Temperatures are measured in degrees and can be treated as simple numbers.
• We must find the temperature on Friday.

Concept / Approach:
The average of a group of values is equal to the sum of those values divided by the number of values. For a group of four days, average = total temperature over those four days / 4. So we can convert each average into a total. Because the two four day blocks overlap on Tuesday, Wednesday and Thursday, subtracting one total from the other will isolate the difference between Monday and Friday, which leads directly to the required Friday temperature.

Step-by-Step Solution:
Step 1: Let the temperatures on Tuesday, Wednesday, Thursday and Friday be T, W, Th and F respectively. Step 2: Use the average for Monday to Thursday. (M + T + W + Th) / 4 = 48. Total for Monday to Thursday = 4 * 48 = 192. Step 3: Use the average for Tuesday to Friday. (T + W + Th + F) / 4 = 52. Total for Tuesday to Friday = 4 * 52 = 208. Step 4: Express Monday's value and relate totals. M = 42, so M + T + W + Th = 192. T + W + Th + F = 208. Subtract the first total from the second: (T + W + Th + F) − (M + T + W + Th) = 208 − 192. This simplifies to F − M = 16. Step 5: Substitute M = 42. F − 42 = 16, so F = 42 + 16 = 58.
Verification / Alternative check:
If Friday is 58°, the Tuesday to Friday total is Tuesday + Wednesday + Thursday + 58. The Monday to Thursday total is Monday + Tuesday + Wednesday + Thursday = 192. Replace Monday with 42 to check consistency: 42 + (T + W + Th) = 192 gives T + W + Th = 150. Then Tuesday to Friday total is 150 + 58 = 208, and the average is 208 / 4 = 52°, which matches the given data.
Why Other Options Are Wrong:
A Friday temperature of 56°, 52°, 50° or 54° would give a total for Tuesday to Friday that is not 208, so the average would no longer be 52°. Each of these alternatives contradicts at least one of the original average statements.
Common Pitfalls:
A common mistake is to try to average 48° and 52° directly, which has no meaning here because the sets of days differ. Another mistake is to forget that each average refers to four days and to multiply or divide by the wrong number when computing totals.
Final Answer:
The temperature on Friday was 58°.