Here’s and example of a SMART MATH problem for AVERAGES.
Problem
The average temperature for the first 9 days was 20 C and that of the first 5 was 25
C and that for the last 5 days was 15
C. What was the temperature on the fifth day?
- 25
C
- 20
C
- 30
C
- 15
C
- 27
C
The Usual Method
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Total temperature for 9 days = 9 x 20 = 180 C
Total temperature for first 5 days = 5 x 25 = 125 C
Total temperature for last 5 days = 5 x 15 = 75 C
Also, total temperature for first 5 days = a + b
Where, a = total temperature for first 4 days and
b = temperature on the 5th day
Similarly, total temperature for last 5 days = b + c
Where, b = temperature on the 5th day and
c = total temperature for last 4 days
…… Eq. 1.
and …… Eq. 2.
Also
Adding Eq. 1 and Eq. 2, we get: a + 2b + c = 200 C
20
C
Hence, temperature on 5th day = 20 C
(Ans: 2)
Estimated Time to arrive at the answer = 45 seconds.
Using Technique
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Since the average temperatures for the first 5 days and the last 5 days is ‘equidistant’ from the average temperature for the 9 days, we can simply take the arithmetic mean of 25 and 15 as 20
C as the temperature of the 5th day.
(Ans: 2)
Estimated Time to arrive at the answer = 5 seconds.
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