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# [Smart Math] AVERAGES PROBLEM 3

Here’s and example of a SMART MATH problem for AVERAGES.

### Problem

In an exam, the average marks obtained by a student in English, Algebra, Geometry and Drawing were 50. His average marks in Algebra, Science, Social Studies and Craft were 70. If the average marks in all 7 subjects were 58. What is his Algebra score?

1. 50
2. 52
3. 60
4. 74
5. 96

### The Usual Method

Since, the average marks in English, Algebra, Geometry and Drawing are 50, total marks in these 4 subjects = 4 x 50 = 200.

Similarly, since his average marks in Algebra, Science, Social Studies and Craft are 70, total marks in these 4 subjects = 4 x 70 = 280.

Also, since average marks in all 7 subjects = 58, total marks in the 7 subjects = 7 x 58 = 406.

Sum of 200 and 280 = 480 includes marks in Algebra twice. Hence marks in Algebra = 480 – 406 = 74.

(Ans: 4)

Estimated Time to arrive at the answer = 60 seconds.

### Using Technique

While reading the question itself, you can figure out that Algebra is a common subject in the two groups. Hence, when we add up the marks of the two groups, the marks of Algebra are repeated.

Also, the sum of marks of the two groups will end in a ‘0’

$\because$ For 50; 0 x 4 = 0

$\because$ For 70; 0 x 4 = 0

And 0 + 0 = 0, so last digit = 0.

The last digit of the sum of marks for all 7 subjects = 6

$\because$ For 58; 8 x 7 = 56, so last digit = 6.

Hence, the last digit of marks of Algebra = 0 – 6 = 4.

From amongst the options, the only option with last digit = 4 is option ‘4’.

(Ans: 4)

Estimated Time to arrive at the answer = 10 seconds.
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