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

**Problem**

**Problem**

A student losses a mark for every wrong answer and scores 2 marks for every correct answer. If he answers all the 60 questions in an exam and scores 39 marks, how many of them were correct?

- 33
- 29
- 27
- 23
- 21

**The Usual Method**

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If the student answered ‘*x*’ out of 60 questions correctly than the number of questions answered incorrectly are (60 – *x*).

Also marks obtained in correctly answered questions = 2*x*

And marks lost in incorrectly answered questions = (60 – *x*)

Hence, 2*x* – (60 – *x*) = 39

**(Ans: 1)**

*Estimated Time to arrive at the answer = 45 seconds.*

**Using Technique**

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If the student would have answered 30 out of 60 questions correctly, his score would have been 30 x 2 – 30 x 1 = 60 – 30 = 30. Since the actual score is > 30, the attempts are also > 30. Hence answer is 33 questions.

**(Ans: 1)**

*Estimated Time to arrive at the answer = 10 seconds.*

(Note: This technique is used because other than option ‘1’, there is no option with score >30 However, this technique with a little bit of tweaking can be used to find the exact answer also. As in this case we find that the answer has to be > 30 since the actual score was 39. This difference between 39 and 30 (middle score) of 9 points stems from the student answering some more than 30 questions correctly and hence incorrectly answering some less than 30 questions. Since for every correct answer, he gets 2 points and for the incorrect one losses 1 point, the difference of 2 + 1 = 3 points is coming by he answering 1 more question correctly. Hence if 9 is the difference the additional questions answered correctly will be . Hence answer will be 30 + 3 = 33.)

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