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Algebra Smart Math

[Smart Math] Algebra Problem 20

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

Algebra

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?

  1. 33
  2. 29
  3. 27
  4. 23
  5. 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 = 2x

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

Hence, 2x – (60 – x) = 39

\therefore 2x-60+x=39

\therefore 3x=99

\therefore x=33

(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 \frac{9}{3}=3. Hence answer will be 30 + 3 = 33.)
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