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Algebra Smart Math

[Smart Math] Algebra Problem 25

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

Algebra

Problem

If x = 3 and \left( x-y \right)^{2}=4, then y could be:

  1. –5
  2. –1
  3. 0
  4. 5
  5. 9

The Usual Method

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x = 3 and \left( x-y \right)^{2}=4

\therefore \left( x-y \right)=\pm 2

Substituting x = 3 in this we get:

3-y=\pm 2

\therefore y=3\pm 2

\therefore y= 5 or 1

From amongst the options, 5 is available and so option ‘4’ is the correct option.

(Ans: 4)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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We know that \left( 3-y \right)^{2}=4. Substitute the values of the option in this equation.

Note that we substitute options starting with the easiest and going towards the tougher ones. In this case, we use the following order: 0 , –1, 5 , –5 and then 9.

Thus for y = 0, \left( 3-0 \right)^{2}\ne 4, so it is not the answer.

For y = –1, \left( 3+1 \right)^{2}\ne 4, so it is not the answer.

For y = 5, \left( 3-5 \right)^{2}=4, so it is the answer.

No need to check further as there can be only one correct answer.

(Ans: 4)

Estimated Time to arrive at the answer = 30 seconds.

(Note: In this particular case, a significant time saving is not achieved as the usual method itself is short. However, you may use this technique in other questions where the usual method takes a longer time.)
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