Algebra Problem 2

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

Algebra Problems

Algebra Problem 2

If x-y=3 and x^{3}-y^{3}=189; x+y =?

  1. 5
  2. 7
  3. 9
  4. 11
  5. 13

The Usual Way

You are suppose to remember the formula
(x-y)^{3}=x^{3}-y^{3}-3xy(x-y)

\therefore (x-y)^{3} = 3^{3} = 27

Also, x^{3}-y^{3} = 189

\therefore 27 = 189 – 3 xy(3)

\therefore 27 = 189 – 9 xy

\therefore xy = \frac{189-27}{9} = \frac{162}{9} = 18
Now, (x+y)^{2}=(x-y)^{2}+4xy = 3^{2} + 4 (18)
= 9 + 72
= 81

(Ans: 2)

Estimated Time to arrive at the answer = 90 seconds

The Smart Way

Simply write the values of ‘x’ and ‘y’ such that x – y = 3 and x + y = the values in the options as shown below:
5 => 4, 1
7 => 5, 2
9 => 6, 3
11 => 7, 4
13 => 8, 5

Now, start cubing the values of ‘x’ and ‘y’ and find the option for which the difference is = 189.

4^{3}-1^{3}=64-1=63\ne 189

 

5^{3}-2^{3}=125-8=117\ne 189

 

6^{3}-3^{3}=216-27=189

 

This should be the answer. There is no need to solve further as there cannot be more than one answer.

\therefore x+y = 9

(Ans: 2)

Estimated Time to arrive at the answer = 15 seconds

 

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