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

### Algebra Problem 2

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

- 5
- 7
- 9
- 11
- 13

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### The Usual Way

You are suppose to remember the formula

$latex (x-y)^{3}=x^{3}-y^{3}-3xy(x-y)$

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

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

$latex \therefore $27 = 189 – 3 $latex xy$(3)

$latex \therefore $27 = 189 – 9 $latex xy$

$latex \therefore $ $latex xy$ = $latex \frac{189-27}{9}$ = $latex \frac{162}{9}$ = 18

Now, $latex (x+y)^{2}=(x-y)^{2}+4xy$ = $latex 3^{2}$ + 4 (18)

= 9 + 72

= 81

**(Ans: 2)**

*Estimated Time to arrive at the answer = 90 seconds*

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### 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.

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

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

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

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

$latex \therefore $ $latex x+y$ = 9

**(Ans: 2)**

*Estimated Time to arrive at the answer = 15 seconds*

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