# Algebra Problem 2

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

### 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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