# Algebra Problem 1

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

### Algebra Problem 1

Find the fraction such that if numerator is multiplied by 2 and 2 is added to the denominator, the fraction equals 2. If the numerator is squared and 2 is added to the denominator, the fraction equals 7.

- 5/3
- 4/8
- 7/5
- 3/2
- 8/5

### The Usual Way

Let the original fraction be x/y.

New Fraction = = 2

2x = 2y + 4 or x = y + 2 …… Eq. 1

Also; = 7

= y + 2 …… Eq. 2

From Eq. 1 and 2;

= x

x = 7 and y = 5

Fraction = 7/5

**(Ans: 3)**

*Estimated Time to arrive at the answer = 60 seconds*

### The Smart Way

Simply read the first part of the question and find those options that satisfy that condition as shown below:

=> = = 2 (Satisfies the condition)

=> = = (does not satisfy the condition)

=> = = 2 (Satisfies the condition)

=> = = (does not satisfy the condition)

=> = (does not satisfy the condition)

This leaves us with options ‘1’ and ‘3’ only. Now, look at the 2nd condition. Apply this to options ‘1’ and ‘3’ only as follows:

=> = = 5 (does not satisfy the condition)

Hence, answer is option ‘3’

Just to verify…c.

=> = = 7 (Satisfies the condition and hence is the answer)

**(Ans: 3)**

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

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