Question

The numerator of a fraction is 5 more than twice the denominator. Also, when 2 is added to the fraction, the numerator increases by 12. If the given fraction is squared and the numerator is divided by the denominator, then what will be the remainder?

• A. 1
• B. 0
• C. 3
• D. 2

Answer 1

The Correct Option is A

- Let the numerator of the fraction be x and the denominator be y. 

- According to the first condition, the numerator is 5 more than twice the denominator:

x = 2y + 5

- According to the second condition, when 2 is added to the fraction, the numerator increases by 12:

(x + 2)/y = x/y + 12

Step 1: Simplifying the Second Equation

Rearranging the second equation:

(x + 2)/y - x/y = 12

Since both terms have a common denominator:

[ (x + 2) - x ] / y = 12

Simplifying:

2 / y = 12

Step 2: Solving for y

Cross-multiplying gives:

y = 2 / 12 = 1 / 6

Since y must be an integer, this result indicates an incorrect step or condition. We need to revisit the conditions.

Step 3: Correcting the Approach

- Revisiting the first equation:

x = 2y + 5

Since there is a contradiction in the conditions, please confirm the correct second condition or any missing details for an accurate solution.