the fraction X?

[sanju09]

What is the fraction X?
I. If 3 is added to both numerator and denominator of the fraction X, the resulting fraction is 40 percent more than the fraction X.
II. The denominator of the fraction X is 1 more than twice the numerator.



[spoiler]made up by Sanjeev K Saxena for Avenues Abroad[/spoiler]

[Anurag@Gurome]

What is the fraction X?
I. If 3 is added to both numerator and denominator of the fraction X, the resulting fraction is 40 percent more than the fraction X.
II. The denominator of the fraction X is 1 more than twice the numerator.

[spoiler]made up by Sanjeev K Saxena for Avenues Abroad[/spoiler]

Let X = A/B

(1) (A + 3)/(B + 3) = (A/B) + 40% of (A/B) = 7A/5B implies there is one equation and 2 variables; NOT sufficient.

(2) B = 1 + 2A implies there is one equation and 2 variables; NOT sufficient.

Combining (1) and (2), 5AB + 15B = 7AB + 21A or 2AB + 21A = 15B
2A(1 + 2A) + 21A = 15(1 + 2A)
2A + 4A² + 21A = 15 + 30A
4A² - 7A - 15 = 0
(4A + 5)(A - 3) = 0 implies A = 3 and B = 7, so the fraction = 3/7; SUFFICIENT.

The correct answer is C.

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Yo the answer is C. Sometimes though it is a DS question, but you got to solve the quadratic equation...

As many times the roots are such that you cannot find an answer or sometimes both the roots are positive...

In such cases the answer turns out to be E and not C inspite of you solving the overall question, getting it right but just a minor mistake can cost you a sum or a DS question as wrong.