Question

The given question consists of a set of statements. Find out whether the data provided in the statements are sufficient to answer the question and mark the option:

If x and y are both positive integers, then how much greater is x than y
$I.x+y=20$
$II.x=y^2$

• A. If Statement I alone is sufficient but Statement II alone is not sufficient to answer the question
• B. If Statement Ii alone is sufficient but Statement I alone is not Sufficient to answer the question
• C. If both statements taken together are sufficient to answer the question but neither statement alone is sufficien
• D. If statements I and II together are not sufficient and additional data is needed to answer the question
• E. If the data either in Statement I alone or Statement II alone are sufficient to answer the question

Answer 1

The correct option is C If both statements taken together are sufficient to answer the question but neither statement alone is sufficien

From Statement I, $x+y=20$
From Statement II, $x=y^2$
On putting $x=y^2$ in Statement I, we get
$Y^2+y=20\Rightarrow y^2+y-20=0$
$\Rightarrow Y^2+5y-4y-20=0\Rightarrow y(y+5)-4(y+5)=0$
$\Rightarrow (y-4)(y+5)=0$
$\therefore y=4-5$
(since, x and y are the positive integers, so we cannot take y = - 5)
Taking y = 4 and putting in Statement I,
$X+4=20$ $\therefore x=20-4=16$
Now, $x-y=16-4=12$
Hence, x is greater than y by 12,
So, both statements are required to answer the question.