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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=y2

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

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=y2
On putting x=y2 in Statement I, we get
Y2+y=20y2+y20=0
Y2+5y4y20=0y(y+5)4(y+5)=0
(y4)(y+5)=0
y=45
(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 x=204=16
Now, xy=164=12
Hence, x is greater than y by 12,
So, both statements are required to answer the question.

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