Each of the questions given below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements.
Give answer a: if the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
Give answer b: if the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
Give answer c: if the data in statement I alone or in statement II alone is sufficientto answer the question.
Give answer d: if the data in both the statements I and II is not sufficient to answer the question.
Give answer e: if the data in both the statements I and II together is necessary to answer the question.
Is the sum of integers x and y greater than 85 ?
I. The product of x and y is greater than 85.
II. One of the variables is greater than 83.
From I : It is given that $$x \times y > 85$$
Let $$x = 100 , y = 100$$
=> $$x \times y = 100 \times 100 = 10000 > 85$$
and $$x + y = 100 + 100 = 200 > 85$$
Again let us assume $$x = 10 , y = 10$$
=> $$x \times y = 10 \times 10 = 100 > 85$$
But, $$x + y = 10 + 10 = 20 < 85$$
Thus, statement I alone is insufficient.
From II : We have no information of the second variable.
Thus, II alone is also insufficient.
From I & II : $$x \geq 84$$
and $$y \geq 2$$
=> $$x + y \geq 86$$, which answers our question.
Thus, I & II together are sufficient.
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