Solution

Given:In this question, we are given:

• The numbers x and y are integers

• Also, xy < 0

To find:We need to determine

Approach & WorkingAs it is given that xy < 0 and both of them are integers, we can say that

• None of x and y can be individually 0.

• If x is greater than 0 or a positive integer, then y is less than zero or negative integer.

• Alternatively, if x is less than 0 or a negative integer, then y is greater than 0 or positive integer.

With this understanding, let us now analyse the individual statements.

Analyse Statement 1As per the information given in statement 1, five times the value of x is 17 more than 3 times the value of y.

• 5x = 17 + 3y

Or, x = 1/5 (17 – 3y)

As both x and y are integers, we can have multiple possible values of x and y:

• x = -5 and y = -14

• x = -2 and y = -9

• x = 1 and y = -4

• x = 4 and y = 1

• x = 7 and y = 6

• x = 10 and y = 11

• x = 13 and y = 16 and so on…

Now, observing the values of x and y, we can see that there is only one specific case where x and y are of opposite signs (when x = 1 and y = -4).

Therefore, from statement 1 we can determine the unique value of x.

Hence, statement 1 is sufficient to answer the question.

Analyse Statement 2As per the information given in statement 2, x is a perfect square.

• From this statement, we can only say that x is a positive integer, and therefore, y is a negative integer.

• However, we cannot conclude the exact value of x.

Hence, statement 2 is not sufficient to answer the question.

Hence the correct answer is Option A.

Answer: A
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