What is the value of |x| + |y| + xy, where x and y are integers?

Question

(1)  xy=17 
(2)  x=\sqrt{17^2}

Self made

Kurtosis · Answer

St1: xy = 17 is prime --> x * y = 1 * 17 or -1 * -17.

|x| + |y| + xy = 1 + 17 + 17 = 35.

Sufficient

St2: Clearly insufficient as we do not know the value of y.

Answer: A

Divyadisha · Answer

|x| + |y| + xy

(1)  xy=17

Since x and y are integers x and y can have values -1, -17 or vice versa or 1,17 or vice versa.

Irrespective of the sign |x| and |y| will be +ve.

1+17+17= 35 Sufficient.

2)  x=\sqrt{17^2}

We don't know the value of y. Not sufficient.

A is the answer

MathRevolution · Answer

There are 2 variables ( x and y) in the original condition. Hence, there is high chance that C is the correct answer. Using both the condition 1) and the condition 2), we get x=17, y=1. The answers are unique and the conditions are sufficient. However, since this is one of key questions, an integer question, we need to apply the common mistake type 4(A). 
In case of the condition 1), from (x,y)=(1,17),(17,1),(-1,-17),(-17,-1), the answer is always |x|+|y|+xy=35. The answer is unique and the condition is sufficient. Hence, the correct answer is A.

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What is the value of |x| + |y| + xy, where x and y are integers?

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