Instructions

Directions for the following four questions: Each question is followed by two statements A and B. Indicate your responses based on data sufficiency

Question 3

Consider integers x, y and z. What is the minimum possible value of $$x^2 + y^2 + z^2$$?

A: x + y + z = 89

B: Among x, y, z two are equal.

Solution

We know that the $$x^2 + y^2 + z^2$$ will be minimum when x = y = z = 89/3
Since that is not an integer, we can consider integer values that are closest to 89/3
Let x = y = 30 and z = 29 => $$x^2 + y^2 + z^2$$ = 2641
If x = y = 29 and z = 31,$$x^2 + y^2 + z^2$$ = 2643
So, the minimum is 2641
So, the question can be answered using statment 1 alone
Using statement 2 alone, we cannot answer the question.
Option a)

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Consider integers x, y and z. What is the minimum possible value of $$x^2 + y^2 + z^2$$?

A: x + y + z = 89

B: Among x, y, z two are equal.