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# If x and z are integers, is at least one of them even?

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Re: If x and z are integers, is at least one of them even? [#permalink]
Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

Remember the relation between the Variable Approach, and Common Mistake Types 3 and 4 (A and B)[Watch lessons on our website to master these approaches and tips]

Step 1: Apply Variable Approach(VA)

Step II: After applying VA, if C is the answer, check whether the question is the key question.

StepIII: If the question is not a key question, choose C as the probable answer, but if the question is a key question, apply CMT 3 and 4 (A or B).

Step IV: If CMT3 or 4 (A or B) is applied, choose either A, B, or D.

Let's apply CMT (2), which says there should be only one answer for the condition to be sufficient. Also, this is an integer question and, therefore, we will have to apply CMT 3 and 4 (A or B).

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find is at least one of them even - where 'x' and 'z' are integers

Second and the third step of Variable Approach: From the original condition, we have 2 variables (x and z). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

But we know that this is a key question [Integer question] and if we get an easy C as an answer, we will choose A or B.

Let’s take a look at each condition.

Condition(1) tells us that x + z = odd.

=> ODD + EVEN =EVEN + ODD = ODD and hence one of the integer is atleast even.

Since the answer is unique YES, the condition (1) is sufficient by CMT 1.

Condition(2) tells us that x - z = odd.

=> ODD - EVEN = EVEN - ODD = ODD and hence one of the integer is atleast even.

Since the answer is unique YES, the condition (2) is sufficient by CMT 1.

Condition (1) and Condition (2) alone are sufficient.

So, D is the correct answer.