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# If x and y are consecutive odd integers, what is the sum of x and y?

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Re: If x and y are consecutive odd integers, what is the sum of x and y? [#permalink]
(1) The product of x and y is negative. The only consecutive odd integers whose product is negative are -1 and 1. -1+1=0 Sufficient.
(2) One of the integers is equal to –1. The second number can be -3 or 1. Insufficient
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Re: If x and y are consecutive odd integers, what is the sum of x and y? [#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 key questions.

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 the value of x + y.

=> where 'x' and 'y' are consecutive odd integers

Second and the third step of Variable Approach: From the original condition, we have 2 variables (x and y). 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 * y < 0.

=> Either 'x' will be negative and 'y' will be positive OR vice-versa.

=> But as they are consecutive odd, the only possible combination is -1 and 1.Therefore x + y = 0

Since the answer is unique, the condition is sufficient by CMT 2.

Condition(2) tells us that one of the integer is -1.

=> Suppose x = -1 then 'y' can be '1' or '-3'.

=> For x = -1 and y = 1: x + y = 0 and for x = -1 and y = -3: x + y = -4

Since the answer is not unique, the condition is not sufficient by CMT 2.

Condition (1) alone is sufficient.

So, A is the correct answer.

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Re: If x and y are consecutive odd integers, what is the sum of x and y? [#permalink]
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Re: If x and y are consecutive odd integers, what is the sum of x and y? [#permalink]
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