Step 1: Analyse Question StemAny number of the form 2n, where n is an integer, is always even. The question clearly says that x, y and z are integers. Therefore,
the term 2z is definitely even. This can be used to break down the question stem and rephrase it.
Is x + y + 2z = even?
Since 2z is even, question can be rephrased as, Is x + y + even = even?
By moving the even term from the LHS to the RHS, this can further be rephrased as, Is x + y = even – even?
Since even – even = even, the question now becomes,
Is x + y = even?Essentially, we are trying to find out if x and y are both odd OR both even.Step 2: Analyse Statements Independently (And eliminate options) – AD / BCEStatement 1: x + z is even
This means that x and z are both odd OR both even. Statement 1 does not provide any information about y.
The data in statement 1 is insufficient to find if x and y are of the same nature.
Statement 1 alone is insufficient. Answer options A and D can be eliminated.
Statement 2: y + z is even
This means that y and z are both odd OR both even. Statement 2 does not provide any information about x.
The data in statement 2 is insufficient to find if x and y are of the same nature.
Statement 2 alone is insufficient. Answer option B can be eliminated.
Step 3: Analyse Statements by combiningFrom statement 1: Both x and z are of the same nature.
From statement 2: Both y and z are of the same nature.
From this, it is clear that both x and y are of the same nature i.e. they are both odd or both even.
The combination of statements is sufficient to answer the question, Is x + y = even, with a definite YES.
Statements 1 and 2 together are sufficient. Answer option E can be eliminated.
The correct answer option is C. _________________
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