Is \(x + y – z + t\) even?

(1) \(x + y + t\) is even
(2) \(t*z\) is odd

Though i did not understand why the OA is E

i would go through my understanding, and SME can help me out here

given that x + y + t - z is even
so for this
two terms (x + y + t) & z
so to have a even result both the terms should be either even or both should be odd

E - E = E
O - O = E

1) info about x + y + t is even .. good for us, but no information about z is given , hence INSUFFICIENT

2) tz is odd

O * O = O
E * O = O
O * E = O

hence we cannot make sure if z is even or ODD, hence INSUFFICIENT

so the answer choices A, B, D are knocked off...

now taking together 1 & 2

x + y + t = even
and z is either even or odd
hence the answer is E
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This is wrong.
Going by examples when you multiply the even(4)with the odd(3) the answer is 12 which is even.

hence whenever a Even is multiplied to a even or odd number it is always an even number. I hope you take note of this point.


This is one of the first points to try in such questions when nothing is mentioned about the type of numbers.
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true that cyberjadugar!

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 4 variables (x and y) and 0 equations, E is most likely to be the answer and so we should consider 1) & 2) first.

There is no restriction each of the variables \(x, y, z\) and \(t\) is an integer.

Condition 1) & 2):

\(x = 1, y = 2, z = 1, t = 1\) : The answer is no.
\(x = 1/2, y = 1, z = 2, t = 1/2\) : The answer is yes.

Therefore, E is the answer.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
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