Is positive integer z an odd integer?

Question

(1) z^3 – 3 is an odd integer.
(2) z – 3 is an odd integer.

PrincePi · Answer

First post, so lets see if I get this right.

(1) So we subtract 3 and this leads to an odd result: z^3-3=odd. This means that z^3=odd+3=ODD+ODD=EVEN. If z^3 is even, then z must also be even. If it were odd, we would get an odd product (ODDxODDxODD=always odd) -> SUFFICIENT

(2) z-3=odd -> z=odd+3=odd+odd=even -> SUFFICIENT

Therefore D.

OptimusPrepJanielle · Answer

Before we start solving, remember:

even - even = even
even - odd = odd
odd - odd = even

Statement 1: z^3 – 3 is an odd integer
Here 3 is odd and z^3 – 3 = odd
Therefore z^3 should be even
Hence z is even
Sufficient

Statement 2: z – 3 is an odd integer
Here 3 is odd and z – 3 = odd
Therefore z should be even
Sufficient

Option D

MathRevolution · Answer

Is positive integer z an odd integer?

There is 1 variable (z) in the original condition. In order to match the number of variables and the number of equations, we need 1 more equation. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that D is the answer.
For the condition 1), since z^3-3=odd, z^2=odd+3=even, z=even. The answer is no and the condition is sufficient.
For the condition 2), since z-3=odd, z=odd+3=even. Again, the answer is no and the condition is sufficient. Therefore, the correct answer is D.

l For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

stonecold · Answer

Both the cases indicate that z is even hence D

Is positive integer z an odd integer?

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