Bunuel wrote:
For x>10, y is the product of the first x positive odd integers and z is the sum of the first x positive odd integers. The difference y−z must be:
A. Even
B. Odd
C. Negative
D. Even only when x is even
E. Odd only when x is even
- Let say Y=11*13*15*17*... and y is a set of x numbers,
- Let say Z=11+13+15+17+... and z is a set of x numbers,
Y-Z ?
- Y must be ODD, because no EVEN integer involved.
- Z can be ODD, if X is ODD. For example, if X=3->11+13+15=ODD
- Z can be EVEN, if X is EVEN. For example, if X=4->11+13+15+17=EVEN.
#Alt. 1
So, Y-Z must be EVEN,
only if X is ODD.
Remember that if X odd, Z odd. Y-Z=ODD-ODD=EVEN.
#Alt. 2
So, Y-Z must be ODD,
only if X is EVEN.
Remember that if X even, Z even. Y-Z=ODD-EVEN=ODD.
E.
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