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For x>10, y is the product of the first x positive odd integers and z

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For x>10, y is the product of the first x positive odd integers and z [#permalink]

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New post 29 Aug 2017, 22:51
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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
[Reveal] Spoiler: OA

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Re: For x>10, y is the product of the first x positive odd integers and z [#permalink]

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New post 29 Aug 2017, 23:45
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


i misread it the first time
Say x is 11
y = Odd number greater than z and Z = 11^2 = 121 = even (odd - odd)
multiplication of odd numbers result in odd number
say x is 12
y = Odd number greater than z and Z = 12^2 = 144 = odd (odd - even)

E
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For x>10, y is the product of the first x positive odd integers and z [#permalink]

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New post 29 Aug 2017, 23:52
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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For x>10, y is the product of the first x positive odd integers and z [#permalink]

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New post 02 Sep 2017, 06:12
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’s say x is 11.

The product of 11 odd integers is odd and the sum of 11 odd integers is odd. Thus, y - z = odd - odd = even.

Let’s say x is 12.

The product of 12 odd integers is odd and the sum of 12 odd integers is even. Thus, y - z = odd - even = odd. We see that the difference y - z is odd only when x is even.

Answer: E
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For x>10, y is the product of the first x positive odd integers and z   [#permalink] 02 Sep 2017, 06:12
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