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w, x, y, and z are consecutive odd integers such that w < x
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04 Oct 2018, 16:54
04 Oct 2018, 16:54
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w, x, y, and z are consecutive odd integers such that w < x < y < z. Which of the following statements must be true?
Indicate all such statements.
A. wxyz is odd
B. w + x + y + z is odd
C. w + z = x + y
Indicate all such statements.
A. wxyz is odd
B. w + x + y + z is odd
C. w + z = x + y
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Re: w, x, y, and z are consecutive odd integers such that w < x
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09 Oct 2018, 08:25
09 Oct 2018, 08:25
1
sandy wrote:
w, x, y, and z are consecutive odd integers such that w < x < y < z. Which of the following statements must be true?
Indicate all such statements.
A. wxyz is odd
B. w + x + y + z is odd
C. w + z = x + y
Indicate all such statements.
A. wxyz is odd
B. w + x + y + z is odd
C. w + z = x + y
A. wxyz is odd
Since w, x, y and z are each ODD, we can write: wxyz = (ODD)(ODD)(ODD)(ODD) = ODD
Statement A is true
B. w + x + y + z is odd
Since w, x, y and z are each ODD, we can write: w + x + y + z = ODD + ODD + ODD + ODD = EVEN
Statement B is NOT true
C. w + z = x + y
This one is a little trickier.
We know that consecutive odd integers increase by 2 each time (e.g., 5, 7, 9, 11, 13, etc)
The given into that says w < x < y < z, tells us that w is the smallest value.
So, we can write:
x = w + 2
y = w + 2 + 2 = w + 4
z = w + 4 + 2 = w + 6
Now take: w + z = x + y
Replace x, y and z to get: w + (w + 6) = (w + 2) + (w + 4)
Simplify: 2w + 6 = 2w + 6
PERFECT!!
Statement C is true
Answer: A, C
Cheers,
Brent
gmatclubot
Re: w, x, y, and z are consecutive odd integers such that w < x [#permalink]
09 Oct 2018, 08:25
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