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all three are consecutive

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all three are consecutive

by sanju09 » Tue Aug 10, 2010 3:40 am
If x < y < z and all three are consecutive non-zero integers, then which of the following must be a positive odd integer?
(A) x + y - z
(B) x z - y
(C) x + y + z
(D) x y + z
(E) x - y - z

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by selango » Tue Aug 10, 2010 3:59 am
X=a

Y=a+1

Z=a+2

A.

x+y-z=a-1,Odd only when a is even.

B.xz-y

a^2+2a-a-1=a^2+a-1

a=2;4+2-1=5

a=3;9+3-1=11

Odd when a is both odd and even.

True

C.x+y+z

3a+3.Odd only when a is even.

D.xy+z

a^2+a+a+2=a^2+2a+2.Odd only when a is odd.

E.x-y-z

-a-3.Odd only when a is even.
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by sanju09 » Tue Aug 10, 2010 4:38 am
selango wrote:X=a

Y=a+1

Z=a+2

A.

x+y-z=a-1,Odd only when a is even.

B.xz-y

a^2+2a-a-1=a^2+a-1

a=2;4+2-1=5

a=3;9+3-1=11

Odd when a is both odd and even.

True

C.x+y+z

3a+3.Odd only when a is even.

D.xy+z

a^2+a+a+2=a^2+2a+2.Odd only when a is odd.

E.x-y-z

-a-3.Odd only when a is even.
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by chris@veritasprep » Tue Aug 10, 2010 7:02 am
Another way to approach this problem is with a scenario driven strategy and understanding of the odd/even number properties (although the algebraic approach also works well here). If the three numbers are consecutive there are only 2 possible scenarios: x = odd, y = even, z = odd or x = even, y = odd, z = even. Consider each answer choice with these two possibilities:

1. odd + even - odd = even or even + odd - even = odd incorrect - could be even or odd
2. (odd)(odd) - even = odd or (even)(even) - odd = odd correct - must be odd. no need to check other choices.

With odd/even problems it is sometimes easiest to simply pick numbers. Other times it is best to use algebra or use the odd/even properties as I have done above. As with almost all GMAT problem types, one approach will work well on one problem but not on another. By understanding all the different approaches, you will be able to attack all problems, regardless of how the test makers present them.
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