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# If a, b, and c are consecutive positive even integers and a > b > c

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Senior Manager
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If a, b, and c are consecutive positive even integers and a > b > c [#permalink]

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06 Feb 2008, 07:40
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If a, b, and c are consecutive positive even integers and a > b > c, which of the following could be equal to a - b - c ?

(A) 6
(B) 2
(C) -1
(D) -3
(E) -4
[Reveal] Spoiler: OA

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Director
Joined: 01 Jan 2008
Posts: 617

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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]

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06 Feb 2008, 07:48
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lumone wrote:
If a, b, and c are consecutive positive even integers and a > b > c,
which of the following could be equal to a - b - c ?

A) 6
(B) 2
(C) -1
(D) -3
(E) -4

a = 2n (n>=3), b = 2n - 2, c = 2n - 4

a -b -c = 2n - (2n-2) - (2n-4) = 6 - 2n <= 0 since n >=3 , even -> E

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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]

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06 Feb 2008, 10:21
maratikus wrote:
lumone wrote:
If a, b, and c are consecutive positive even integers and a > b > c,
which of the following could be equal to a - b - c ?

A) 6
(B) 2
(C) -1
(D) -3
(E) -4

a = 2n (n>=3), b = 2n - 2, c = 2n - 4

a -b -c = 2n - (2n-2) - (2n-4) = 6 - 2n <= 0 since n >=3 , even -> E

i have no idea what you did but i shifted the chain until it reached 10 8 6 and got E
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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]

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06 Feb 2008, 11:15
maratikus,

a = 2n (n>=3), b = 2n - 2, c = 2n - 4

Why cant it be n>=2
If n =2 we get
a = 4 b= 2 c = 0

Not sure where I am going wrong?

-Jack

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Director
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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]

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06 Feb 2008, 12:00
jackychamp wrote:
maratikus,

a = 2n (n>=3), b = 2n - 2, c = 2n - 4

Why cant it be n>=2
If n =2 we get
a = 4 b= 2 c = 0

Not sure where I am going wrong?

-Jack

a,b,c - consecutive POSITIVE even integers, 0 is not a positive integer

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Director
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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]

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06 Feb 2008, 12:03
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bmwhype2 wrote:
i have no idea what you did but i shifted the chain until it reached 10 8 6 and got E

I have no idea why you shifted the chain to 10 8 6 but both of us solved the problem correctly.

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Director
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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]

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06 Feb 2008, 12:22
lumone wrote:
If a, b, and c are consecutive positive even integers and a > b > c,
which of the following could be equal to a - b - c ?

A) 6
(B) 2
(C) -1
(D) -3
(E) -4

a-b = 2

therefore 2-c = x
also note since even-even-even = even eliminate c),d)

if 2-c > 2 , c<= 0

hence x < 0

only E fits this,

ans = e)

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Senior Manager
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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]

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14 Mar 2008, 07:13
maratikus wrote:
bmwhype2 wrote:
i have no idea what you did but i shifted the chain until it reached 10 8 6 and got E

I have no idea why you shifted the chain to 10 8 6 but both of us solved the problem correctly.

And I have no idea what you all did and still can't solve the problem.

Is anyone able to explain with more details?

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Manager
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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]

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14 Mar 2008, 08:24
lumone wrote:
maratikus wrote:
bmwhype2 wrote:
i have no idea what you did but i shifted the chain until it reached 10 8 6 and got E

I have no idea why you shifted the chain to 10 8 6 but both of us solved the problem correctly.

And I have no idea what you all did and still can't solve the problem.

Is anyone able to explain with more details?

The long way is plugging in numbers for a > b > c,
Remember they are consecutive positive even integers
CBA could be 2,4,6 or 4, 6, 8 or 6, 8, 10 and so on. Then you plug into a - b - c.
The first two sets of numbers aren't in the answers so this is why I say it's the LONG way.

I would use the formula provided above by maratikus.
It says A (the largest number) is 2N, then B would be 2N-2 (b/c it's consecutive even),
Then that would make the smallest number C, 2N-4.
Then you'd plug in ABC into formula as seen below. Hope this helps.

a = 2n (n>=3), b = 2n - 2, c = 2n - 4

a -b -c = 2n - (2n-2) - (2n-4) = 6 - 2n <= 0 since n >=3 , even -> E

If a, b, and c are consecutive positive even integers and a > b > c,
which of the following could be equal to a - b - c ?

A) 6
(B) 2
(C) -1
(D) -3
(E) -4

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VP
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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]

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14 Mar 2008, 11:59
consectutive even , X , X + 2 , X + 4 where X = Even

now subtract X - (X+2) - (X+4)

doing this leaves us with -X + -2

what even number can we substitute in X to yield an answer choice

E works -4 (plug in 2 for X)

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Current Student
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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]

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07 Jul 2015, 22:40
since a,b,c are consecutive a-b is always 2 (even)
(a-b) - c =<0 since least positive even integer that c can assume is 2.

and since even - even is always even. -4 is only suitable choice

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Manager
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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]

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09 Jul 2015, 03:15
A simple way of doing this is to just pick three positive consecutive even integers.

1) 6-4-2=0 In the order of a-b-c. Since 0 is not in the options, we go up the order.

2) 8-6-4=-2. Again -2 is not in the option.

3) 10-8-6=-4. This is in the option and we cant go any further up the order as the next solution is -6 which is irrelevant considering the options given.

Hope this helps.

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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]

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27 Feb 2016, 09:26
maratikus wrote:
lumone wrote:
If a, b, and c are consecutive positive even integers and a > b > c,
which of the following could be equal to a - b - c ?

A) 6
(B) 2
(C) -1
(D) -3
(E) -4

a = 2n (n>=3), b = 2n - 2, c = 2n - 4

a -b -c = 2n - (2n-2) - (2n-4) = 6 - 2n <= 0 since n >=3 , even -> E

since n >=3 , even -> E
I understand all the substitutions,but how is the answer arrived as E? someone please explain.

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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]

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29 Feb 2016, 08:37
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theperfectgentleman wrote:
maratikus wrote:
lumone wrote:
If a, b, and c are consecutive positive even integers and a > b > c,
which of the following could be equal to a - b - c ?

A) 6
(B) 2
(C) -1
(D) -3
(E) -4

a = 2n (n>=3), b = 2n - 2, c = 2n - 4

a -b -c = 2n - (2n-2) - (2n-4) = 6 - 2n <= 0 since n >=3 , even -> E

since n >=3 , even -> E
I understand all the substitutions,but how is the answer arrived as E? someone please explain.

We can represent 3 consecutive integers as 2x - 2, 2x, and 2x + 2 (c, b, and a respectively).

Since the integers are positive then x must be more than 1.

a - b - c = (2x + 2) - 2x - (2x - 2) = 2(2 - x), which will be even non-positive integer. Only E fits.
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Kudos [?]: 135738 [1], given: 12707

Re: If a, b, and c are consecutive positive even integers and a > b > c   [#permalink] 29 Feb 2016, 08:37
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