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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, 08:40
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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
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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, 08:48
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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  (2n2)  (2n4) = 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, 11:21
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  (2n2)  (2n4) = 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, 12:15
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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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]
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06 Feb 2008, 13:00
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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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]
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06 Feb 2008, 13:03
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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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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]
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06 Feb 2008, 13:22
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 ab = 2 therefore 2c = x also note since eveneveneven = even eliminate c),d) if 2c > 2 , c<= 0 hence x < 0 only E fits this, ans = 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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14 Mar 2008, 08:13
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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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]
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14 Mar 2008, 09:24
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 2N2 (b/c it's consecutive even), Then that would make the smallest number C, 2N4. 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  (2n2)  (2n4) = 6  2n <= 0 since n >=3 , even > EIf 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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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]
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14 Mar 2008, 12:59
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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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]
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07 Jul 2015, 23:40
since a,b,c are consecutive ab is always 2 (even) (ab)  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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Re: If a, b, and c are consecutive positive even integers and a > b > c [#permalink]
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09 Jul 2015, 04:15
A simple way of doing this is to just pick three positive consecutive even integers.
1) 642=0 In the order of abc. Since 0 is not in the options, we go up the order.
2) 864=2. Again 2 is not in the option.
3) 1086=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, 10:26
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  (2n2)  (2n4) = 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, 09:37
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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  (2n2)  (2n4) = 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 nonpositive integer. Only E fits.
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