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# What is the mean of four consecutive even integers a , b , c

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Director
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What is the mean of four consecutive even integers a , b , c [#permalink]  25 Oct 2009, 10:53
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What is the mean of four consecutive even integers $$a$$ , $$b$$ , $$c$$ , $$d$$ ?

1. $$a + d = b + c$$
2. $$b + c = d - a$$
Director
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Re: even consecutive [#permalink]  25 Oct 2009, 10:56
Is there something missing in the Q? I didn't understand the Q
Director
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Re: even consecutive [#permalink]  25 Oct 2009, 11:13
Nopes, question is correct
Manager
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Re: even consecutive [#permalink]  25 Oct 2009, 18:36
Is C the OA?

Since they are 4 even consecutive integers , b, c, d can be represented as a+2, a+4, a+6 resp

So mean is a+a+2+a+4+a+6 divided by 4 => a+3 ------> eqn 1

Now 1)

a+d = b+c

which means Mean = a+b+c+d divided by 4 => b+c divided by 2

We know nothing about a or any number. So insuff

Now from 2)

b+c = d-a

We get Mean = d/2 which yields nothing - so insuff

Together

a+d = b+c and
b+c = d-a

equating the two above we get

a+d = d-a or
2a = 0
a =0

Hence we get a

From eqn ---->1 we know Mean = a+3

Hence Mean = 0+3 = 3

Sufficient by both 1 and 2

Correct me if I am wrong. Would appreciate it
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Re: even consecutive [#permalink]  25 Oct 2009, 18:47
IMO B

What is the mean of four consecutive even integers a , b , c , d ?

1. a + d = b + c
2. b + c = d - a

lets assume the numbers as a, a+2, a+4, a+6 since they are four consecutive integers

S1 ) given that a+d = b+c

2a +6 = 2a + 6 - no new information is given that is different from question stem - insufficient

S2) given that b+c = d-a

==>

a+2+a+4 = a+6-a

2a+6 =6 ==> a = 0, so the numbers are 0, 2,4,6 and we can calculate mean - sufficient.Hence

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Manager
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Re: even consecutive [#permalink]  25 Oct 2009, 18:52
srini123 wrote:
IMO B

What is the mean of four consecutive even integers a , b , c , d ?

1. a + d = b + c
2. b + c = d - a

lets assume the numbers as a, a+2, a+4, a+6 since they are four consecutive integers

S1 ) given that a+d = b+c

2a +6 = 2a + 6 - no new information is given that is different from question stem - insufficient

S2) given that b+c = d-a

==>

a+2+a+4 = a+6-a

2a+6 =6 ==> a = 0, so the numbers are 0, 2,4,6 and we can calculate mean - sufficient.Hence

Yeah I think this is the answer. I did not think about it though. Nice catch Sri
Director
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Re: even consecutive [#permalink]  26 Oct 2009, 01:33
Question: The stem does not specify the order of elements. it can d<a<b<c or a<b<c<d...does the solution hold true in both the cases? I am lazy to calculate today
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Re: even consecutive [#permalink]  26 Oct 2009, 08:23
Order not known..imo c..
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Re: even consecutive [#permalink]  26 Oct 2009, 09:48
What is the mean of four consecutive even integers a , b , c , d ?

1. a + d = b + c
2. b + c = d - a

If we don't know the order of ab,c,d i think the answer would be E

from S1 and S2 all we know is a=0

if the order was d,c,b,a then numbers are -6,-4,-2,0 and mean is -4
if the order was a,b,c,d then numbers are 0,2,4,6 and mean is 4

still both together are not sufficient. hence E

is this right ?

what is OA ?
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Re: even consecutive   [#permalink] 26 Oct 2009, 09:48
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