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

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Math Forum Moderator
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What is the mean of four consecutive even integers a ,b ,c [#permalink]

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05 Jan 2010, 05:13
What is the mean of four consecutive even integers a ,b ,c ,d ?
i) a+d=b+c
ii) d-a=b+c...
although it is given as B ,i have a query...
do we take the four consecutive even integers a ,b ,c ,d to be written in ascending order...
if not then the ans should be C.....
if the int are in ascending order , shudn't it be mentioned?
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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08 Jan 2010, 11:32
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chetan2u wrote:
jeeteshsingh wrote:
chetan2u wrote:
What is the mean of four consecutive even integers a ,b ,c ,d ?
i) a+d=b+c
ii) d-a=b+c...
although it is given as B ,i have a query...
do we take the four consecutive even integers a ,b ,c ,d to be written in ascending order...
if not then the ans should be C.....
if the int are in ascending order , shudn't it be mentioned?

Dont really understand your question.....(in red)

The question is asking for the mean... of a,b,c,d all even integers... this means... we need to find the value of (a+b+c+d)/4 which would be an even integer for sure.
ST1: gives a+d = b+c...
This gives mean as (a+d)/2 or (b+c)/2.... hence NOT SUFF...

ST2: gives d-a = b+c --> d = a+b+c
Therefore mean = (a+b+c+d)/4 = (d+d)/4 = d/2 .... Hence SUFF.... and answer is B

Why would the order be required???

Cheers!
JT

u are giving ans as B... first why i think order is reqd...
if the seq is a,b,c,d... x,x+2,x+4,x+6....SII gives d-a=b+c.... means x+6-x=x+4+x+2....x=0 so nos are 0,2,4,6
mean =3......
but the eq d-a=b+c can be satisfied if ascending order is a,b,d,c eg. -2,0,2,4... here d-a=2-(-2)=4=4+0=4...
mean in this case is 1...
so two diff ans not suff...
SIn SII combined are suff.....
i would like the moderators to clarify on the issue pl...

If the question says that a,b,c,d are 4 consecutive even integers... I don't think they would consider them to be as 8,2,6,4..... ! Anyway... lets wait for Bunuel or someone else to comment on this! For me... Ans as B looks pretty convincing!
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06 Jan 2010, 05:16
looking for sum1 to clarify!
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5213 [0], given: 112

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Kudos [?]: 409 [0], given: 47

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07 Jan 2010, 12:24
chetan2u wrote:
What is the mean of four consecutive even integers a ,b ,c ,d ?
i) a+d=b+c
ii) d-a=b+c...
although it is given as B ,i have a query...
do we take the four consecutive even integers a ,b ,c ,d to be written in ascending order...
if not then the ans should be C.....
if the int are in ascending order , shudn't it be mentioned?

Dont really understand your question.....(in red)

The question is asking for the mean... of a,b,c,d all even integers... this means... we need to find the value of (a+b+c+d)/4 which would be an even integer for sure.
ST1: gives a+d = b+c...
This gives mean as (a+d)/2 or (b+c)/2.... hence NOT SUFF...

ST2: gives d-a = b+c --> d = a+b+c
Therefore mean = (a+b+c+d)/4 = (d+d)/4 = d/2 .... Hence SUFF.... and answer is B

Why would the order be required???

Cheers!
JT
_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!!

|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~

Kudos [?]: 409 [0], given: 47

Math Forum Moderator
Joined: 02 Aug 2009
Posts: 4907

Kudos [?]: 5213 [0], given: 112

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07 Jan 2010, 17:24
jeeteshsingh wrote:
chetan2u wrote:
What is the mean of four consecutive even integers a ,b ,c ,d ?
i) a+d=b+c
ii) d-a=b+c...
although it is given as B ,i have a query...
do we take the four consecutive even integers a ,b ,c ,d to be written in ascending order...
if not then the ans should be C.....
if the int are in ascending order , shudn't it be mentioned?

Dont really understand your question.....(in red)

The question is asking for the mean... of a,b,c,d all even integers... this means... we need to find the value of (a+b+c+d)/4 which would be an even integer for sure.
ST1: gives a+d = b+c...
This gives mean as (a+d)/2 or (b+c)/2.... hence NOT SUFF...

ST2: gives d-a = b+c --> d = a+b+c
Therefore mean = (a+b+c+d)/4 = (d+d)/4 = d/2 .... Hence SUFF.... and answer is B

Why would the order be required???

Cheers!
JT

u are giving ans as B... first why i think order is reqd...
if the seq is a,b,c,d... x,x+2,x+4,x+6....SII gives d-a=b+c.... means x+6-x=x+4+x+2....x=0 so nos are 0,2,4,6
mean =3......
but the eq d-a=b+c can be satisfied if ascending order is a,b,d,c eg. -2,0,2,4... here d-a=2-(-2)=4=4+0=4...
mean in this case is 1...
so two diff ans not suff...
SIn SII combined are suff.....
i would like the moderators to clarify on the issue pl...
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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08 Jan 2010, 20:03
hi .. i also think it should be given in ascending order... want to confirm it so that not found wanting in future...
i m not sure where but i had done a q somewhere ,where the ans took the possiblity of they not being in an order..
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: What is the mean of four consecutive even integers a ,b ,c [#permalink]

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07 Dec 2011, 13:03
Anyone want to try this one ?? Not sure. I think the answer should be E as we donot know the order of consecutive integers.
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Re: What is the mean of four consecutive even integers a ,b ,c [#permalink]

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08 Dec 2011, 12:25
chetan2u wrote:
What is the mean of four consecutive even integers a ,b ,c ,d ?
i) a+d=b+c
ii) d-a=b+c...
although it is given as B ,i have a query...
do we take the four consecutive even integers a ,b ,c ,d to be written in ascending order...
if not then the ans should be C.....
if the int are in ascending order , shudn't it be mentioned?

Statement 2: d-a=b+c

therefore d-c=a+b ; as we know c and d are consecutive even integers; d-c=2 which gives us a+b=2
there is only one pair of consecutive a and b that works; 0 and 2. Therefore statement 2 is sufficient alone.

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Re: What is the mean of four consecutive even integers a ,b ,c [#permalink]

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22 Apr 2014, 09:28
AbhiJ wrote:
Anyone want to try this one ?? Not sure. I think the answer should be E as we donot know the order of consecutive integers.

I agree , plus we can use the following sequence:
a<b<c<d
-6<-4<-2<0

In this case;

-6-0= -4-2

and mean will be -4-2/2= -3

while if we take the seq as 0<2<4<6

mean will be 4+2/2= 3

thus E

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Re: What is the mean of four consecutive even integers a ,b ,c [#permalink]

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22 Apr 2014, 09:57
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chetan2u wrote:
What is the mean of four consecutive even integers a ,b ,c ,d ?
i) a+d=b+c
ii) d-a=b+c...
although it is given as B ,i have a query...
do we take the four consecutive even integers a ,b ,c ,d to be written in ascending order...
if not then the ans should be C.....
if the int are in ascending order , shudn't it be mentioned?

BELOW IS REVISED VERSION OF THIS QUESTION WITH A SOLUTION:

What is the mean of four consecutive even integers $$a$$, $$b$$, $$c$$ and $$d$$, where $$a<b<c<d$$?

(1) $$a + d = b + c$$. That statement is true for ANY four consecutive even integers. Not sufficient.

(2) $$b + c = d - a$$. Let $$a=2k$$, for some integer $$k$$. Now, since $$a$$, $$b$$, $$c$$ and $$d$$ are consecutive even integers then $$b=2k+2$$, $$c=2k+4$$ and $$d=2k+6$$. So, we have that $$(2k+2)+(2k+4)=(2k+6)-2k$$ --> $$k=0$$ --> $$a=0$$, $$b=2$$, $$c=4$$ and $$d=6$$ --> $$mean=3$$. Sufficient.

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Re: What is the mean of four consecutive even integers a ,b ,c   [#permalink] 22 Apr 2014, 09:57
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