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

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Manager
Joined: 14 Jan 2006
Posts: 95
Schools: HKUST
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What is the mean of four consecutive even integers a , b , c [#permalink]  03 Sep 2009, 15:35
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Question Stats:

0% (00:00) correct 100% (01:48) wrong based on 2 sessions
What is the mean of four consecutive even integers $$a$$ , $$b$$ , $$c$$ , $$d$$ ?

1. $$a + d = b + c$$
2. $$b + c = d - a$$
Manager
Joined: 25 Aug 2009
Posts: 176
Followers: 1

Kudos [?]: 68 [0], given: 12

Re: GMAT Test 18 [#permalink]  03 Sep 2009, 15:42
a,b,c and d are 4 consecutive even integers.

Let a = 2n where n belongs to integers
b = 2n+ 2
c = 2n +4
d = 2n + 6

mean = $$\frac{(8n + 12)}{4}$$

=> mean = 2n + 3; we need value of n.
1.) a + d = b + c
=> 2n + 2n +6 = 2n + 2 + 2n + 4
=> 0 = 0 , we can not find value of n, hence, insufficient..

2.) b + c = d - a
=> 4n + 6 = 2n + 6 - 2n
=> n = 0

Hence, sufficient..

SVP
Joined: 29 Aug 2007
Posts: 2497
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Re: GMAT Test 18 [#permalink]  03 Sep 2009, 20:02
nikhilpoddar wrote:
What is the mean of four consecutive even integers $$a$$ , $$b$$ , $$c$$ , $$d$$ ?

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

Intresting question. B as OA is correct.

The mean of 4 consecutive even integers can never be even. In fact it is always an odd integer. Using st. 2, if $$b + c = d - a$$, the only possible values for a, b, c, and d are 0, 2, 4, and 6 respectively. So mean is 3.
_________________
Manager
Joined: 15 Jun 2009
Posts: 164
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Re: GMAT Test 18 [#permalink]  04 Sep 2009, 08:48
We can take four numbers as a, a+2(b),a+4(c), a+6(d)....

solve by given stmt..

B....mean is 3...
Re: GMAT Test 18   [#permalink] 04 Sep 2009, 08:48
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