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# need an algebric explanation for this

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Director
Joined: 20 Sep 2006
Posts: 640
need an algebric explanation for this [#permalink]

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13 Feb 2009, 09:26
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If q, r, and s are consecutive even integers and q < r < s, which of the following CANNOT be the value of s^2 – r^2 – q^2?

1. -20
2. 0
3. 8
4. 12
5. 16
Director
Joined: 29 Aug 2005
Posts: 836
Re: need an algebric explanation for this [#permalink]

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13 Feb 2009, 10:07
C.
r=2j
$$(2j+2)^2-(2j)^2 - (2j-2)^2=4j(4-j)=T$$
Try j=-1;j=0;j=1; j=2.
T cannot be equal to 8
SVP
Joined: 29 Aug 2007
Posts: 2457
Re: need an algebric explanation for this [#permalink]

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14 Feb 2009, 09:51
botirvoy wrote:
C.
r = 2j
$$(2j+2)^2 - (2j)^2 - (2j-2)^2 = 4j (4-j) = T$$
Try j=-1; j=0; j=1; j=2.
T cannot be equal to 8

Thats the approach.

rao_1857 wrote:
If q, r, and s are consecutive even integers and q < r < s, which of the following CANNOT be the value of s^2 – r^2 – q^2?

1. -20
2. 0
3. 8
4. 12
5. 16

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SVP
Joined: 28 Dec 2005
Posts: 1500
Re: need an algebric explanation for this [#permalink]

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23 Mar 2009, 19:08
botirvoy wrote:
C.
r=2j
$$(2j+2)^2-(2j)^2 - (2j-2)^2=4j(4-j)=T$$
Try j=-1;j=0;j=1; j=2.
T cannot be equal to 8

how would you know to approach a question in this way ? i started off by saying r=q+2 and s=r+2=q+4 ... and then i went on to solve the actual quadratic :-S ... any advice ?
Re: need an algebric explanation for this   [#permalink] 23 Mar 2009, 19:08
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# need an algebric explanation for this

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