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# DS Question from GMATPrep

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Manager
Joined: 25 Apr 2006
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DS Question from GMATPrep [#permalink]  10 May 2006, 14:25
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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions
Hi,

I can't figure out this GMATPrep question that I got wrong. If someone could help, I'd greatly appreciate it. The answer was C (standard DS answer choices).

Thanks,
Marcus

In the xy-plane, does the line with equation y=3x+2 contain the point (r,s)?

(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s)(3r+2-s)=0
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Director
Joined: 16 Aug 2005
Posts: 946
Location: France
Followers: 1

Kudos [?]: 11 [0], given: 0

In the xy-plane, does the line with equation y=3x+2 contain the point (r,s)?

(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s)(3r+2-s)=0

From (1):
3r+2-s = 0
=> s = 3r + 2 (its on the line y=3x+2)

or 4r+9-s = 0
=> s = 4r + 9 (its not on line y=3x+2)

Hence not sufficient.

From (2):
s = 4r - 6 (not on the line)

or s = 3r + 2 (it is on the line)

Hence not sufficient.

If both (1) and (2) are taken into account:
3r+2-s=0 is true and hence they say the answer is C. But I'm not sure how to prove that 3r+2-s=0 is true and not the other 2 equations ... if someone can show that then it would be great.
Manager
Joined: 17 Jan 2006
Posts: 92
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Kudos [?]: 5 [0], given: 0

from 1

3r+2-s=0 insuff

from 2

4r -6-s=0 insuff

combining 1 and 2 ,solving

r=8 s=26

(8,26) ---> is on line y=3x+2

therefore ans =C
Intern
Joined: 10 Jan 2006
Posts: 25
Followers: 0

Kudos [?]: 1 [0], given: 0

From 1

3r + 2 - s = 0 OR 4r + 9 -s = 0 (Not Suff)

From 2

3r + 2 - s = 0 OR 4r - 6 - s = 0 (Not Suff)

Now combing both together we could have either

4r + 9 - s = 0 AND 4r - 6 - s = 0
OR
3r + 2 - s = 0

(reason is obvious, but let me know if it has to be explained)

if 4r + 9 - s = 0 and 4r - 6 - s = 0 then

4r + 9 - s = 4r - 6 - s
=>9 = 6 an impossibility hence
3r+ 2 - s = 0

Therefore (C) is correct
Intern
Joined: 04 May 2006
Posts: 49
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Kudos [?]: 0 [0], given: 0

Quote:
Now combing both together we could have either

4r + 9 - s = 0 AND 4r - 6 - s = 0
OR
3r + 2 - s = 0

(reason is obvious, but let me know if it has to be explained)

_________________

If A equals success, then the formula is: A = X + Y + Z, X is work. Y is play. Z is keep your mouth shut.
Albert Einstein

Senior Manager
Joined: 05 Jan 2006
Posts: 382
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Kudos [?]: 36 [0], given: 0

take a look at this discussion!

http://www.gmatclub.com/phpbb/viewtopic.php?t=28246
Intern
Joined: 10 Jan 2006
Posts: 25
Followers: 0

Kudos [?]: 1 [0], given: 0

mendiratta_1812 wrote:
Quote:
Now combing both together we could have either

4r + 9 - s = 0 AND 4r - 6 - s = 0
OR
3r + 2 - s = 0

(reason is obvious, but let me know if it has to be explained)

Well if the product or 2 numbers is 0 the number1 = 0 OR number2 =0, right ?
Here we have
XY = 0 AND
XZ = 0 if we take Y = 4r + 9 -s and Z = 4r - 6 - s and 3r + 2 - s)

Since X is common in both equations then either X = 0 i.e both expressions become 0 OR X != 0 and Y = 0 as well as Z = 0 for both expressions to be zero. The third case is X, Y, Z are all 0 which is a subset of Y = 0 and Z = 0.
Director
Joined: 16 Aug 2005
Posts: 946
Location: France
Followers: 1

Kudos [?]: 11 [0], given: 0

saha wrote:
From 1

3r + 2 - s = 0 OR 4r + 9 -s = 0 (Not Suff)

From 2

3r + 2 - s = 0 OR 4r - 6 - s = 0 (Not Suff)

Now combing both together we could have either

4r + 9 - s = 0 AND 4r - 6 - s = 0
OR
3r + 2 - s = 0

(reason is obvious, but let me know if it has to be explained)

if 4r + 9 - s = 0 and 4r - 6 - s = 0 then

4r + 9 - s = 4r - 6 - s
=>9 = 6 an impossibility hence
3r+ 2 - s = 0

Therefore (C) is correct

I believe saha showed it correctly, OA is C
_________________

I believe its yogurt!

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