In the xy- plane, does the line with equation y=3x + 2 contain point (r,s)?
(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s) (3r+2-s)=0
I say that they equal each other....but get stuck going down that road...no variables...
Target Test Prep is 20% off right now!
Use code FLASH20
Available with Beat the GMAT members only code
MORE DETAILS
GMAT PREP DS
This topic has expert replies
-
givemeanid
- Master | Next Rank: 500 Posts
- Posts: 277
- Joined: Sun Jun 17, 2007 2:51 pm
- Location: New York, NY
- Thanked: 6 times
- Followed by:1 members
Does y=3x + 2 contain point (r,s)?
In other words, is s = 3r + 2.
Rearranging the equations, the question is whether 3r + 2 - s = 0?
(1) (3r+2-s)(4r+9-s) = 0
So, either 3r+2-s = 0 or 4r+9-s = 0
NOT SUFFICIENT.
(2) (4r-6-s) (3r+2-s) = 0
So, either 4r-6-s = 0 or 3r+2-s = 0
NOT SUFFICIENT.
Combining both, 3r+2-s = 0.
SUFFICIENT.
Answer is (C).
In other words, is s = 3r + 2.
Rearranging the equations, the question is whether 3r + 2 - s = 0?
(1) (3r+2-s)(4r+9-s) = 0
So, either 3r+2-s = 0 or 4r+9-s = 0
NOT SUFFICIENT.
(2) (4r-6-s) (3r+2-s) = 0
So, either 4r-6-s = 0 or 3r+2-s = 0
NOT SUFFICIENT.
Combining both, 3r+2-s = 0.
SUFFICIENT.
Answer is (C).
So It Goes
-
gabriel
- Legendary Member
- Posts: 986
- Joined: Wed Dec 20, 2006 11:07 am
- Location: India
- Thanked: 51 times
- Followed by:1 members
DS questions go in the DS sectionsykedaddy wrote:In the xy- plane, does the line with equation y=3x + 2 contain point (r,s)?
(1) (3r+2-s)(4r+9-s)=0
(2) (4r-6-s) (3r+2-s)=0
I say that they equal each other....but get stuck going down that road...no variables...
...What does the emphasized text above mean. In other words how do you combine the two equations to arrive at 3r + 2 - s = 0, definitively? Please explain.givemeanid wrote:Does y=3x + 2 contain point (r,s)?
In other words, is s = 3r + 2.
Rearranging the equations, the question is whether 3r + 2 - s = 0?
(1) (3r+2-s)(4r+9-s) = 0
So, either 3r+2-s = 0 or 4r+9-s = 0
NOT SUFFICIENT.
(2) (4r-6-s) (3r+2-s) = 0
So, either 4r-6-s = 0 or 3r+2-s = 0
NOT SUFFICIENT.
Combining both, 3r+2-s = 0.
SUFFICIENT.
Answer is (C).
-
givemeanid
- Master | Next Rank: 500 Posts
- Posts: 277
- Joined: Sun Jun 17, 2007 2:51 pm
- Location: New York, NY
- Thanked: 6 times
- Followed by:1 members
-
Patrick_GMATFix
- GMAT Instructor
- Posts: 1052
- Joined: Fri May 21, 2010 1:30 am
- Thanked: 335 times
- Followed by:98 members
The explanation below is pasted from a different thread
the Q tests your understanding that point (r,s) can belong to the line only if its coordinates fit the equation of the line. In other words we can rephrase this from "is (r,s) on line y=3x+2?" to "Is s=3r+2?"
This Q tests your understanding that the solution of a factored equation that is set to 0 is whatever values will make each factor 0. For instance, statemetn (1) tells us that (3r+2-s)(4r+9-s) = 0. This means that
a. 3r+2-s = 0 --> s=3r+2, or
b. 4r+9-s=0 --> s=4r+9
Since we don't know which is correct, we cannot answer the rephrase. Statement (2) will work the same way. Only when you merge the statements can you definitively know that s=3r+2. The correct answer is C
You can see a video of this solution for a step by step demo; this is QID 1088
-Patrick
the Q tests your understanding that point (r,s) can belong to the line only if its coordinates fit the equation of the line. In other words we can rephrase this from "is (r,s) on line y=3x+2?" to "Is s=3r+2?"
This Q tests your understanding that the solution of a factored equation that is set to 0 is whatever values will make each factor 0. For instance, statemetn (1) tells us that (3r+2-s)(4r+9-s) = 0. This means that
a. 3r+2-s = 0 --> s=3r+2, or
b. 4r+9-s=0 --> s=4r+9
Since we don't know which is correct, we cannot answer the rephrase. Statement (2) will work the same way. Only when you merge the statements can you definitively know that s=3r+2. The correct answer is C
You can see a video of this solution for a step by step demo; this is QID 1088
-Patrick
