Data Sufficiency

Please elaborate on the concepts being used.

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

x=r, y=s --> s=3r+2 OR 3r+2-s=0
st(1) (3r+2-s)(4r+9-s) = 0 Not Sufficient, as 4r+9-s also can be 0
st(2) (4r-6-s)(3r+2-s) = 0 Not Sufficient, as 4r-6-s also can be 0
Combined st(1&2): only 3r+2-s can be 0 from both statements Sufficient

answer C

BarryLi wrote:Please elaborate on the concepts being used.

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

BarryLi wrote:Please elaborate on the concepts being used.

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

It is not difficult to see that 3r+2-s has the same form of the line y=3x+2.

What is the significance of 4r+9-s in (1), and how can it also be zero?

What is the significance of 4r-6-s in (2), and how can it also be zero?

I would greatly appreciate other responses.

when xy=0 either x=0 or y=0
so st 1 is not suff
same wth st 2.
only on combining 1 & 2 we can confrim tht 3r+2-s=0.
hence C.
the only concept used here are for (r,s) to be on the given line equation, it shud satisfy, s=3r+2.

BarryLi wrote:

BarryLi wrote:Please elaborate on the concepts being used.

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

It is not difficult to see that 3r+2-s has the same form of the line y=3x+2.

What is the significance of 4r+9-s in (1), and how can it also be zero?

What is the significance of 4r-6-s in (2), and how can it also be zero?

I would greatly appreciate other responses.

ok, now that you've spotted the click, one point which was made - both factors could be zero for st(1) to be turned into 0. To prove that only (3r+2-s)=0 perform the following steps --> if not (3r+2-s) in st(1) is 0 then (4r+9-s) must be 0; if not (3r+2-s) in st(2) is 0, then (4r-6-s) must be 0.
Solve the system of two equations with two variables to check if only (3r+2-s) is 0, before answering C

{4r+9-s=0 <> {s=4r+9
{4r- 6-s=0 <> {s=4r- 6 <> 4r-6=4r+9, 9+6=0 (15)

hope this resolves the doubt

BarryLi wrote:

BarryLi wrote:Please elaborate on the concepts being used.

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

It is not difficult to see that 3r+2-s has the same form of the line y=3x+2.

What is the significance of 4r+9-s in (1), and how can it also be zero?

What is the significance of 4r-6-s in (2), and how can it also be zero?

I would greatly appreciate other responses.

BarryLi wrote:Please elaborate on the concepts being used.

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

If (r,s) is a point on the line y = 3x + 2, then s = 3r + 2, and 3r - s = -2. Thus, the question can be rephrased:

Does 3r - s = -2?

Statement 1: (3r+2-s)(4r+9-s) = 0
Either 3r+2-s = 0 or 4r+9-s = 0.
If 3r+2-s = 0, then 3r - s = -2.
If 4r+9-s = 0, then 4r - s = -9.
Insufficient.

Statement 2: (4r-6-s)(3r+2-s) = 0
Either 4r-6-s=0 or 3r+2-s = 0.
If 4r-6-s = 0, then 4r - s = 6.
If 3r+2-s = 0, then 3r - s = -2.
Insufficient.

Statements 1 and 2 combined:
4r - s = -9 (from statement 1) and 4r - s = 6 (from statement 2) cannot both be true. 4r - s cannot be equal to more than one value.
Thus, the only way the equations in the two statements can both equal 0 is if 3r - s = -2.
Sufficient.

The correct answer is C.