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# Line A passes through point (r, s) on the coordinate plane. Is the

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Math Expert
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Line A passes through point (r, s) on the coordinate plane. Is the  [#permalink]

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29 Jul 2015, 03:46
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65% (01:39) correct 35% (01:28) wrong based on 156 sessions

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Line A passes through point (r, s) on the coordinate plane. Is the slope of A > 0?

(1) Line A passes through point (0, 0).
(2) Line A passes through point (u, t), where r > u and t > s.

Kudos for a correct solution.

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Line A passes through point (r, s) on the coordinate plane. Is the  [#permalink]

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29 Jul 2015, 09:02
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Bunuel wrote:
Line A passes through point (r, s) on the coordinate plane. Is the slope of A > 0?

(1) Line A passes through point (0, 0).
(2) Line A passes through point (u, t), where r > u and t > s.

Kudos for a correct solution.

Given : Line A passes through point (r, s) on the coordinate plane

Question : Is the slope of A > 0?

Statement 1: Line A passes through point (0, 0).
To calculate the slope of the line we need co-ordinates of atleast two points and we have only one. Hence
NOT SUFFICIENT

Statement 2: Line A passes through point (u, t), where r > u and t > s.

Slope = (y2 - y1) / (x2 - x1)
i.e. Slope = (s - t) / (r - u)

But since r>u therefore r-u = Positive value
and since t>s therefore s-t = Negative value

i.e. Slope = = (-ve) / (+ve) = (-ve)
i.e. Slope is Negative i.e. < 0
SUFFICIENT

Answer: option B
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Posts: 104
Re: Line A passes through point (r, s) on the coordinate plane. Is the  [#permalink]

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29 Jul 2015, 04:06
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Bunuel wrote:
Line A passes through point (r, s) on the coordinate plane. Is the slope of A > 0?

(1) Line A passes through point (0, 0).
(2) Line A passes through point (u, t), where r > u and t > s.

Kudos for a correct solution.

Slope = change of y/ change of x

(1) Insufficient because we do not know slope > 0 or < 0

(2) Slope > 0: sufficient

Answer: B
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Re: Line A passes through point (r, s) on the coordinate plane. Is the  [#permalink]

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29 Jul 2015, 04:08
1
1
Bunuel wrote:
Line A passes through point (r, s) on the coordinate plane. Is the slope of A > 0?

(1) Line A passes through point (0, 0).
(2) Line A passes through point (u, t), where r > u and t > s.

Kudos for a correct solution.

Statement 1: Insufficient. It is best to draw a coordinate plane and create some lines with positive slope or negative slope. There are infinite possibilities to do so with (0, 0) as a point of line A.

Statement 2: Plug in some values for (r, s) which satisfy r > u and t > s. (3, 5) then e.g. (u,t) = (2, 6) >>> Slope of -1 (6-5 / 2-3).

Try more with different values, what if (r, s) is in the third quadrant? (r, s) = (-5, -2), then some point (u, t) = (-7, 1), slope will also be negative (1+5/-7+5).

Answer B.
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Re: Line A passes through point (r, s) on the coordinate plane. Is the  [#permalink]

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29 Jul 2015, 05:03
Bunuel wrote:
Line A passes through point (r, s) on the coordinate plane. Is the slope of A > 0?

(1) Line A passes through point (0, 0).
(2) Line A passes through point (u, t), where r > u and t > s.

Kudos for a correct solution.

IMO: B

Statement 1: Passing through (0,0) and (r,s), then slope of the line =$$\frac{y2 - y1}{x2-x1}$$
Slope = r/s
We will end up with negative slope if r and s are of opp signs
or with positive slopes if r and s are of same signs
Hence not suff

Statement 2: Line A passes through point (u, t), where r > u and t > s.

r>u --> we can infer that it shifts towards right side (east) of the plane
s<t --> we can infer that it shifts towards bottom side (south) of the plane.

Thus formed as below in the fig:
Attachment:

2.jpg [ 22.6 KiB | Viewed 3448 times ]

If we shift the point (u,t) from Quadrant 1 to Quadrant 2 ..The point (r,s) will also shift respectively.
In other words the whole line is shifted from one space to another, with the slope remaining same.
Thus no change in slope(constant). And the slope is negative.
Hence suff
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Joined: 02 Sep 2009
Posts: 59725
Re: Line A passes through point (r, s) on the coordinate plane. Is the  [#permalink]

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17 Aug 2015, 09:28
Bunuel wrote:
Line A passes through point (r, s) on the coordinate plane. Is the slope of A > 0?

(1) Line A passes through point (0, 0).
(2) Line A passes through point (u, t), where r > u and t > s.

Kudos for a correct solution.

800score Official Solution:

The slope of a line is determined by the formula:
Slope = m = (change in y)/(change in x).

To establish the sufficiency of the statements, substitute the given values into the formula.

Statement (1): m = (s – 0)/(r – 0) tells us that the slope of A is s/r, but, because it doesn't tell us whether s and r are positive or negative, the slope cannot be determined. Thus, Statement (1) is insufficient.
Note: Be careful that you do not assume, because s and r do not have a negative sign before them, that they are positive. The both variables can be positive or negative.

Statement (2): m = (s – t)/(r – u) tells us that the numerator in this equation is negative, because t > s. The denominator (r – u) is positive because r > u. So the slope of line A is negative, and thus Statement (2) is sufficient.

Since Statement (1) is insufficient and Statement (2) is sufficient, the correct answer is B.
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Re: Line A passes through point (r, s) on the coordinate plane. Is the  [#permalink]

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27 Nov 2019, 21:44
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Re: Line A passes through point (r, s) on the coordinate plane. Is the   [#permalink] 27 Nov 2019, 21:44
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# Line A passes through point (r, s) on the coordinate plane. Is the

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