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If line M passes through the coordinate system shown above, is the slo

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If line M passes through the coordinate system shown above, is the slo  [#permalink]

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New post 30 Aug 2018, 04:49
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C
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Difficulty:

  45% (medium)

Question Stats:

57% (00:32) correct 43% (00:34) wrong based on 14 sessions

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If line M passes through the coordinate system shown above, is the slope of line M greater than zero?

(1) Line M passes through Quadrant III.
(2) Line M passes through Quadrant I.

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Re: If line M passes through the coordinate system shown above, is the slo  [#permalink]

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New post 30 Aug 2018, 07:58
Bunuel wrote:
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If line M passes through the coordinate system shown above, is the slope of line M greater than zero?

(1) Line M passes through Quadrant III.
(2) Line M passes through Quadrant I.


Question stem:- Is the slope of line M greater than zero?

Slope>0 when
a) Line passes through 2 quadrants (Q3Q1)
b) Line passes through 3 quadrants (Q3Q2Q1, Q3Q4Q1)

St1:- Line M passes through Quadrant III.
Insufficient

st2:- Line M passes through Quadrant I.
Insufficient

Combined, Line M passes through Quadrant I & III.
Condition (a) and (b) of positive slope are satisfied.
Sufficient .

Ans. (C)
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Re: If line M passes through the coordinate system shown above, is the slo  [#permalink]

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New post 30 Aug 2018, 08:14
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Bunuel wrote:
Image
If line M passes through the coordinate system shown above, is the slope of line M greater than zero?

(1) Line M passes through Quadrant III.
(2) Line M passes through Quadrant I.


Target question: Does line M have a POSITIVE slope?

Statement 1: Line M passes through Quadrant III
Consider the two lines shown here:
Image

Both lines satisfy the condition that line M passes through Quadrant III.
Case a: For the blue line, the answer to the target question is YES, the slope is line M is IS positive
Case b: For the red line, the answer to the target question is NO, the slope is line M is NOT positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Line M passes through Quadrant I
Consider the two lines shown here:
Image

Both lines satisfy the condition that line M passes through Quadrant I.
Case a: For the blue line, the answer to the target question is YES, the slope is line M is IS positive
Case b: For the red line, the answer to the target question is NO, the slope is line M is NOT positive
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statements 1 and 2 combined
If line M passes through Quadrant III AND through Quadrant I, then the slope of line M must be positive.
For example:
Image

So, the answer to the target question is YES, the slope is line M is IS positive
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
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Re: If line M passes through the coordinate system shown above, is the slo &nbs [#permalink] 30 Aug 2018, 08:14
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