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Bunuel
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If a line passes through the point (3, 5) and has a positive slope 09 Feb 2023, 11:25
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55% (hard)

Question Stats:

54% (01:12) correct 46% (01:39) wrong based on 178 sessions

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If a line passes through the point (3, 5) and has a positive slope, then which of the following must be true about the y-intercept (c) of the line ?

I. c < 0
II. c = 0
III. c > 0

A. I only
B. II only
C. I and II only
D. I, II and III
E. None of the above
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E
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stne
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If a line passes through the point (3, 5) and has a positive slope 15 Feb 2023, 10:32
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Bunuel
If a line passes through the point (3, 5) and has a positive slope, then which of the following must be true about the y-intercept (c) of the line ?

I. c < 0
II. c = 0
III. c > 0

A. I only
B. II only
C. I and II only
D. I, II and III
E. None of the above
Show more
A line has a positive slope when it moves from the 3rd Quadrant to the 1st quadrant
Please refer to the attached graph. The point shown is \((3,5)\)
Attachment:
GMAT slope 1.jpg
GMAT slope 1.jpg [ 12.52 KiB | Viewed 2983 times ]

We can see that the \(y\)-intercept can satisfy all of the three options.

I. \(c < 0,\hspace{2mm} \) need not necessarily be true as \(c=0,\) e.g. line \(2\) and \(c>0\) e.g.line \(1\) are also possible.
II. \(c = 0,\hspace{1mm} \) need not necessarily be true as \(c >0,\) e.g. line \(1\) and \(c<0\) e.g.line \(3\) are also possible.
III. \(c>0,\hspace{0mm} \) need not necessarily be true as \(c =0,\) e.g. line \(2\) and \(c< 0\) e.g.line \(3\) are also possible.

Ans E

Hope it's clear

Bunuel
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Thank you, seems there was an issue with my external HDD. Saved image to system HDD and was able to upload.
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If a line passes through the point (3, 5) and has a positive slope 25 Sep 2023, 20:37
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stne
Bunuel
If a line passes through the point (3, 5) and has a positive slope, then which of the following must be true about the y-intercept (c) of the line ?

I. c < 0
II. c = 0
III. c > 0

A. I only
B. II only
C. I and II only
D. I, II and III
E. None of the above
A line has a positive slope when it moves from the 3rd Quadrant to the 1st quadrant
Please refer to the attached graph. The point shown is \((3,5)\)
Attachment:
GMAT slope 1.jpg

We can see that the \(y\)-intercept can satisfy all of the three options.

I. \(c < 0,\hspace{2mm} \) need not necessarily be true as \(c=0,\) e.g. line \(2\) and \(c>0\) e.g.line \(1\) are also possible.
II. \(c = 0,\hspace{1mm} \) need not necessarily be true as \(c >0,\) e.g. line \(1\) and \(c<0\) e.g.line \(3\) are also possible.
III. \(c>0,\hspace{0mm} \) need not necessarily be true as \(c =0,\) e.g. line \(2\) and \(c< 0\) e.g.line \(3\) are also possible.

Ans E

Hope it's clear

Bunuel
Test....................
It works for me.
What type of attachment are you trying to upload?
Thank you, seems there was an issue with my external HDD. Saved image to system HDD and was able to upload.
Show more


Since all three are possible why can't the answer choice be option D?
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Bunuel
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If a line passes through the point (3, 5) and has a positive slope 26 Sep 2023, 00:23
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lowkyprofessional
stne
Bunuel
If a line passes through the point (3, 5) and has a positive slope, then which of the following must be true about the y-intercept (c) of the line ?

I. c < 0
II. c = 0
III. c > 0

A. I only
B. II only
C. I and II only
D. I, II and III
E. None of the above
A line has a positive slope when it moves from the 3rd Quadrant to the 1st quadrant
Please refer to the attached graph. The point shown is \((3,5)\)
Attachment:
GMAT slope 1.jpg

We can see that the \(y\)-intercept can satisfy all of the three options.

I. \(c < 0,\hspace{2mm} \) need not necessarily be true as \(c=0,\) e.g. line \(2\) and \(c>0\) e.g.line \(1\) are also possible.
II. \(c = 0,\hspace{1mm} \) need not necessarily be true as \(c >0,\) e.g. line \(1\) and \(c<0\) e.g.line \(3\) are also possible.
III. \(c>0,\hspace{0mm} \) need not necessarily be true as \(c =0,\) e.g. line \(2\) and \(c< 0\) e.g.line \(3\) are also possible.

Ans E

Hope it's clear

Bunuel
Test....................
It works for me.
What type of attachment are you trying to upload?
Thank you, seems there was an issue with my external HDD. Saved image to system HDD and was able to upload.


Since all three are possible why can't the answer choice be option D?
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This is because the question asks "which of the following MUST be true," not "which of the following COULD be true," and while each option could be true, none of them is necessarily true.
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If a line passes through the point (3, 5) and has a positive slope 20 Jul 2025, 04:07
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why cant be option d ?
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If a line passes through the point (3, 5) and has a positive slope 20 Jul 2025, 06:37
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krsatyam15
why cant be option d ?
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It is explained right above - https://gmatclub.com/forum/if-a-line-pa ... l#p3272117
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