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14 Feb 2023, 22:08
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Difficulty:
75%
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Question Stats:
39% (01:57) correct
61%
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wrong
based on 44
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If d is the distance between the x-intercept of a line P and the origin, is d > 1?
(l) The y-intercept of the line is 3.
(2) The slope of line P is equal to the y-intercept of line P.
(l) The y-intercept of the line is 3.
(2) The slope of line P is equal to the y-intercept of line P.
04 Mar 2023, 14:13
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If d is the distance between the x-intercept of a line P and the origin, is d > 1?
(l) The y-intercept of the line is 3.
Insufficient because the line can have any slope. If slope = 0 (horizontal line) then d > 1 (d = 3)
If the slope is undefined (the line is vertical) then d < 1 (d = 0)
(2) The slope of line P is equal to the y-intercept of line P.
slope = y-intercept.
If we use the slope-intercept form
\(y = mx + b\) where
b = y-intercept and
m = slope and
x = x-intercept
\(y = b(x) + b\\
y = b(x+1)\)
we can see here, no matter what b is, it's always going to be (x + 1) so x is always = - 1.
since x = x-intercept = d (distance of x-intercept to 0, 0 origin)
therefore:
d is always < 1 (d = x = -1)
hence: B Statement 2 alone is sufficient.
Very tricky question. Without using the slope intercept form it's very easy to assume that d (x-intercept) changes given different y-intercept and slope combination.
(l) The y-intercept of the line is 3.
Insufficient because the line can have any slope. If slope = 0 (horizontal line) then d > 1 (d = 3)
If the slope is undefined (the line is vertical) then d < 1 (d = 0)
(2) The slope of line P is equal to the y-intercept of line P.
slope = y-intercept.
If we use the slope-intercept form
\(y = mx + b\) where
b = y-intercept and
m = slope and
x = x-intercept
\(y = b(x) + b\\
y = b(x+1)\)
we can see here, no matter what b is, it's always going to be (x + 1) so x is always = - 1.
since x = x-intercept = d (distance of x-intercept to 0, 0 origin)
therefore:
d is always < 1 (d = x = -1)
hence: B Statement 2 alone is sufficient.
Very tricky question. Without using the slope intercept form it's very easy to assume that d (x-intercept) changes given different y-intercept and slope combination.
16 Mar 2023, 11:51
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Bunuel can u tell how statement 2 is sufficient ?
