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Difficulty:
95%
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26% (02:02) correct
74%
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wrong
based on 113
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Line P and Q intersect at a point (2,-5), is the slope of line P is greater than that of line Q?
(1) X intercept of P is less than Q
(2) Y intercept of P is more than Q.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
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(1) X intercept of P is less than Q
(2) Y intercept of P is more than Q.
(A) Statement 1 alone is sufficient, but statement 2 alone is not.
(B) Statement 2 alone is sufficient, but statement 1 alone is not.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Each statement alone is sufficient.
(E) Neither statement is sufficient, even when combined.
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Bunuel
y = mx+c
\(m= \frac{y-c}{x}\)
\(m= \frac{-5-c}{2} \) ( \(x=2\) and \( y = -5 \) given)
Hence we need \(c\) or \(y\) - intercept to find the value of the slope.
(1) X intercept of P is less than Q
Not what we are looking for, CANNOT give the value of the slope.
INSUFF.
(2) Y intercept of P is more than Q.
Exactly what we are looking for.
As the value of \(c\) increases slope will decrease. Hence slope of \(p\) is less than slope of \(q.\)
SUFF.
Ans B
Hope it's clear.
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- Stne
Posts: 211
The answer will be D.
the equation of line is x/a+y/b=1 a and b are x intercept and y intercept.
slope = -b/a
also when using
y=mx+c
x intercept = -c/m hence y/c= x -x intercept => -5/c= 2-(x intercept) => c= -c/(2-xintercept) when
So x intercept is small the slope is small.
The answer is D.
the equation of line is x/a+y/b=1 a and b are x intercept and y intercept.
slope = -b/a
also when using
y=mx+c
x intercept = -c/m hence y/c= x -x intercept => -5/c= 2-(x intercept) => c= -c/(2-xintercept) when
So x intercept is small the slope is small.
The answer is D.
Posts: 8
I don't understand why it's not D?
Statement (2) suff, I get it.
But why (1) insuff?
If we know the x intercept (0,y) dont this means we can find the slope? (and which is greater too..)
Statement (2) suff, I get it.
But why (1) insuff?
If we know the x intercept (0,y) dont this means we can find the slope? (and which is greater too..)
rudi0setyawan
For (1) consider the following example:
If P is y = 2x - 9 and Q is y = x - 7, then the slope of P (2) is more than that of Q (1).
If P is y = -2x - 1 and Q is y = x - 7, then the slope of P (-2) is less than that of Q (1).
Attachment:
desmos-graph (1).png [ 27.19 KiB | Viewed 3523 times ]
Attachment:
desmos-graph.png [ 26.66 KiB | Viewed 3474 times ]
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dear experts please suggest my approach is correct or not
Attachments
IMG_5114.JPG [ 1.97 MiB | Viewed 2828 times ]
Bunuel
Can you show a similar example for option B too.
TBT
Check the image above. Line Q's y-intercept will be somewhere in the red region of y axis. Q will pass through that point and (2,-5), so the slope of Q would in any case be positive (it goes from bottom left to up right) and it will be steeper than line P, thus the slope of Q will be more than that of P.
Hope it's clear.
Attachment:
2.png [ 23.16 KiB | Viewed 3010 times ]
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GMAT 1: 680 Q49 V34
Posts: 122
Bunuel
Hey Bunuel, for statement B, there can still be a cases when y intercept of line P is greater than Q and slope of P can be greater than Q and opposite can be true too i.e slope of P less than Q, so how can we be sure of B?
rickyric395
Please show a drawing proving your point. Thank you!
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GMAT 1: 680 Q49 V34
Posts: 122
Posting a separate comment as quoting can be done max 3 times.
Hey Bunuel, I made a mistake, I considered only absolute values , eg- Q passes through (0,4) and P passes through (0,8) then absolute of slope(P > Q). but in that case, slopes would be -ve and hence Q's slope will always be greater.
Thanks .
Hey Bunuel, I made a mistake, I considered only absolute values , eg- Q passes through (0,4) and P passes through (0,8) then absolute of slope(P > Q). but in that case, slopes would be -ve and hence Q's slope will always be greater.
Thanks .
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