Good ques...
acc to me .. Ans is E
plz specify OA
ta
gmatprep question
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Source: Beat The GMAT — Data Sufficiency |
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girish3131
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neoreaves
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I think OA is C
we know that y = mx + c
for line L : y = m1x + c1
for line M : y = m2x + c2
What we need to know is m1m2<0 ?
1) x intercept = -c/m ( Just put y = 0 and solve)
(-c1/m1)(-c2/m2) > 0
Insufficient
2)c1*c2<0 insufficient
C) Combining inequalities in 1) and 2)
m1m2<0
Thus answer should be C
we know that y = mx + c
for line L : y = m1x + c1
for line M : y = m2x + c2
What we need to know is m1m2<0 ?
1) x intercept = -c/m ( Just put y = 0 and solve)
(-c1/m1)(-c2/m2) > 0
Insufficient
2)c1*c2<0 insufficient
C) Combining inequalities in 1) and 2)
m1m2<0
Thus answer should be C
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kstv
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The lines intersect at (4,3) so the lines are in the I st Quadrant
The slope of a line is = y intercept/x intercept
Let us asssume for line 1 the x and y intercept are x1, y1 and line 2 x2,y2
given x1*x2 is +ve and y1*y2 is +ve taking 1 & 2 together
so either x1 and x2 are both +ve or both -ve same for y1 and y2
but since they both pass through (4,3) they have to be +ve and product of slope is +ve
x1*x2 is +ve Given in Q stem 1 and we do not consider that y1*y2 is +ve
y1*y2 can be + or - already discussed when it is +ve
if it is -ve y1 & y2 have diff signs say y1 is +ve y2 is -ve
slope of 1st line y1/x1 both are +ve so slope is +ve slope of 2nd line y2/x2 y2 is -ve
so product of their slope is -ve
The slope of a line is = y intercept/x intercept
Let us asssume for line 1 the x and y intercept are x1, y1 and line 2 x2,y2
given x1*x2 is +ve and y1*y2 is +ve taking 1 & 2 together
so either x1 and x2 are both +ve or both -ve same for y1 and y2
but since they both pass through (4,3) they have to be +ve and product of slope is +ve
x1*x2 is +ve Given in Q stem 1 and we do not consider that y1*y2 is +ve
y1*y2 can be + or - already discussed when it is +ve
if it is -ve y1 & y2 have diff signs say y1 is +ve y2 is -ve
slope of 1st line y1/x1 both are +ve so slope is +ve slope of 2nd line y2/x2 y2 is -ve
so product of their slope is -ve
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outreach
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there are three scenarios at which the 2 lines will intersect the x and y axis after passing through pt P
-line can intersect each axis at (+,+). in this case the slope is negative
-line can intersect each axis at (-,+) or (+,-). in both the cases the slope will be positive
- (-,-) is not possible bcz line passed thr pt (4,3)
opt 1: product of their x-intercepts is positive
in this case the 2 lines can intersect the x and y axis at
- (+,+) and (+,+) => products of their slope will be positive
- (+,+) and (+,-) => products of their slope will be negative
insufficient
opt 2:, product of their y-intercepts is negative
- (+,+) and (+,-) => products of their slope will be negative
- (-,+) and (+,-) => products of their slope will be positive
insufficient
opt 1 and opt 2 combined
(+,+) and (+,-) => products of their slope will be negative
hence C
-line can intersect each axis at (+,+). in this case the slope is negative
-line can intersect each axis at (-,+) or (+,-). in both the cases the slope will be positive
- (-,-) is not possible bcz line passed thr pt (4,3)
opt 1: product of their x-intercepts is positive
in this case the 2 lines can intersect the x and y axis at
- (+,+) and (+,+) => products of their slope will be positive
- (+,+) and (+,-) => products of their slope will be negative
insufficient
opt 2:, product of their y-intercepts is negative
- (+,+) and (+,-) => products of their slope will be negative
- (-,+) and (+,-) => products of their slope will be positive
insufficient
opt 1 and opt 2 combined
(+,+) and (+,-) => products of their slope will be negative
hence C
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harshavardhanc
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i don't think the point really matters here.duongthang wrote:k and l cut each other at the point (4,3), is the products of their slope is nagative
1, product of their x-intercepts is positive
2, product of their y-intercepts is negative
we know that the slope is y-intercept/X-intercept.
We need to find out if (y1/x1) * (y2 /X2) or ( y1*y2) / (x1*x2) is negative.
Statement 1 says (x1 * x2) is +ve. We don't know what is the sign of (y1 * y2), so we can't say that ( y1*y2) / (x1*x2) will be -ve.
Hence, insufficient.
Statement 2 says (y1 * y2) is -ve. We don't know what is the sign of (x1 * x2), so we can't say that ( y1*y2) / (x1*x2) will be -ve.
Hence, insufficient.
But, combining these two statements we can definitely say that ( y1*y2) / (x1*x2) will be -ve.
Hence, IMO C.
Regards,
Harsha
Harsha
