In the x-y plane, what is the y-intercept of line L?
a. The slope of line L is 3 times its y-intercept
b.The x-intercept of line L is -1/3.
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X-Y PLANE
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Geva@EconomistGMAT
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In a line equation y=mx+n, the y intercept of the line is n (when x=0). Thus, the question is really asking "what is n in the line equation?"
Stat. (1) the line can be y=3x+1, or y=6x+2, or any other line which maintains the ratio of 3 to 1 between the slope and the y intercept. No single value for the y intercept n, so insufficient.
Stat (2): it takes some work, but stat. (2) actually says the same thing as stat. (1):
x intercept happens when y=0. Stat.(2) then effectively says that in the equation y=mx+n, when y=0, x=-1/3. Plug these values into x and y, and get:
0=m*-1/3+n
m/3 = n
or
m=3n - which is exactly what stat. (1) had said. the same examples apply - y=3x+1, or y=6x+2, or any other line with a 3 to 1 ratio between slope m and y intercept n. Thus, no single value for n, and insufficient.
combined: since the two statements say the same thing, they don't really add any new information to each other, and nothing new is learned from combining the two. still insufficient, and the answer is E.
Stat. (1) the line can be y=3x+1, or y=6x+2, or any other line which maintains the ratio of 3 to 1 between the slope and the y intercept. No single value for the y intercept n, so insufficient.
Stat (2): it takes some work, but stat. (2) actually says the same thing as stat. (1):
x intercept happens when y=0. Stat.(2) then effectively says that in the equation y=mx+n, when y=0, x=-1/3. Plug these values into x and y, and get:
0=m*-1/3+n
m/3 = n
or
m=3n - which is exactly what stat. (1) had said. the same examples apply - y=3x+1, or y=6x+2, or any other line with a 3 to 1 ratio between slope m and y intercept n. Thus, no single value for n, and insufficient.
combined: since the two statements say the same thing, they don't really add any new information to each other, and nothing new is learned from combining the two. still insufficient, and the answer is E.
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diebeatsthegmat
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line L : y=ax+b now we have to find b-y-intercept of line Ldanjuma wrote:In the x-y plane, what is the y-intercept of line L?
a. The slope of line L is 3 times its y-intercept
b.The x-intercept of line L is -1/3.
statement 1: the slope a=3b ( insufficient cos b is still unknown)
statement 2: to find x intercept, let y=0 => x= -b/a =-1/3( insufficicent cos both b and a are unknown. b and a can be any number such as -1/3 or -2/6... its ratio, we can say nothing about exact numbers of a and b )
1+2/ x=-1/3=-b/a since a=3b => -1/3=-b/-3b =-1/3
insufficient ( b was devided all in numerator and deminator)
E
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thebigkats
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line on xy plane is y = ax +b where line intercepts y axis at b
Slope of the line = a
according to line #a -
a = 3b ==> still doesn't tell us anything about b
accordingly to line #b
(0 - b) / a = x = -1/3 (replace y with 0 becasue that is where it intercepts x axis)
-b/a = -1/3 ==> b/a = 1/3 ==> a = 3b ==> same as statement #a
Hence inconclusive using either or both #a and #b
Slope of the line = a
according to line #a -
a = 3b ==> still doesn't tell us anything about b
accordingly to line #b
(0 - b) / a = x = -1/3 (replace y with 0 becasue that is where it intercepts x axis)
-b/a = -1/3 ==> b/a = 1/3 ==> a = 3b ==> same as statement #a
Hence inconclusive using either or both #a and #b
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prashant misra
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ArunangsuSahu
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y=mx+c
Statement 1:
Gives m=3c...INSUFFICIENT
Statement 2:
Gives -c/m=-1/3
or, m=3c..INSUFFICIENT
Combining there is no CONCLUSION..SO INSUFFICIENT
(E) is the answer
Statement 1:
Gives m=3c...INSUFFICIENT
Statement 2:
Gives -c/m=-1/3
or, m=3c..INSUFFICIENT
Combining there is no CONCLUSION..SO INSUFFICIENT
(E) is the answer
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ronnie1985
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Both the statements yield the same info and hence insufficient.
(E) is answer
(E) is answer
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y = mx + cdanjuma wrote:In the x-y plane, what is the y-intercept of line L?
a. The slope of line L is 3 times its y-intercept
b.The x-intercept of line L is -1/3.
Statement 1 : m = 3c
Statement 2 : -c/m = -1/3
Both statements are essentially the same (insufficient).
Hence choose E.
Last edited by ganeshrkamath on Mon Aug 12, 2013 11:46 pm, edited 1 time in total.
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Brent@GMATPrepNow
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Target question: What is the y-intercept of line L?danjuma wrote:In the x-y plane, what is the y-intercept of line L?
a. The slope of line L is 3 times its y-intercept
b.The x-intercept of line L is -1/3.
IMPORTANT: If the x-intercept is -1/3 (as per statement 2), the slope of the line is guaranteed to be 3 times its y-intercept (as per statement 1).
Here's why.
From statement 2, we know that (-1/3, 0) is one point on the line. Let's let (0, k) be the coordinates of the y-intercept of the line. In other words, let's let the y-intercept equal k.
Using the slope formula, the slope = (k - 0)/(0 - (-1/3)) = k/(1/3) = 3k
So, if the y-intercept is k, the slope must be 3k.
In other words, if we're given statement 2, then statement 1 provides no new information. So, if statement 2 is sufficient, then statement 1 must also be sufficient (since it provides no new info). Likewise, if statement 2 is NOT sufficient, then statement 1 is NOT sufficient. At this point, we know that the answer must be either D (they're both sufficient) or E (neither is sufficient).
So, which is it?
Well, if we examine statement 2 on its own (the x-intercept is -1/3), we can see that we do not have enough information to determine the y-intercept of line L.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Moreover, since statement 1 provides no additional information, it too is NOT SUFFICIENT.
And the combined statements are NOT SUFFICIENT
Answer = E
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Brent
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