What is the y-intercept of line l?
1) Slope of line l is 3 times its y intercept
2) X intercept of the line is -1/3
OA is E
Tricky DS
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NOTE: When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.In the xy-plane, what is the y-intercept of line l?
1) the slope of line l is 3 times its y-intercept
2) the x-intercept of line l is -(1/3)
Target question: What is the y-intercept of line L?
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, statement 1 provides no new information beyond the information that statement 1 provides. So, if statement 2 is sufficient, then statement 1 must also be sufficient (since it provides no new info). Conversely, 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
Since statement 1 provides no additional information, it too is NOT SUFFICIENT.
So, the combined statements are NOT SUFFICIENT
Answer = E
For additional proof, consider these two lines:
Both lines satisfy the conditions in statements 1 and 2, however the y-intercepts are different.
Cheers,
Brent
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An alternate approach is to TEST CASES.In the xy-plane, what is the y-intercept of line L?
(1) The slope of line L is 3 times its y-intercept
(2) The x-intercept of line L is (-1/3)
The equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
Statement 1: The slope of line L is 3 times its y-intercept
Case 1: b=1
Since the slope is 3 times the y-intercept, m = 3b = 3*1 = 3.
Resulting equation:
y = 3x + 1.
In this case, the y-intercept is 1.
Case 2: b=2
Since the slope is 3 times the y-intercept, m = 3b = 3*2 = 6.
Resulting equation:
y = 6x + 2.
In this case, the y-intercept is 2.
Since the y-intercept can be different values, INSUFFICIENT.
Statement 2: The x-intercept of line L is -1/3
Implication:
(-1/3, 0) is on line L.
Check whether (-1/3, 0) is on the lines yielded by Cases 1 and 2.
Case 1: y = 3x + 1
(-1/3, 0) is on this line.
Thus, it's possible that the equation for line L is y = 3x + 1, in which case the y-intercept is 1.
Case 2: y = 6x + 2
(-1/3, 0) is on this line.
Thus, it's possible that the equation for line L is y = 6x + 2, in which case the y-intercept is 2.
Since the y-intercept can be different values, INSUFFICIENT.
Statements combined:
Since both statements are satisfied by Cases 1 and 2, it's possible that the y-intercept is 1 or that the y-intercept is 2.
Since the y-intercept can be different values, INSUFFICIENT.
The correct answer is E.
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CONCEPT : To specify a Line on X-Y Plot we need two inputsNijo wrote:What is the y-intercept of line l?
1) Slope of line l is 3 times its y intercept
2) X intercept of the line is -1/3
OA is E
e.g. X-Intercept and Slope
or Y-Intercept and Slope
or X-Intercept and Y-Intercept
or any two points on the line
Question : Y intercept of the Line?
Statement 1) Slope = 3 x Y-Intercept
Infinite values of slopes are possible and therefore infinite of Y intercepts
INSUFFICIENT
Statement 2) X intercept of the line is -1/3
For the same X-Intercept, Line may have positive or negative slope therefore various values of Y-Intercepts are possible
INSUFFICIENT
Combining the two Statements
For a Given X-Intercept, Line may have positive or negative slope therefore various values of Y-Intercepts are possible
INSUFFICIENT
Answer: Option E
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Just to piggyback on Brent's response, we know that the x-intercept of the line y = mx + b is -b/m. (Supposing that m is not 0.) Here's how!
Suppose we have the line y = mx + b. At the x-intercept, we know the y-value will be 0, so this gives us the equation 0 = mx + b. Subtracting b from both sides gives -b = mx. We then divide by m to find -b/m.
This is a useful trick to remember, not least for a question like this.
S1 tells us that m = 3b. Not sufficient.
S2 tells us that -1/3 = -b/m, which (after crossmultiplying) is just m = 3b. Not sufficient either.
S1 + S2 just says the same thing twice, so the answer is E.
Suppose we have the line y = mx + b. At the x-intercept, we know the y-value will be 0, so this gives us the equation 0 = mx + b. Subtracting b from both sides gives -b = mx. We then divide by m to find -b/m.
This is a useful trick to remember, not least for a question like this.
S1 tells us that m = 3b. Not sufficient.
S2 tells us that -1/3 = -b/m, which (after crossmultiplying) is just m = 3b. Not sufficient either.
S1 + S2 just says the same thing twice, so the answer is E.