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Origin

by oquiella » Wed Oct 28, 2015 5:43 pm
37. Does the straight line MN pass through the origin?
(1) Its equation is 4x + 7y = 0
(2) Its slope is (- 4/7).


A: A

PLease explain "origin" and why the slope would not make statement 2 sufficient.
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by theCEO » Wed Oct 28, 2015 10:35 pm
oquiella wrote:37. Does the straight line MN pass through the origin?
(1) Its equation is 4x + 7y = 0
(2) Its slope is (- 4/7).


A: A

PLease explain "origin" and why the slope would not make statement 2 sufficient.
Equation for straight line = y=mx + c, where m = slope and c = intercept.
When c = 0, the line passes through the origin (0,0)

1) Its equation is 4x + 7y = 0
7y = -4x + 0
y = (-4/7)x + 0, therefore this line passes through origin
sufficent

2) Its slope is (- 4/7).
y = mx + c
y = (-4/7)x + c
We don't know the value for y, or c so we cannot solve for c
insufficent

ans = a
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by GMATGuruNY » Thu Oct 29, 2015 3:21 am
oquiella wrote:37. Does the straight line MN pass through the origin?
(1) Its equation is 4x + 7y = 0
(2) Its slope is (- 4/7).
The ORIGIN = (0, 0).

Statement 1:
Since (x, y) = (0, 0) is a solution for 4x + 7y = 0, line MN passes through the origin.
SUFFICIENT.

Statement 2:
Case 1: y = (-4/7)x
(x, y) = (0, 0) is a solution for y = (-4/7)x.
Thus:
In this case, line MN passes through the origin.

Case 2: y = (-4/7)x + 1
(x, y) = (0, 0) is NOT a solution for y = (-4/7)x + 1.
Thus:
In this case, line MN does NOT pass through the origin.
INSUFFICIENT.

The correct answer is A.
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by Brent@GMATPrepNow » Thu Oct 29, 2015 8:53 am
oquiella wrote:Does the straight line MN pass through the origin?

(1) Its equation is 4x + 7y = 0
(2) Its slope is (- 4/7).
Target question: Does the straight line MN pass through the origin?
In other words, Does the straight line MN pass through the point (0, 0)??

Statement 1: Its equation is 4x + 7y = 0
IMPORTANT: The equation defines ONE AND ONLY ONE LINE.
So, we COULD just plot the line on the x-y plane and check whether or not it passes through (0, 0).
Since we COULD answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Its slope is (- 4/7)
Okay, so we know how steep the line is, but this isn't enough to answer the target question.
We can move the line up and still retain the slope of -4/7.
In fact, there are INFINITELY MANY lines that satisfy this condition.
So, it could be the case that the line passes through (0, 0), and it could be the case that the line DOES NOT pass through (0, 0)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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by Max@Math Revolution » Wed Nov 04, 2015 9:59 am
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

37. Does the straight line MN pass through the origin?
(1) Its equation is 4x + 7y = 0
(2) Its slope is (- 4/7).

If we modify the question, we want to know whether the y-intercept=0.
From condition 1, 7y=-4x, y=-4x/7. This is sufficient enough, the answer becomes (A).

For cases where we need 1 more equation, such as original conditions with "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations", we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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