Data Sufficiency

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.

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

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.

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.