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## In the xy coordinate plane, . . .

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### Top Member

Vincen Master | Next Rank: 500 Posts
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#### In the xy coordinate plane, . . .

Thu Sep 14, 2017 2:22 pm
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
In the xy coordinate plane, does the point (3,4) lie on line t?

(1) The line 5y-45=-x is perpendicular to the line t.

(2) The line with the equation y=(3/4)x-11 intersects the line t when y=-11.

The OA is C.

Please show a step by step approach here and explain why it is not sufficient each statement alone. Thanks.

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### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
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Thu Sep 14, 2017 11:03 pm
Vincen wrote:
In the xy coordinate plane, does the point (3,4) lie on line t?

(1) The line 5y-45=-x is perpendicular to the line t.

(2) The line with the equation y=(3/4)x-11 intersects the line t when y=-11.

The OA is C.

Please show a step by step approach here and explain why it is not sufficient each statement alone. Thanks.
Say the equation of line t is given by y = mx + c; where m = magnitude of slopes of the line and c = y-intercept

Statement 1: The line 5y-45=-x is perpendicular to the line t.

If a line is perpendicular to each other, the product of their magnitude of slopes is equal to - 1.

Let's find out the magnitude of the line 5y - 45 = -x

We can write 5y - 45 = -x as y = (-1/5)x + 45/5 => magnitude = -1/5

=> m.(-1/5) = - 1

m = 5. Thus, the magnitude of the line t is 5, however, we do not have any idea about c. We cannot determine whether the point (3,4) lies on line t. Insufficient.

Statement 2: The line with the equation y=(3/4)x - 11 intersects the line t when y = -11.

By plugging-in y = -11 in the equation y = (3/4)x - 11, we get -11 = 3x/4 - 11 => x = 0.

Thus, the equation of line t is y = c. however, we do not have any idea about c. We cannot determine whether the point (3,4) lies on line t. Insufficient.

Statement 1 & 2:

Even after combining the two statements, we cannot get the value of c. Insufficient.

The correct answer: C

Hope this helps!

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-Jay
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