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co-ordinate geometry

Expert replies
by srcc25anu » Mon Mar 28, 2011 5:48 am
A line with the equation y = px + q is reflected over the line y = x. Is the reflection of this line parallel to the line y = mx + n?

(1) m = p + 2

(2) m = 3p

OA C
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Source: — Data Sufficiency |

by AIM GMAT » Mon Mar 28, 2011 6:15 am
Hey anu,

Whats the source of this question ? Is it GMAT question or CAT one ... coz its pretty annoying ... !!!
Thanks & Regards,
AIM GMAT
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by srcc25anu » Mon Mar 28, 2011 6:24 am
its from grockit.com
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by Anurag@Gurome » Mon Mar 28, 2011 7:39 am
srcc25anu wrote:A line with the equation y = px + q is reflected over the line y = x. Is the reflection of this line parallel to the line y = mx + n?

(1) m = p + 2

(2) m = 3p

OA C
Image

Slope of line y = px + q is p and slope of line y = mx + n is m.
(1) m = p + 2 implies there is just one equation and 2 variables. Until we know the values of m and p, we cannot say whether reflection of y = px + q is parallel to the line y = mx + n. So, (1) is NOT SUFFICIENT.

(2) m = 3p again implies there is just one equation and 2 variables. Until we know the values of m and p, we cannot say whether reflection of y = px + q is parallel to the line y = mx + n. So, (2) is NOT SUFFICIENT.

Combining (1) and (2), 3p = p + 2 implies p = 1 and m = 3. So, now we can find the angle that each of the two lines make with x -axis. Hence, combining the statements is SUFFICIENT to answer the question.

The correct is C.
Anurag Mairal, Ph.D., MBA
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