Line L passes through points R(0, -5 ) and S(4,0)

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Line \(L\) passes through points \(R(0, -5 )\) and \(S(4,0)\) (see figure above). Point \(P\) with coordinates \((x, y)\) is a point on Line L. Is \(xy > 0?\)

\((1) \ x > 4\)
\((2) \ y > - 5\)

The OA is the option _A_

Source: Manhattan GMAT
Source: — Data Sufficiency |

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by deloitte247 » Thu Sep 05, 2019 5:17 am

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Question=> is xy>0
Statement 1: x>4
Point P is on line L, given that x > 4, then point P must be in the I-quadrant (First quadrant) which is the right of point S (4,0), and as the slope is positive, y will also be positive; so xy>0.
Statement 1 is SUFFICIENT

Statement 2: y > -5
Point P will be to the right of point R (0,-5) which means either in the first or fourth quadrant.
If it is in the first quadrant, both x and y will be positive, hence; xy>0 but if it is in the fourth quadrant, x is positive and y is negative. Hence, xy < 0.
Since the information provided cannot ascertain whether xy > 0 or xy < 0, statement 2 is therefore NOT SUFFICIENT.

Hence, statement 1 alone is SUFFICIENT.
Answer = option A