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kamalakarthi
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Statement 1: Lines n and p intersect at point (5,1).
With only one point with which to work and no other information, we cannot determine anything about the slopes of the lines.
Insufficient.
Statement 2: The y intercept of line n is greater than the y intercept of line p.
The lines could have various different slopes irrespective of the relative values of their y intercepts.
Insufficient.
Statements Combined:
From Statement 1 we know that the lines intersect in a particular spot, (5, 1), above the x axis and to the right of the y axis.
From Statement 2 we know that when x = 0, the y value of line n is greater than the y value of line p.
No matter what those y intercepts are, the change in y for n when x goes from 0 to 5 will be less than the change in y for p when x goes from 0 to 5, because n is starting from a higher y when x = 0, and both n and p go to y = 1 when x = 5.
For example if the y intercepts of n and p are 2 and 1 respectively, when x increases from 0 to 5, the change in the y of n will be -1 and the change in the y of p will be 0. So n would have a negative slope and p would have a slope of 0.
Since for a given positive change in x the change in y is less for n than for p, the slope of n is less than the slope of p.
Sufficient.
The correct answer is C.
