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sj296
Let's say the line 'm' is

y = px + C, where C is greater than 4 ........(1)

Statement 1:

Line 'm' is perpendicular to the line 'n', y - 2x - 3 = 0

=> y = 2x + 3

Since line m is perpendicular to line n, the slope of line m = -1/2 (the product of the slopes of two perpendicular lines = -1)

so eq (1) would become

y = (-1/2)x + C

to find x-intercept of the line m, put y = 0

x = -C*(-2) = 2C

Since C is greater than 4, 2C will be greater than 8. hence, x-intercept will be greater than 8.

So, we can say Yes, the x-intercept is greater than 5

Sufficient

Statement 2:

Line m passes through (4,5) & y-intercept is more than 4

This is an insufficient condition. Check the x-intercept of the line passing through (0, 4.5) & (4,5), and x-intercept of the line passing through (0,6) & (4,5)

Hence, OA should be A

Posted from my mobile device

In both the cases that you mentioned in statement 2, x intercept will be greater than 5. For more simplification, just plot those points on graph and you will see.
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sj296
Let's say the line 'm' is

y = px + C, where C is greater than 4 ........(1)

Statement 1:

Line 'm' is perpendicular to the line 'n', y - 2x - 3 = 0

=> y = 2x + 3

Since line m is perpendicular to line n, the slope of line m = -1/2 (the product of the slopes of two perpendicular lines = -1)

so eq (1) would become

y = (-1/2)x + C

to find x-intercept of the line m, put y = 0

x = -C*(-2) = 2C

Since C is greater than 4, 2C will be greater than 8. hence, x-intercept will be greater than 8.

So, we can say Yes, the x-intercept is greater than 5

Sufficient

Statement 2:

Line m passes through (4,5) & y-intercept is more than 4

This is an insufficient condition. Check the x-intercept of the line passing through (0, 4.5) & (4,5), and x-intercept of the line passing through (0,6) & (4,5)

Hence, OA should be A

Posted from my mobile device

In both the cases that you mentioned in statement 2, x intercept will be greater than 5. For more simplification, just plot those points on graph and you will see.



Let's take two points

(0,4.5) and (4,5)

The line would be y = 0.125 x + 4.5

The x-intercept = -4.5/0.125 = -36

Let's take another set of two points (0,6) and (4,5)
the line would be y = 6-0.25x

the x-intercept = 24

You can also take y = 5 as well

Hence the statement 2 is not sufficient.

Hope you get what I am saying.
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