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In the coordinate geometry plane, region P is defined by all the point

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In the coordinate geometry plane, region P is defined by all the point [#permalink]

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New post 09 Jan 2018, 21:30
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In the coordinate geometry plane, region P is defined by all the points (x,y) for which 3y + 12 > 2x. Does point (a,b) lie within region P?

(1) 4b = a – 8
(2) b < 0 and a > 3

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Re: In the coordinate geometry plane, region P is defined by all the point [#permalink]

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New post 09 Jan 2018, 23:21
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Bunuel wrote:
In the coordinate geometry plane, region P is defined by all the points (x,y) for which 3y + 12 > 2x. Does point (a,b) lie within region P?

(1) 4b = a – 8
(2) b < 0 and a > 3



3y + 12 > 2x can also be written as 2x - 3y < 12. So all the points (x,y) in the coordinate geometry which satisfy this inequation: 2x - 3y < 12, will be said to lie Within region P. All those which do not satisfy this inequation obviously do not lie within the region P.

(1) 4b = a - 8 Or a - 4b = 8. Or a = 8 + 4b.
Substituting values of a, b as x, y in the inequation, we get LHS = 2x - 3y = 2 (8+4b) - 3b = 16 + 5b. But RHS = 12.
We cant say whether 16 + 5b is < 12 until we know the value of b. So Insufficient.

(2) b is negative and a > 3. If a=4 and b=-1, then 2x - 3y = 2*4 - 3*-1 = 11, which is < 12.
But if a=4 and b=-2, we have 2x - 3y = 2*4 - 3*-2 = 14, which is > 12. So we cant say. Insufficient.

Combining the two statements, we have LHS = 16 + 5b and we are given that b < 0, a > 3. So a = 4b + 8 > 3 or 4b > 3-8 or 4b > -5 or b > -5/4 or b > -1.25.
So be has to be negative but greater than -1.25. So b lies between -1.25 and 0.

At b=-1.25, 16 + 5b becomes = 16 + 5*-1.25 = 16 - 6.25 or 9.75. And at b=0, 16 + 5b becomes 16 + 5*0 = 16.
So the range of 16 + 5b (or the range of 2x - 3y here) is that it lies between 9.75 and 16. Which passes the value 12. So it might be < 12 or it might be > 12.

Not sufficient. Hence E answer
Re: In the coordinate geometry plane, region P is defined by all the point   [#permalink] 09 Jan 2018, 23:21
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In the coordinate geometry plane, region P is defined by all the point

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