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M12-13

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M12-13 [#permalink]

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New post 10 Sep 2017, 23:36
RekhaKulkarni wrote:
Hi, Can anyone tell me what will be the final equation of the line once we know what a and b are?


From a=-b and a-b=1, we can get that a = 1/2 and b = -1/2. So, we know that k passes through the point (1/2, -1/2) and is perpendicular to line y = 2x (slope = 2)

The two lines are perpendicular if and only if the product of their slopes is -1, so m*2 = -1 and m = -1/2 (the slope of line k).

Finally, the equation of a straight line that passes through a point \(P_1(x_1, y_1)\) with a slope m is: \(y-y_1=m(x-x_1)\). Substitute: \(y-(-\frac{1}{2})=-\frac{1}{2}(x-\frac{1}{2})\) --> \(y = -\frac{x}{2} - \frac{1}{4}\).

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For Coordinate Geometry check:

24. Coordinate Geometry



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New post 13 Sep 2017, 23:20
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. i read the whole thread, and still didn't understand the explanation. I do understand that we don't need to find the value of a and b, question is why would we discard 1) and 2) as insufficient, what's the reasoning behind it.

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New post 13 Sep 2017, 23:32
d975490 wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. i read the whole thread, and still didn't understand the explanation. I do understand that we don't need to find the value of a and b, question is why would we discard 1) and 2) as insufficient, what's the reasoning behind it.


(1) and (2) individually are insufficient for the same reason: different values of a and b satisfy each statement, giving different points of (a, b), thus giving different equations of line k that is perpendicular to line y = 2x.

For example, for (1), if x = 2 and y = -2, then the equation of line k would be y = -x/2 - 1 (apply the approach used HERE) but of x = 1 and y = -1, then the equation of line k would be y = -x/2 - 1/2. Two different answers, hence insufficient.

Hope it's clear.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: M12-13   [#permalink] 13 Sep 2017, 23:32

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