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Which of the following points could lie in the same quadrant  [#permalink]

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Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A. (–b, –a)
B. (–a, –b)
C. (b, –a)
D. (a, –b)
E. (–b, a)

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Which of the following points could lie in the same quadrant  [#permalink]

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romeokillsu wrote:
Bunuel wrote:
WoundedTiger wrote:
Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A. (–b, –a)
B. (–a, –b)
C. (b, –a)
D. (a, –b)
E. (–b, a)

First of all discard all options which have -a as the x-coordinate and -b as y-coordinate: eliminate B, and D.

(a, b) = (+, +), (+, -), (-, +), (-, -). Substitute in each option, to see which will match.

A. (–b, –a) --> (-, -), (+, -), (-, +), (+, +). Match. No need to continue.

Please explain by example.. Thank you

If a is positive and b is positive: (a, b) = (+, +), then (–b, –a) = (-, -). For example, if (a, b) = (1, 1), then (–b, –a) = (-1, -1). So, (a, b) and (–b, –a) are NOT in the same quadrant.

If a is positive and b is negative: (a, b) = (+, -), then (–b, –a) = (+, -). For example, if (a, b) = (1, -1), then (–b, –a) = (1, -1). So, (a, b) and (–b, –a) are in the same quadrant.

If a is negative and b is positive: (a, b) = (-, +), then (–b, –a) = (-, +). For example, if (a, b) = (-1, 1), then (–b, –a) = (-1, 1). So, (a, b) and (–b, –a) are in the same quadrant.

If a is negative and b is negative: (a, b) = (-, -), then (–b, –a) = (+, +). For example, if (a, b) = (-1, -1), then (–b, –a) = (1, 1). So, (a, b) and (–b, –a) are NOT in the same quadrant.

Hope it's clear.
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Re: Which of the following points could lie in the same quadrant  [#permalink]

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WoundedTiger wrote:
Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A. (–b, –a)
B. (–a, –b)
C. (b, –a)
D. (a, –b)
E. (–b, a)

First of all discard all options which have -a as the x-coordinate and -b as y-coordinate: eliminate B, and D.

(a, b) = (+, +), (+, -), (-, +), (-, -). Substitute in each option, to see which will match.

A. (–b, –a) --> (-, -), (+, -), (-, +), (+, +). Match. No need to continue.

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Re: Which of the following points could lie in the same quadrant  [#permalink]

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Bunuel wrote:
WoundedTiger wrote:
Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A. (–b, –a)
B. (–a, –b)
C. (b, –a)
D. (a, –b)
E. (–b, a)

First of all discard all options which have -a as the x-coordinate and -b as y-coordinate: eliminate B, and D.

(a, b) = (+, +), (+, -), (-, +), (-, -). Substitute in each option, to see which will match.

A. (–b, –a) --> (-, -), (+, -), (-, +), (+, +). Match. No need to continue.

I don;t understand how you did this . Could you elaborate by example?

e.g if (a,b) = (3,4), then how can (-4,-3) lie in the same quadrant?

(3,4) is in the first quadrant and (-4,-3) is in the 3rd.
Confusing
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Re: Which of the following points could lie in the same quadrant  [#permalink]

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Bunuel wrote:
WoundedTiger wrote:
Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A. (–b, –a)
B. (–a, –b)
C. (b, –a)
D. (a, –b)
E. (–b, a)

First of all discard all options which have -a as the x-coordinate and -b as y-coordinate: eliminate B, and D.

(a, b) = (+, +), (+, -), (-, +), (-, -). Substitute in each option, to see which will match.

A. (–b, –a) --> (-, -), (+, -), (-, +), (+, +). Match. No need to continue.

Please explain by example.. Thank you
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Re: Which of the following points could lie in the same quadrant  [#permalink]

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Great explanation Bunuel. Thanks a lot!!!!
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Re: Which of the following points could lie in the same quadrant  [#permalink]

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Bunuel,

Could you please explain on what basis you eliminated B&D ? Also could you share some background information on how you got the answer as A ? I.e. Those points matched only for two quadrants, how diid you conclude this as the answer ?

Basically I'm confused over the method you have used and on what basis you have concluded the answer too.

I got the correct answer as A, but i used just (2, -1) randomly as (a, b) and checked for all the options and only option A coordinates were on same quadrant as (2, -1). Please correct me if I'm wrong.

Thanks.
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Re: Which of the following points could lie in the same quadrant  [#permalink]

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Swaroopdev wrote:
Bunuel,

Could you please explain on what basis you eliminated B&D ? Also could you share some background information on how you got the answer as A ? I.e. Those points matched only for two quadrants, how diid you conclude this as the answer ?

Basically I'm confused over the method you have used and on what basis you have concluded the answer too.

I got the correct answer as A, but i used just (2, -1) randomly as (a, b) and checked for all the options and only option A coordinates were on same quadrant as (2, -1). Please correct me if I'm wrong.

Thanks.

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Re: Which of the following points could lie in the same quadrant  [#permalink]

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Bunuel, yes i have gone through the whole thing and only then posted those questions. What i don't understand in that is how you came to conclusion when only two points matched and other two didn't. And the rest i have put up in my previous post.

Thanks.
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Re: Which of the following points could lie in the same quadrant  [#permalink]

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Swaroopdev wrote:
Bunuel,

Could you please explain on what basis you eliminated B&D ?

Thanks.

Given point: (a, b).

If a is positive, then -a is negative, and vise-versa. So, point (-a, ...) cannot be in the same quadrant as (a, b)
If b is positive, then -b is negative, and vise-versa. So, point (..., -b) cannot be in the same quadrant as (a, b)

Swaroopdev wrote:
Bunuel, yes i have gone through the whole thing and only then posted those questions. What i don't understand in that is how you came to conclusion when only two points matched and other two didn't. And the rest i have put up in my previous post.

Thanks.

I don't understand what you mean by "only two points matched and other two didn't".
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Re: Which of the following points could lie in the same quadrant  [#permalink]

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Swaroopdev wrote:
Bunuel, yes i have gone through the whole thing and only then posted those questions. What i don't understand in that is how you came to conclusion when only two points matched and other two didn't. And the rest i have put up in my previous post.

Thanks.

I believe you are confusing a must be true question with this question (a "could be true" ) question. In a could be true question, as soon as match 1 option , no need to check for ALL possible cases. For a must be true question, you need to make sure that ALL possible values are satisfied for an option to be the correct one.
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Engr2012, Bunuel my confusion was not regarding checking other options such as B, C, D and E but with the below solution. Below two points are proved to be of same quadrant and two are not, is it okay only if two quadrant checks out fine or even if one quadrant is matched we can conclude the answer ?

If a is positive and b is positive: (a, b) = (+, +), then (–b, –a) = (-, -). For example, if (a, b) = (1, 1), then (–b, –a) = (-1, -1). So, (a, b) and (–b, –a) are NOT in the same quadrant.

If a is positive and b is negative: (a, b) = (+, -), then (–b, –a) = (-, -). For example, if (a, b) = (1, -1), then (–b, –a) = (1, -1). So, (a, b) and (–b, –a) are in the same quadrant.

If a is negative and b is positive: (a, b) = (-, +), then (–b, –a) = (-, +). For example, if (a, b) = (-1, 1), then (–b, –a) = (-1, 1). So, (a, b) and (–b, –a) are in the same quadrant.

If a is negative and b is negative: (a, b) = (-, -), then (–b, –a) = (+, +). For example, if (a, b) = (-1, -1), then (–b, –a) = (1, 1). So, (a, b) and (–b, –a) are NOT in the same quadrant.
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Re: Which of the following points could lie in the same quadrant  [#permalink]

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Swaroopdev wrote:
Engr2012, Bunuel my confusion was not regarding checking other options such as B, C, D and E but with the below solution. Below two points are proved to be of same quadrant and two are not, is it okay only if two quadrant checks out fine or even if one quadrant is matched we can conclude the answer ?

If a is positive and b is positive: (a, b) = (+, +), then (–b, –a) = (-, -). For example, if (a, b) = (1, 1), then (–b, –a) = (-1, -1). So, (a, b) and (–b, –a) are NOT in the same quadrant.

If a is positive and b is negative: (a, b) = (+, -), then (–b, –a) = (-, -). For example, if (a, b) = (1, -1), then (–b, –a) = (1, -1). So, (a, b) and (–b, –a) are in the same quadrant.

If a is negative and b is positive: (a, b) = (-, +), then (–b, –a) = (-, +). For example, if (a, b) = (-1, 1), then (–b, –a) = (-1, 1). So, (a, b) and (–b, –a) are in the same quadrant.

If a is negative and b is negative: (a, b) = (-, -), then (–b, –a) = (+, +). For example, if (a, b) = (-1, -1), then (–b, –a) = (1, 1). So, (a, b) and (–b, –a) are NOT in the same quadrant.

Good question. But Bunuel and I have mentioned, there are 2 things that you need to note for this question:

1. this is a could be true question, so even 1 correct/matching solution should tell you to stop.
2. Based on above 4 cases, you are able to get 1 value (-b,-a) to the point for the same quadrant. yes, for a question such as this one, you can conlcude once you get 1 matching option.

Bunuel provided these explanations in addition to his oginal solution post above. This post of his should not be treated as the complete solution.
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Re: Which of the following points could lie in the same quadrant  [#permalink]

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Engr2012 and Bunuel, thanks to both of you, now my doubts are cleared. Director  S
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Re: Which of the following points could lie in the same quadrant  [#permalink]

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WoundedTiger wrote:
Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A. (–b, –a)
B. (–a, –b)
C. (b, –a)
D. (a, –b)
E. (–b, a)

Really, a fast way to solve question is just to consider a mixed pair of coordinates, for example (-3,2). If we have a pair of coordinates with the same values then none of these answers would apply.

Thus
"A"
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Which of the following points could lie in the same quadrant  [#permalink]

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Hi All,

Co-ordinate Geometry (or "graphing", as most people call it) is a relatively rare category in the GMAT Quant section; you'll likely see just 1 of these questions on Test Day. The question is perfect for TESTing VALUES. Here's how:

We're asked which of the 5 answers COULD be in the same quadrant as (A,B), where neither A nor B equals 0. This makes me think that we'll have to consider more than one possibility, since there are 4 different quadrants on a graph.

Here are the examples that I would consider:
(A,B)

You'll notice that each of the 5 answer choices changes the "sign" of at least one of the variables (and sometimes switches the variables around). If you start off in Quadrant 1, the only way to end up in that SAME Quadrant is if both the a and b are positive. That doesn't happen in ANY of the answer choices, so we need to look at a diffent Quadrant. I'm going to start with Quadrant 2:

(A,B)
(-1,2)

So, if we plug A = -1 and B = 2 into the 5 answer choices, do any of them give us an answer that puts us in Quadrant 2? One of them DOES....

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Re: Which of the following points could lie in the same quadrant  [#permalink]

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WoundedTiger wrote:
Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A. (–b, –a)
B. (–a, –b)
C. (b, –a)
D. (a, –b)
E. (–b, a)

Let's test some coordinates...

How about: a = 1 and b = -2.
This means the point (a, b) = (1, -2), which is in QUADRANT IV

Now plug a = 1 and b = -2 into each answer choice...

A) (-b, -a) = [( -(-2), -1] = (2, -1), which is also in QUADRANT IV
PERFECT!

Cheers,
Brent
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Re: Which of the following points could lie in the same quadrant  [#permalink]

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WoundedTiger wrote:
Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A. (–b, –a)
B. (–a, –b)
C. (b, –a)
D. (a, –b)
E. (–b, a)

Just a quick observation that is (I hope) interesting in its own right:

If x*y and w*z are both different from zero, points (x,y) and (w,z) will be in the same quadrant if, and only if,
x*w> 0 ("x-coordinates" have the same sign) and y*z>0 ("y-coordinates" have the same sign).

Conclusion:

(B) is refuted, because a and -a (x-coordinates in question stem and in this alternative choice) do not have the same signs (a is not zero)
(C) is refuted, because if a and b (x-coordinates...) have the same signs , then b and -a (y-coordinates...) don´t have
(D) is refuted, because b and -b (y-coordinates...) do not have the same signs (b is not zero)
(E) is refuted, because if a and -b (x-coordinates...) have the same signs , then b and a (y-coordinates...) don´t have

Regards,
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Re: Which of the following points could lie in the same quadrant  [#permalink]

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$$M(x_1, y_1)$$ and $$N(x_2, y_2)$$ lie in the same quadrant, thus: $$x_1 * y_1$$ and $$x_2 * y_2$$ have the same sign. (the opposite is not true)
--> Quickly eliminate C, D, E.

Down to A & B.
B. the x-coordinate is -a. Point (-a,...) and Point (a,...) can't lie in the same quadrant. -> B is out.

A is the winner.

WoundedTiger wrote:
Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A. (–b, –a)
B. (–a, –b)
C. (b, –a)
D. (a, –b)
E. (–b, a)

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Re: Which of the following points could lie in the same quadrant  [#permalink]

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WoundedTiger wrote:
Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

A. (–b, –a)
B. (–a, –b)
C. (b, –a)
D. (a, –b)
E. (–b, a)

Let’s suppose that (a, b) lies in Quadrant IV. That is, a is positive and b is negative.

Thus, -b is positive and -a is negative, so (-b, -a) also lies in Quadrant IV.

Alternate Solution:

If we assume that both a and b are positive, and thus (a, b) is in Quadrant I, we see that none of the answer choices will lie in Quadrant I.

Now let’s assume that a is positive (a = 1) and b is negative (b = -2); then (1, -2) lies in Quadrant IV. Looking at the answer choices, we see that choice A gives us (-b, -a) =(2, -1), which is also in Quadrant IV.

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