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MGMAT CAT 2: PS Problem

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MGMAT CAT 2: PS Problem

by josh80 » Sun Nov 10, 2013 9:40 am
Which of the following points could lie in the same quadrant of the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?

(-b, -a)

(-a, -b)

(b, -a)

(a, -b)

(-b, a)
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by GMATGuruNY » Sun Nov 10, 2013 10:42 am
josh80 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 ?

(-b, -a)

(-a, -b)

(b, -a)

(a, -b)

(-b, a)
Every answer choice includes at least one negative sign.
Test coordinate pairs that include at least one negative value.

Case 1: a=1 and b=-1, so that (a, b) = (1, -1)
Plug a=1 and b=-1 into the answer choices to see whether one of the answer choices yields a point in the same quadrant as (1,-1).

A: (-b, -a) = ( -(-1), -1 ) = (1, -1).
Success!

The correct answer is A.
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by [email protected] » Sun Nov 10, 2013 12:44 pm
Hi josh80,

Co-ordinate Geometry (or "graphing", as most people call it) is a relatively small 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)
(1,2) - Quadrant 1
(-1,2) - Quadrant 2
(-1,-2) - Quadrant 3
(1,-2) - Quadrant 4

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?

[spoiler]Answer A: (-b,-a) = (-2,1). [/spoiler] THAT answer puts in Quadrant 2. It's a match for what the question asked us for, so it has to be the answer.

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by Mathsbuddy » Sun Nov 17, 2013 9:26 am
(a,b) options: (+,-), (-,+), (+,+), (-,-).
Substituting into each answer gives:
(A) (-b, -a) : (+,-), (-,+), (-,-), (+,+)
(B) (-a, -b) : (-,+), (+,-), (-,-), (+,+)
(C) (b, -a) : (-,-), (+,+), (+,-), (-,+)
(D) (a, -b) : (+,+), (-,-), (+,-), (-,+)
(E) (-b, a) : (+,+), (-,-), (-,+), (+,-)

The colours above indicate that only answer A satisfies the condition.
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by Mathsbuddy » Sun Nov 17, 2013 9:38 am
Another approach:

x can never equal -x
y can never equal -y

so we can instantly eliminate B and D.

x and y must share the same sign,

so we can also eliminate C and E

This leaves answer A in only a matter of seconds, without any substitution required.
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