Problem Solving

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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)

OA A

Note that a and b can be positive or negative. Thus, the point in questions is (±a, ±b).

Let's take suitable values for a and b. Say a = ±1 and b = ±2. Thus, the point is (±1, ±2).

Say the point is in

1. First quadrant: thus, the point is (1, 2)

We see that all the options have at least one negative coordinate; thus, the point (a, b) is not in the first quadrant.

2. Second quadrant: thus, the point is (-1, 2)

We see that option A (-b, -a) with the assumed values would be (-2, 1). The point (-2, 1) is also in the second quadrant. Thus, option A can be the correct answer.

Since this is a PS question, and only one option can be correct, the correct option is A.

The correct answer: A

Hope this helps!

-Jay
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AAPL wrote:Manhattan GMAT

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)

If a is positive and b is negative, then (a, b) lies in Quadrant IV.

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 are 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), which is (2, -1), which is also in Quadrant IV.

Answer: A

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)
(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:

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....

Final Answer: A

GMAT assassins aren't born, they're made,
Rich