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Problem solving

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by Newaz111 » Mon May 04, 2015 6:03 am
In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points is in the same quadrant as the fourth vertex of the square?

A. (-5, -3)
B. (-5, 3)
C. (5, -3)
D. (3, -5)
E. (3, 5)
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by [email protected] » Mon May 04, 2015 11:34 am
Hi Newaz111,

This question really tests your attention-to-detail and organizational skills. If you "slip" a negative sign incorrectly, then you'll get the question wrong, thus a certain amount of note-taking is necessary.

We're told that C < 0 and D > 0, so let's start by TESTing VALUES....

IF.....
C = -2,
D = 2

The 3 co-ordinates that we're given will become...

(C,D) = (-2, 2) --> Quadrant 2
(C,-D) = (-2, -2) --> Quadrant 3
(-C,-D) = (2, -2) --> Quadrant 4

The last co-ordinate of the square will be in Quadrant 1, which means we need a POSITIVE X-co-ordinate and a POSITIVE Y-co-ordinate....

Final Answer: E

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Rich
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by VivianKerr » Sun May 24, 2015 9:55 pm
It might help you to visualize by drawing the vertices of the square.

Remember this rule on the GMAT: you are given limitations on variables for a reason.

Why would they tell us that c < 0 and d > 0? It must matter somehow.

If c is always negative, then (c, d) will become (-c, d), since a positive number multiplied by a negative number is always negative. The "d" will not be affected, since a positive multiplied by a positive is always positive.

By the same line of thinking:

(c, -d) = (-c, -d)
(-c, -d) = (c, -d)

Let's plot (-c, d), (-c, -d), and (c, -d) on the coordinate grid, and it will be easy to see the missing quadrant.

Image

The first quadrant, in which "c" and "d" are positive, is missing. Look for an answer choice with a positive value for both x and y. It must be [spoiler](E)[/spoiler].
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