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)
Problem solving
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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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](https://s3.postimg.cc/uqexlke3z/Untitled.jpg)
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].
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](https://s3.postimg.cc/uqexlke3z/Untitled.jpg)
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].
Vivian Kerr
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GMAT Rockstar, Tutor
https://www.GMATrockstar.com
https://www.yelp.com/biz/gmat-rockstar-los-angeles
Former Kaplan and Grockit instructor, freelance GMAT content creator, now offering affordable, effective, Skype-tutoring for the GMAT at $150/hr. Contact: [email protected]
Thank you for all the "thanks" and "follows"!
![Smile :-)](./images/smilies/smile.png)