In a rectangular coordinate system, what are the coordinates of point

Question

In a rectangular coordinate system, what are the coordinates of point C?

(1) The distance between the point C and point A(5, 5) is 4 units
(1) The distance between the point C and point B(1, 5) is 2 units

gmatophobia · Answer

Statements 1 and Statement 2 are individually not sufficient. As C can be any point on the circumference of the circle with the given coordinates and radius.

For example, in statement 1, C can be a point on the circumference of the circle with the center at (5,5) and radius = 4 units.

Hence, the statements individually are not sufficient and we can eliminate A, B, and D.

Combined

From statement 1 we know 
 (x-5)^2 + (y-5)^2 = 4^2  -- Eq(1)

From statement 2 we know 
 (x-1)^2 + (y-5)^2 = 2^2 -- Eq(2)

Eq(1) - Eq(2)
 (x-5)^2 - (x-1)^2 = 4^2 -2^2

(x-5+x-1)(x-5-x+1) = (4+2)(4-2)

(2x-6)(-4) = 6*2

(2x-6) = -3

x = \frac{3}{2}

y =

(x-1)^2 + (y-5)^2 = 2^2

(\frac{3}{2}-1)^2 + (y-5)^2 = 2^2

(y-5)^2 = 4 - \frac{1}{4}

(y-5)^2 = 3.75

y = 5 \pm \sqrt{3.75}

We can have two pairs of (x,y), therefore, the statements combined are also not sufficient to find a unique pair of (x,y)

Option E

axeller · Answer

1 min solution for E. Not the best drawing but shows that there could be two answers. WhatsApp Image 2024-01-09 at 22.02.36_dde0d52c.jpg

SamzayWarrior · Answer

In such a question, how do we avoid the C trap? once I got the value of x- I presumed we can get the value of y and thus both statements are sufficient- without taking further time to plug fractional value. Can you help?KarishmaB Bunuel chetan2u GMATPill

chetan2u · Answer

Whenever you have square of a variable, as in this instance  y^2 , it will surely have two values. 
In most cases, two different real values, while in some, the values could be same. Not in GMAT, but you can have certain complex values too.

So always check for the two values when you have quadratic equation.

Bunuel · Answer

I also find quick sketches very useful: https://gmatclub.com/forum/download/file.php?id=74231 With statement (1), point C can be anywhere on the green circle, and with statement (2), it can be anywhere on the purple circle. These circles intersect at two points, indicating that point C could be located at either of them. These possible locations are marked in orange on the image above. Untitled.png

KarishmaB · Answer

I would also do what  Bunuel  did above. 
When I read - "what are the coordinates of point C?" I do not think I have to find C(x, y). I think - "Is C a unique point?"
So I quickly draw the given points as shown by Bunuel above. 
I would always try to eliminate variables even when the question gives me some. Rarely would I introduce some myself!

In a rectangular coordinate system, what are the coordinates of point

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In a rectangular coordinate system, what are the coordinates of point

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