sanju09 wrote:If (x + 2) ^2 = 9 and (y + 3) ^2 = 25, then what is the maximum value of x/y?
(A) 1/8
(B) 1/2
(C) 5/8
(D) 5/2
(E) 10/3
Let's determine values for x and y.
(x + 2)^2 = 9
√(x + 2)^2 = √9
|x + 2| = 3
We need to determine the value of x when (x + 2) is positive and when (x + 2) is negative.
x + 2 = 3
x = 1
OR
-(x + 2) = 3
-x - 2 = 3
-x = 5
x = -5
So x = 1 or x = -5.
In a similar fashion, we determine the value of y.
(y + 3)^2 = 25
√(y + 3)^2 =√25
|y + 3| = 5
We need to determine the value of y when (y + 3) is positive and when (y + 3) is negative.
y + 3 = 5
y = 2
OR
-(y + 3) = 5
-y - 3 = 5
-y = 8
y = -8
y = 2 or y = -8
We can maximize the value of x/y if x and y are both positive or if x and y are both negative. If x and y are both positive, then x/y = 1/2. If x and y are both negative, then x/y = -5/-8 = 5/8. Since 5/8 > 1/2, the maximum value of x/y is 5/8.
Answer:
C
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