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max and min using inequalities

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by selango » Sun Jul 25, 2010 7:22 pm
(x+1)^2<=36

-->x+1<=6 or x+1<=-6

x<=5 or x>=-7

-7=<x<=5

(y-1)^2<=64

-->y-1<=8 or y-1<=-8

-7=<y<=9

Maximum value of xy=49

Minimum value of xy=0

Please correct me if I am wrong..
Last edited by selango on Sun Jul 25, 2010 7:50 pm, edited 1 time in total.
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by Stuart@KaplanGMAT » Sun Jul 25, 2010 7:25 pm
selango wrote:(x+1)^2<=36

-->x+1<=6 or x+1<=-6

x<=5 or x>=-7

-7=>x<=5

(y-1)^2<=64

-->y-1<=8 or y-1<=-8

-7=>y<=9

Maximum value of xy=49

Minimum value of xy=0

Please correct me if I am wrong..
hi!

Everything was great until your final conclusion:
Minimum value of xy=0
We can pick x=-7 and y=+9 to get xy = -63 for our minimum value.
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by selango » Sun Jul 25, 2010 7:31 pm
Just missed it...Thanks stuart..
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by Rahul@gurome » Sun Jul 25, 2010 7:36 pm
It is given that (y-1)^2 < 64 and not that (y-1)^2 <= 64.
This means -7 < y < 9 and so y is not attaining the exact values of -7, and 9.
So can we answer the question?
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by dinesh19aug » Sun Jul 25, 2010 7:45 pm
Hello,
Max value of xy is possible if X and Y both are positive so that xy>0 or BOTH X and Y are negative.

Eq 1: (x+1)^2 <= 36
(x+1)<= sqrt(36)
-6 <= (x+1) <= 6
-7 <= x <= 5

Eq2: (y-1)^2 < 64
-7 < y < 9

Now max value can be found by multiple when x,y>0 or +ive, which gives us 45
OR
when x,y<0==> which gives us 49 .......... However I DO NOT agree with this. If you look at the question value of X>= 7
So X =-7
BUT Y >-7, then we cannot take the value of Y = -7, it should be -6
Hence XY = -7 * -6 = 42, which is less than 45 (x,y>0)

So max value = 45

Same holds true for minm value ===> X = -7 and Y<9, so max possible value is -8
Hence Min value = -7 * 8 = 56

If the question was something like combine the two eqn

Ex : -7 <= X <= 5 ---- Eq1
-7< Y < 9 ----- Eq2

Then XY will be ==> -49 < XY <45
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by Stuart@KaplanGMAT » Sun Jul 25, 2010 11:35 pm
Rahul@gurome wrote:It is given that (y-1)^2 < 64 and not that (y-1)^2 <= 64.
This means -7 < y < 9 and so y is not attaining the exact values of -7, and 9.
So can we answer the question?
You're correct - I just looked at the first reply and didn't read the original post.

With the conditions as stated in the OP, this couldn't be an actual GMAT question (it would have to be less than or equal to, as phrased by the 2nd poster).
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by outreach » Sun Jul 25, 2010 11:52 pm
Maximum value of xy=5*9=45
Minimum value of xy=-7*9=-63
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