if -1/2<or equal to x<or equal to-1/3
and -1/4<or equal to y< or equal to -1/5
which is the minimum value of xy^2 ?
choices
-1/75
-1/50
-1/48
-1/32
-1/16
the explanation says that the minimum value means farthest from 0. thats true , yes. however i believe farthest from 0 we achive by taking lowest possibilies of x and y ( that is 1/3 form x and 1/5 from y) and get -1/75 as answerr
but the official answer they took was 1/2 and 1/4 and got -1/32
i am all confused here
please help
kaplan 800 question
This topic has expert replies
Hi,
Personnally, when manipulating inequatlities of negative numbers I convet them to inequalties of positive numbers to make them regular and easy to treat;
Fo this one,I would take the positive number (-x) which would be 1/3 < -x < 1/2
I would consider y^2 as the same of (-y)^2 and get,
1/25 < y^2 < 1/16 as 1/5 <-y < 1/4
then, the product -xy^2 as a positive number, would fit the following inequality : 1/75 < -xy^2 < 1/32
Now, it's easy to get xy^2 inequality as follows:
-1/32 < xy^2< -1/75
it's then obvious that the minimum value of xy^2 is -1/32
I hope I am right
Personnally, when manipulating inequatlities of negative numbers I convet them to inequalties of positive numbers to make them regular and easy to treat;
Fo this one,I would take the positive number (-x) which would be 1/3 < -x < 1/2
I would consider y^2 as the same of (-y)^2 and get,
1/25 < y^2 < 1/16 as 1/5 <-y < 1/4
then, the product -xy^2 as a positive number, would fit the following inequality : 1/75 < -xy^2 < 1/32
Now, it's easy to get xy^2 inequality as follows:
-1/32 < xy^2< -1/75
it's then obvious that the minimum value of xy^2 is -1/32
I hope I am right
I appologize for my Frenchy-English.
I am working on it.
I am working on it.
- jayhawk2001
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For min and max values question, it is important to know the sign of
the end-result.
In this case, we know that the xy^2 will be negative. So, minimum
value of xy^2 will have to be a number which is farther away from zero.
(A simple example would be to compare -1 and -3, -3 is the minimum since it is farther away from 0 compared to -1.)
So, min (xy^2) is in essence min (x) * max (y^2) which yields
-1/2 * 1/16 = -1/32. Please note that we can split min (xy^2) as
above only because we already know what the sign of the
end result will be.
the end-result.
In this case, we know that the xy^2 will be negative. So, minimum
value of xy^2 will have to be a number which is farther away from zero.
(A simple example would be to compare -1 and -3, -3 is the minimum since it is farther away from 0 compared to -1.)
So, min (xy^2) is in essence min (x) * max (y^2) which yields
-1/2 * 1/16 = -1/32. Please note that we can split min (xy^2) as
above only because we already know what the sign of the
end result will be.
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- Stacey Koprince
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Also, just FYI - this might be what is messing you up:
-75 is further from zero than -32.
BUT -1/75 is closer to zero than -1/32.
Think about two fractions that are much easier to understand: -1/2 and -1/3. Which one is closer to zero? -1/3. And that has the larger number in the denominator.
-75 is further from zero than -32.
BUT -1/75 is closer to zero than -1/32.
Think about two fractions that are much easier to understand: -1/2 and -1/3. Which one is closer to zero? -1/3. And that has the larger number in the denominator.
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Stacey Koprince
GMAT Instructor
Director of Online Community
Manhattan GMAT
Contributor to Beat The GMAT!
Learn more about me