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1 <=x<=5 ans 1>=y>=-2

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Carcass
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1 <=x<=5 ans 1>=y>=-2 [#permalink] New post   09 Jan 2023, 11:06
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\(1 \leq x \leq 5\)

\(1 \geq y \geq -2\)


Quantity A
Quantity B
xy
-10



A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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D
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Re: 1 <=x<=5 ans 1>=y>=-2 [#permalink] New post   09 Jan 2023, 14:29
can someone explain why is the answer not A? since for all possible value of xy, xy > -10?
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Re: 1 <=x<=5 ans 1>=y>=-2 [#permalink] New post   10 Jan 2023, 01:37
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You have to test all the boundaries you do have

so xy is

1*1=1
5*1=5
-2*1=-2
5*-2=-10

Therefore

xy is between -10 and 5

\(-10 \leq xy \leq 5\)

xy could be -10 and the answer is C or all values up to 5 and the answer is A

D is the answer
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Re: 1 <=x<=5 ans 1>=y>=-2 [#permalink] New post   15 Jan 2023, 07:57
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x is positive and any number between 1 and 5

y is positive or negative between 1 and -2

xy could be anything as a combination of these numbers

D is the answer
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Re: 1 <=x<=5 ans 1>=y>=-2 [#permalink] New post   03 May 2023, 05:10
Carcass wrote:
You have to test all the boundaries you do have

so xy is

1*1=1
5*1=5
-2*1=-2
5*-2=-10

Therefore

xy is between -10 and 5



Dear Carcass, is xy between -10 and 5 or between -10 and 1?
It doesn't affect the answer, I'm just wondering about the correct range.
Thank you!
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Re: 1 <=x<=5 ans 1>=y>=-2 [#permalink] New post   03 May 2023, 08:35
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Flip the inequality with y

\(1 \leq x \leq 5\)

\(-2 \leq y \leq 1\)

here we have to find all the min and max values

You have to multiply vertically and in cross

-2,-10,1,and 5

therefore xy is between the lowermost values which is -10 and the uppermost value which is 5 included
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Re: 1 <=x<=5 ans 1>=y>=-2 [#permalink] New post   03 May 2023, 08:51
Carcass wrote:
Flip the inequality with y

\(1 \leq x \leq 5\)

\(-2 \leq y \leq 1\)

here we have to find all the min and max values

You have to multiply vertically and in cross

-2,-10,1,and 5

therefore xy is between the lowermost values which is -10 and the uppermost value which is 5 included


I'm trying to understand why 1 would not be in the range.

So x can be 1 and y can be 1, then xy = 1. This will not be included in the range?

Thank you!
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Re: 1 <=x<=5 ans 1>=y>=-2 [#permalink] New post   03 May 2023, 09:42
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You have to consider the extremes when we are dealing with minimum and maximum questions, the boundaries.

1 is inside the range
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Re: 1 <=x<=5 ans 1>=y>=-2 [#permalink] New post   03 May 2023, 09:49
Carcass wrote:
You have to consider the extremes when we are dealing with minimum and maximum questions, the boundaries.

1 is inside the range


Oh, now I see!!! Thank you so much!
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Re: 1 <=x<=5 ans 1>=y>=-2 [#permalink]
03 May 2023, 09:49
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