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If x^2<25, which of the following expressions must be true?

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If x^2<25, which of the following expressions must be true?  [#permalink]

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New post 14 Apr 2019, 06:19
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If x^2<25, which of the following expressions must be true?

I. |x-3| < 10
II. |2x – 3| < 8
III. |2x^2| < 42


A. I only
B. II only
C. III only
D. I and II only
E. I and III only
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Re: If x^2<25, which of the following expressions must be true?  [#permalink]

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New post 14 Apr 2019, 08:52
mangamma wrote:
If x^2<25, which of the following expressions must be true?

I. |x-3| < 10
II. |2x – 3| < 8
III. |2x^2| < 42


A. I only
B. II only
C. III only
D. I and II only
E. I and III only


\(x^2<5^2.......-5<x<5\)..

So our choices should contain this range..
I. |x-3|<10....
x-3<10 or X<13 AND 3-x<10.....x>-7.....Thus -7<x<13..
YES, it contains -5<x<5

II. |2x-3|<8....
2x-3<8 or 2x<11 or x<5.5 AND 3-2x<8.....2x>-5....Thus -2.5<x<5.5..
No, it does not contain -5<x<-2.5

III. \(|2x^2|<42.....x^2<21\)
This does not contain 21<x^2<25..

Only I

A
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Re: If x^2<25, which of the following expressions must be true?  [#permalink]

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New post 14 Apr 2019, 18:06
Hi,
Thank You for such a detailed solution.

Kindly resolve my confusion here:

X lies between -5 and 5. Then, which other expression would hold true: any expression wherein x is a subset of -5 to 5.
3rd option was the only one in which this was true. Please help.
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Re: If x^2<25, which of the following expressions must be true?  [#permalink]

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New post 14 Apr 2019, 19:03
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vinayakvaish wrote:
Hi,
Thank You for such a detailed solution.

Kindly resolve my confusion here:

X lies between -5 and 5. Then, which other expression would hold true: any expression wherein x is a subset of -5 to 5.
3rd option was the only one in which this was true. Please help.


x lies between -5 and 5...
in option III, X lies between -√21 and √21, that is -4.6 and 4.6..
This range does not cover for X between -5 and -4.6 nor for X between 4.6 and 5.
If x is 4.7, then it is not contained in option III.. so, III is not correct
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Re: If x^2<25, which of the following expressions must be true?  [#permalink]

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New post 15 Apr 2019, 06:03
Thank You! I had supposed the opposite. Very silly of me.
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Re: If x^2<25, which of the following expressions must be true?   [#permalink] 15 Apr 2019, 06:03
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If x^2<25, which of the following expressions must be true?

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