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

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mangamma
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If x^2<25, which of the following expressions must be true? [#permalink] 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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chetan2u
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Re: If x^2<25, which of the following expressions must be true? [#permalink] New post  14 Apr 2019, 08:52
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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] 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] 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] New post  15 Apr 2019, 06:03
Thank You! I had supposed the opposite. Very silly of me.
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If x^2<25, which of the following expressions must be true? [#permalink] New post  19 Jun 2021, 03:23
chetan2u wrote:
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


But the question is which of the following must be true. and we are given that -5<x<5. So the option which shows that X values lie in the range of -5<x<5 will be the answer. options A, B have values of X outside this range. So that can or cannot be true. -4.6<x<4.6 comes in the range of solution of -5<x<5 so this is must be true. Please clarify why you are considering the opposite way?
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Re: If x^2<25, which of the following expressions must be true? [#permalink] New post  19 Jun 2021, 06:19
Nidhijain94

To fulfill/satisfy -5<x<5 , x has to have bigger range. Only -7<x<13 works. Hence A is the Answer.
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Re: If x^2<25, which of the following expressions must be true? [#permalink] New post  19 Jun 2021, 06:41
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Nidhijain94 wrote:
chetan2u wrote:
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


But the question is which of the following must be true. and we are given that -5<x<5. So the option which shows that X values lie in the range of -5<x<5 will be the answer. options A, B have values of X outside this range. So that can or cannot be true. -4.6<x<4.6 comes in the range of solution of -5<x<5 so this is must be true. Please clarify why you are considering the opposite way?



Nidhi,

A simpler question will be
If x=10, then what must be true.
1) x>0
2) x is even

Similarly in this question, we know x lies between 5 and -5, so what must be true.
Anything that contains this entire range. It doesn’t matter that it may contain lot of unnecessary numbers, same way as x=10 means x>0.

If we were looking for the range of x, then we cannot take any value that does not fit in. But here we are not looking at the range but what MUST be true.
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Re: If x^2<25, which of the following expressions must be true? [#permalink] New post  21 Jun 2021, 14:24
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Solution:

A "must be true" question involves locating just "one plug in point" that can disprove the statement and help in elimination.

If we

In II- Take x=-4 then x^2 < 25 |2x – 3| = |2(-4) - 3| =|-11| =11 and 11 is NOT less than 8 (Eliminate B and D)

In III- Take x =4.9 then x^2 < 25 and this would give us |2x^2| = |2*4.9*4.9| = 48.02 and it is NOT less than 42.(Eliminate C and E)

(option a)

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Re: If x^2<25, which of the following expressions must be true? [#permalink] New post  24 Mar 2024, 00:13
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