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f(x) = |x 2| + |2.5 x| + |3.6 x|

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KarunMendiratta
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f(x) = |x 2| + |2.5 x| + |3.6 x| [#permalink] New post   24 Sep 2021, 10:34
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\(f(x) = |x – 2| + |2.5 – x| + |3.6 – x|\)

Quantity A
Quantity B
Minimum value of \(f(x)\)
2.5


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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B
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motion2020
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Re: f(x) = |x 2| + |2.5 x| + |3.6 x| [#permalink] New post   24 Sep 2021, 14:27
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the absolute is minimized when its value is 0

setting up pair-wise function as below

\(min f(x)=|x–2|, x=2\)
\(min f(x)=|2.5-x|, x=2.5\)
\(min f(x)=|3.6-x|, x=3.6\)

we can notice that x is different, and we must choose one value for \(x\), because it's one and not pair-wise function

let us choose the middle value, \(x=2.5\), \(f(2.5)=|2.5–2|+|2.5–2.5|+|3.6–2.5|=1.6\)

answer is B, as Quantity A=1.6 < Quantity B=2.5


KarunMendiratta wrote:
\(f(x) = |x – 2| + |2.5 – x| + |3.6 – x|\)

Quantity A
Quantity B
Minimum value of \(f(x)\)
2.5


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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Re: f(x) = |x 2| + |2.5 x| + |3.6 x| [#permalink] New post   12 Nov 2021, 10:55
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WHY you didn't choose 3.6?
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motion2020
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Re: f(x) = |x 2| + |2.5 x| + |3.6 x| [#permalink] New post   13 Nov 2021, 13:03
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taukir wrote:
WHY you didn't choose 3.6?
because I am checking the distance and need to minimize the distance.

The inquired value of 3.6 is not median, and hence is far away from both the first and the second elements in our ordered set of values: {2, 2.5, 3.6}
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Re: f(x) = |x 2| + |2.5 x| + |3.6 x| [#permalink] New post   17 May 2022, 01:46
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OA is C.
But i am getting B.
when x is 2, f(x) is 2.1
when x is 2.5, f(x) is 1.6.
it means the minimum value though anything, is certainly less than 2.5.

Hence, B is the answer

Can somebody provide solution ?

Posted from my mobile device
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f(x) = |x 2| + |2.5 x| + |3.6 x| [#permalink] New post   17 Jul 2022, 10:57
AjinkyaGupta88 wrote:
OA is C.
But i am getting B.
when x is 2, f(x) is 2.1
when x is 2.5, f(x) is 1.6.
it means the minimum value though anything, is certainly less than 2.5.

Hence, B is the answer

Can somebody provide solution ?

Posted from my mobile device


The right answer is indeed B - which is the 'official' answer to the question, in the first post.
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Re: f(x) = |x 2| + |2.5 x| + |3.6 x| [#permalink] New post   19 Sep 2023, 16:45
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Re: f(x) = |x 2| + |2.5 x| + |3.6 x| [#permalink]
19 Sep 2023, 16:45
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