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If x is a number such that –2 ≤ x ≤ 2 which of the following

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Re: Inequality - Absolute value  [#permalink]

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New post 20 Nov 2013, 10:03
Bunuel wrote:
emailmkarthik wrote:
Hey Bunuel,

Do you have any alternate easier method to tackle this problem?


If x is a number such that –2 ≤ x ≤ 2, which of the following has the largest possible absolute value?
A. 3x – 1
B. x^2 + 1
C. 3 – x
D. x – 3
E. x^2 – x

First of all notice that we can eliminate options C and D right away: \(|3-x|=|x-3|\), so these two options will have the same maximum value and since we cannot have two correct answers in PS questions then none of them is correct.

Evaluate each option by plugging min and max possible values of x:

A. 3x – 1 --> max for x=-2 --> |3*(-2)-1|=7.
Attachment:
MSP40111b1fh8bi1bf48ff500001bihb6c5hie997cf.gif


B. x^2 + 1 --> max for x=-2 or x=2 --> |2^2 + 1|=5.
Attachment:
MSP566209hcf53gca1831500002g3b78339ag7a6gh.gif


E. x^2 – x --> max for x=-2 --> |(-2)^2 - (-2)|=6.
Attachment:
MSP5861i671ha12e2ie48c00005gbb4caa2heiag53.gif


Answer: A.



Not necessary for solving this question but how did you draw graph of x2 -x ?
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Re: If x is a number such that –2 ≤ x ≤ 2 which of the following  [#permalink]

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New post 24 Mar 2014, 07:20
Today is so not my day... Keep getting easy Qs wrong. Missed the 'absolute' part in this one... But apart from that, I don't understand what this whole argument/discussion is about. Surely it's quite straightforward (if you're not careless like me, that is)
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Re: If x is a number such that –2 ≤ x ≤ 2 which of the following  [#permalink]

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New post 10 Mar 2016, 23:20
do not overlook the word "absolute".
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Re: If x is a number such that –2 ≤ x ≤ 2 which of the following  [#permalink]

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New post 06 Jan 2017, 11:14
–2 ≤ x ≤ 2
x = -2,-1,0,1,2
Substitute
3x - 1 = 3(-2) - 1 = -7 ; | - 7 | = 7
Rest all max absolute value is 5,6,2
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If x is a number such that –2 ≤ x ≤ 2 which of the following  [#permalink]

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New post 22 Jan 2017, 10:36
Great Question.
Here is what i did in this one ->
We need the maximum absolute value.
So actually we just need the maximum magnitude as the sign won't matter.
Option 1->Maximum at x=-2 => Value=-7 =>Magnitude =7
Option 2->Maximum at x=-2 or 2=> Value=5 =>Magnitude =5
Option 3->Maximum at x=-2=>Value=5=>Magnitude =5
Option 4->Maximum at x=-2=>Value=-5=>Magnitude=5
Option 5->Maximum at x=-2=>Value=6=>Magnitude=6

Hence A.

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Re: If x is a number such that –2 ≤ x ≤ 2 which of the following  [#permalink]

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New post 21 Jun 2017, 14:53
x is a number such that –2 ≤ x ≤ 2

In order to solve this problem you can substitute values of +2 and -2 based and can quickly get the absolute value.

A. 3x – 1 =====> 3*-2-1 = -7 = l-7l = 7 ======> Maximum ab. value
B. x^2 + 1 =====> 4+1 = 5
C. 3 – x =====> 2-(-2) = 4
D. x – 3 =====> 3-(-2) = 5
E. x^2 – x =====> 4-(-2) = 6

So, only 7 is the maximum value.

A is the correct answer.
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If x is a number such that –2 ≤ x ≤ 2 which of the following  [#permalink]

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New post 31 Oct 2018, 10:02
Hi Bunuel,
Thanks for the wonderful explanation but i have a doubt regarding when i must substitute the largest value of a variable to attain largest ans choice and when the value must be minimum for a case such as this. Could you please throw some insight on the same or share links?
This would help a great ton.

Thanks in advance.

Can anyway tag Bunuel on this? im unable too as this says i have to be a user for more than 5 days to have attachments in my post dunno why :(
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If x is a number such that –2 ≤ x ≤ 2 which of the following &nbs [#permalink] 31 Oct 2018, 10:02

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