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

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Director
Joined: 26 Feb 2006
Posts: 639
If x is a number such that –2 ≤ x ≤ 2, which of the following has the  [#permalink]

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Updated on: 03 Jul 2015, 08:26
3
9
00:00

Difficulty:

35% (medium)

Question Stats:

63% (01:14) correct 37% (01:15) wrong based on 659 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-is-a-number-such-that-2-x-2-which-of-the-following-112162.html

Originally posted by Himalayan on 12 Jan 2007, 23:44.
Last edited by Bunuel on 03 Jul 2015, 08:26, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
VP
Joined: 01 May 2006
Posts: 1476
Re: If x is a number such that –2 ≤ x ≤ 2, which of the following has the  [#permalink]

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13 Jan 2007, 01:57
2
(A) for me

1) |3*x-1| is peaking when x=-2 at |3*-2 - 1| = 7

2) |x^2 + 1| is peaking when either x=2 or x=-2 at |2^2 + 1| = 5

3) |3 - x| is peaking when x=-2 at |3 - (-2)| = 5

4) |x - 3| is peaking when x=-2 at |(-2) - 3| = 5

2) |x^2 - x| = |x*(x-1)| is peaking when x=-2 (the farest value of x from the roots 0 and 1) at |(-2)^2 - (-2)| = 6
Senior Manager
Joined: 24 Nov 2006
Posts: 256
Re: If x is a number such that –2 ≤ x ≤ 2, which of the following has the  [#permalink]

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13 Jan 2007, 07:51
AK wrote:
Agree with Fig, Master of Absolute

Yep. One more for A (good job, Fig).

As the stem asks for the highest absolute value, one can just plug in the value of x that will make the corresponding expression peak. For example, in "3 - x" one has to use x = -2 to get 3 -- 2 = 5. With practice this is immediate.
Math Expert
Joined: 02 Sep 2009
Posts: 59587
Re: If x is a number such that –2 ≤ x ≤ 2, which of the following has the  [#permalink]

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03 Jul 2015, 08:27
3
Himalayan wrote:
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

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.

B. x^2 + 1 --> max for x=-2 or x=2 --> |2^2 + 1|=5.

E. x^2 – x --> max for x=-2 --> |(-2)^2 - (-2)|=6.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-is-a-number-such-that-2-x-2-which-of-the-following-112162.html
_________________
Re: If x is a number such that –2 ≤ x ≤ 2, which of the following has the   [#permalink] 03 Jul 2015, 08:27
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