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The absolute value of (x + a) will be the greatest if x is the coordin

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EgmatQuantExpert
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The absolute value of (x + a) will be the greatest if x is the coordin [#permalink] New post   Updated on: 11 Mar 2024, 07:32
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The absolute value of (x + a) will be the greatest if x is the coordinate of which of the five points P, Q, R, S and T on the number line above?

(A) P
(B) Q
(C) R
(D) S
(E) T

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This is a Warm-up Question for the e-GMAT Question Series on Absolute Value.

Provide your solution below. Kudos for participation. Happy Solving! :-D

Best Regards
The e-GMAT Team

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E

Originally posted by EgmatQuantExpert on 19 May 2015, 06:33.
Last edited by Bunuel on 11 Mar 2024, 07:32, edited 6 times in total.
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Re: The absolute value of (x + a) will be the greatest if x is the coordin [#permalink] New post   01 Jul 2015, 06:10
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carrerswitch wrote:
Hi,

Could you please explain why modulus of (x+a) means distance from -a to x and not distance from a to x?

Thanks


Hi carrerswitch,

Let me explain the concept with a different example. When we need to find the distance between two numbers, let's say 5 and 2, we write 5 - 2 = 3.

In the same way when we need to find the distance between 5 and -2 we write 5 - (-2) = 5 + 2 = 7.

Now we know that |x| = Distance of x from 0 i.e. | x - 0|.

So, distance of x from a can be written as | x - a|. In the same manner distance of -a from x can be written as | x - (-a)| = |x + a|

Hope this helps :)

Regards
Harsh
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Re: The absolute value of (x + a) will be the greatest if x is the coordin [#permalink] New post   22 May 2015, 02:40
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Official Explanation

Correct Answer: E

The question asks us to maximize the value of |x+a|

|x+a| measures the distance of x from the point –a on the number line.

Out of the five points, the point that is the most distant from –a is T.

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Re: The absolute value of (x + a) will be the greatest if x is the coordin [#permalink] New post   19 May 2015, 14:03
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EgmatQuantExpert wrote:


The absolute value of (x + a) will be the greatest if x is the coordinate of which of the five points P, Q, R, S and T on the number line above?
(A) P
(B) Q
(C) R
(D) S
(E) T

This is a Warm-up Question for the e-GMAT Question Series on Absolute Value.

Provide your solution below. Kudos for participation. The Official Answer and Explanation will be posted on 20th May.

Till then, Happy Solving! :-D

Best Regards
The e-GMAT Team


Mod (x+a) represents distance of x from -a. T is farthest from -a and hence mod (x+a) will be maximum at T. Confirm by substituting x with (-a-2) and (a+4) respectively.
Option E.
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Re: The absolute value of (x + a) will be the greatest if x is the coordin [#permalink] New post   01 Jul 2015, 06:43
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EgmatQuantExpert wrote:


The absolute value of (x + a) will be the greatest if x is the coordinate of which of the five points P, Q, R, S and T on the number line above?
(A) P
(B) Q
(C) R
(D) S
(E) T


For maximum Absolute value of (x + a)

1) Sign of both x and a must be same i.e. either both must be positive or both must be negative i.e. both x and a must be on the same side on Number Line

2) We need to pick the the highest value of a or x and both a and x must be farthest from Zero so that their absolute values are maximum.

The figure says it all that both conditions are satisfied when the value of x is taken at Point T (Farthest from Zero) and we can observe that a is positive (being towards the right of Zero on Number Line)

Answer: Option E
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Re: The absolute value of (x + a) will be the greatest if x is the coordin [#permalink] New post   09 Dec 2017, 08:58
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|x+a| = |x-(-a)|
The point which lies farthest from the point x= -a on the number line.
Thus its point T.
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Re: The absolute value of (x + a) will be the greatest if x is the coordin [#permalink] New post   11 Mar 2024, 07:22
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Re: The absolute value of (x + a) will be the greatest if x is the coordin [#permalink]
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