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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

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
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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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EgmatQuantExpert


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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|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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Hello from the GMAT Club BumpBot!

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