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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

Re: The absolute value of (x + a) will be the greatest if x is the coordin [#permalink]

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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

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.
_________________

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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