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Same approach : it's better to plug 2 values mentally with the respect of abs always positive (or 0) than to solve the original equation (saving energy... 4 hours is long)

If |d-9| = 2d, then d= [#permalink]
23 Jan 2011, 07:37

1

This post received KUDOS

Expert's post

aurobindo wrote:

If |d-9| = 2d, then d= (A) -9 (B) -3 (C) 1 (D) 3 (E) 9

You can approach this problem in several ways. For example: given |d-9| = 2d --> as LHS (|d-9|) is an absolute value then it's non-negative so RHS (2d or simply d) must also be non-negative thus answer choices A and B are out. Next you can quickly substitute the values to see that d=3 satisfies given inequality: |3-9|=|-6|=6=2*3.

Or you can try algebraic approach and expand |d-9| for 2 ranges: If \(0\leq{d}\leq{9}\) then \(-(d-9)=2d\) --> \(d=3\) --> you have an answer D right away; Just to check the second range: If \({d}>9\) then \(d-9=2d\) --> \(d=-9\) --> not a valid solution as \(d\) cannot be negative (also this value is not in the range we are considering).

Re: If |d-9| = 2d, then d= [#permalink]
02 Oct 2013, 00:35

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Re: If |d-9| = 2d, then d= [#permalink]
22 Oct 2014, 10:36

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Re: If |d-9| = 2d, then d= [#permalink]
15 Jan 2015, 21:47

Expert's post

Hi All,

Since the answer choices to this question are NUMBERS, we can use them (along with some Number Property knowledge) to quickly get to the solution by TESTing THE ANSWERS.

We're given |D - 9| = 2D and we're asked to solve for D

Since the "left" side of the equation will end up as either a 0 or a POSITIVE, the "right side" of the equation CAN'T be negative, so we know that D CANNOT be NEGATIVE. Eliminate A and B.

The solution MUST be one of the remaining 3 answers, so we can just TEST them until we find the correct one.

Could D = 1? |1-9| = |-8| = 8 2D = 2(1) = 2 -8 does NOT = 2 Eliminate C.

Could D = 3? |3-9| = |-6| = 6 2(3) = 6 6 DOES = 6 This IS the answer.

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