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If |d-9| = 2d, then d= (A) -9 (B) -3 (C) 1 (D) 3 (E) 9 [#permalink]
 18 Jan 2007, 07:49
Question Stats:
70% (01:41) correct
29% (00:54) wrong based on 48 sessions
If |d-9| = 2d, then d=
(A) -9
(B) -3
(C) 1
(D) 3
(E) 9
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Manager
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if d>9, on solving eqn u get d = -9 which is impossible since d>9.
if d<9, on sloving u get d = 3. Hence D is correct answer
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Director
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d has two solutions : d=3 and d=-9
D !
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Senior Manager
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IMO
2d is an absolute value, so d can't be negative.
Out of the +ve nos. d can be only 3
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SVP
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Sumithra wrote: IMO
2d is an absolute value, so d can't be negative.
Out of the +ve nos. d can be only 3
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) 
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If |d-9| = 2d, then d=
(A) -9
(B) -3
(C) 1
(D) 3
(E) 9
now the two eqs are
1) when (d-9) > 0
d-9 = 2d
d = -9
2) when (d-9) < 0
9-d = 2d
d = 3
the two initial solns are d = -9 and 3
but when we substitute d = -9 in original equation we get
|-9-9| = 2 * -9
18 = -18
which is not possible
Hence only solution is d = 3.
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Intern
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Schools: ISB, IIM-A
WE 1: 4 yrs in finance
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vsaxenaGMAT wrote: if d>9, on solving eqn u get d = -9 which is impossible since d>9.
if d<9, on sloving u get d = 3. Hence D is correct answer GOOD EXPLANATION 
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Rahul
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GMAT Club team member
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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 can not be negative (also this value is not in the range we are considering). Answer: D. Hope it's clear.
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