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Inequality

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by rintoo22 » Fri Mar 22, 2013 1:25 pm
If |d - 9| = 2d, then d =

A. -9
B. -3
C. 1
D. 3
E. 9

d-9 = 2d => d = -9 ---------1
-d+9 = 2d => d = 3 ---------2

No.2 satisfies the value so the answer should be D. However the QA, the answer is given as B. Am I missing somthing ?
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by Anju@Gurome » Fri Mar 22, 2013 2:07 pm
rintoo22 wrote:No.2 satisfies the value so the answer should be D. However the QA, the answer is given as B. Am I missing somthing ?
No, you are correct.
d cannot have any negative value, as 2d |d - 9| ≥ 0
rintoo22 wrote:If |d - 9| = 2d, then d =
If d ≥ 9, |d - 9| = (d - 9) = 2d ---> d = -9 --> Not possible as we started with d ≥ 9
If d < 9, |d - 9| = -(d - 9) = 2d ---> d = 3

Hence, d = 3

The correct answer is D.
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

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by srcc25anu » Fri Mar 22, 2013 3:33 pm
The easiest approach here would be to just plug in answer choices.

A. If d= -9, then |-9-9|=|-18|=18
2d = 2*-9 = -18 INCORRECT

B. If d= -3, then |-3-9|=|-12|=12
2d = 2*-3 = -6 INCORRECT

C. If d= 1, then |1-9|=|-8|=8
2d = 2*1 = 2 INCORRECT

D. If d=3, |3-9|=|-6|=6
2d = 2*3 = 6. Correct.

hence ANS D
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by indiheats » Sat Mar 23, 2013 11:42 am
The way I would go about is finding the two potential answers first

a. + |d-9| = 2d ; d-9=2d; -9=3d; d=-3
b - |d-9| = 2d ; -d+9=2d; 9=d

Then substituting both -3 and 9 for "d" in the original statement |d-9| = 2d shows that only -3 is a viable answer... because both sides equal each other


The answer is D, -3.
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