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If |d - 9| = 2d, then d=
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10 Mar 2021, 09:39
10 Mar 2021, 09:39
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If |d - 9| = 2d, then d=
(A) -9
(B) -3
(C) 1
(D) 3
(E) 9
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(A) -9
(B) -3
(C) 1
(D) 3
(E) 9
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Joined: 10 Apr 2015
Posts: 6218
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Re: If |d - 9| = 2d, then d=
[#permalink]
10 Mar 2021, 10:20
10 Mar 2021, 10:20
1
Carcass wrote:
If |d - 9| = 2d, then d=
(A) -9
(B) -3
(C) 1
(D) 3
(E) 9
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
(A) -9
(B) -3
(C) 1
(D) 3
(E) 9
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
We have two cases to consider:
d - 9 = 2d and d - 9 = -2d
case a: If d - 9 = 2d, then d = -9
When we check this solution for extraneous roots, we get: |-9 - 9| = (2)(-9)
Simplify to get: |-18| = -18
NO GOOD!
So, d = -9 is NOT a valid solution
case b: If d - 9 = -2d, then d = 3
When we check this solution for extraneous roots, we get: |3 - 9| = (2)(3)
Simplify to get: |-6| = 6
WORKS!
So, d = 3 IS a valid solution.
Answer: D
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Status:GRE Quant Tutor
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WE:Engineering (Computer Software)
If |d - 9| = 2d, then d=
[#permalink]
29 Dec 2021, 04:17
29 Dec 2021, 04:17
Given that |d - 9| = 2d and we need to find the value of d
Let's solve this using two methods
Method 1: Substitution
Now LHS (Left Hand Side) = Absolute value of a number => it can never be negative
and RHS (Right Hand Side) = 2d
=> negative values of d cannot satisfy this as LHS will be non-negative and RHS will become negative
So, options A and B are out.
Now, let's substitute the value of d from choices C,D,E and see which one satisfies the equation
(C) 1. Put d=1 in |d - 9| = 2d and see if satisfies or not
=> | -1 -9 | = |-10| = 10 \(\neq\) 2*-1 = -2 => NOT POSSIBLE
(D) 3. Put d=3 in |d - 9| = 2d and see if satisfies or not
=> | 3 -9 | = |-6| = 6 = 2*3 = 6 => POSSIBLE
(E) 9. Put d=9 in |d - 9| = 2d and see if satisfies or not
=> | 9 -9 | = |0| = 0 \(\neq\) 2*9 = 18 => NOT POSSIBLE
Method 2: Algebra
|d - 9| = 2d
=> d-9 = 2d or d-9 = -2d
=> 2d-d = -9 or d+2d = 9
=> d = -9 or 3d = 9 or d = \(\frac{9}{3}\) = 3
=> d = -9 or d = 3
If we substitute these values of d back in |d-9| = 2d then we will see that d=-9 does not satisfy the equation
=> d = 3
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
Let's solve this using two methods
Method 1: Substitution
Now LHS (Left Hand Side) = Absolute value of a number => it can never be negative
and RHS (Right Hand Side) = 2d
=> negative values of d cannot satisfy this as LHS will be non-negative and RHS will become negative
So, options A and B are out.
Now, let's substitute the value of d from choices C,D,E and see which one satisfies the equation
(C) 1. Put d=1 in |d - 9| = 2d and see if satisfies or not
=> | -1 -9 | = |-10| = 10 \(\neq\) 2*-1 = -2 => NOT POSSIBLE
(D) 3. Put d=3 in |d - 9| = 2d and see if satisfies or not
=> | 3 -9 | = |-6| = 6 = 2*3 = 6 => POSSIBLE
(E) 9. Put d=9 in |d - 9| = 2d and see if satisfies or not
=> | 9 -9 | = |0| = 0 \(\neq\) 2*9 = 18 => NOT POSSIBLE
Method 2: Algebra
|d - 9| = 2d
=> d-9 = 2d or d-9 = -2d
=> 2d-d = -9 or d+2d = 9
=> d = -9 or 3d = 9 or d = \(\frac{9}{3}\) = 3
=> d = -9 or d = 3
If we substitute these values of d back in |d-9| = 2d then we will see that d=-9 does not satisfy the equation
=> d = 3
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
