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|x 1| = 3 |x 3|
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20 Nov 2023, 02:09
20 Nov 2023, 02:09
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|x − 1| = 3 |x − 3|
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
|x| |
2 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
Re: |x 1| = 3 |x 3|
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21 Nov 2023, 22:52
21 Nov 2023, 22:52
1
|x − 1| = 3 |x − 3| --Eqn1
we can write √x^2 = |x| when the power of root is even
so keeping that in mind we can write as √(x-1)^2 = 3 * √(x-3)^2
Squaring both the sides , we get , (x-1)^2 = 9(x-3)^2 --> x^2 -2x+1 = 9(x^2 -6x +9) --> x^2 -2x+1 = 9x^2 -54x+81
--> 8x^2 -52x + 80 =0 , Dividing both sides by 4 we get --> 2x^2 -13x +20 = 0 --> 2x^2 -8x -5x +20=0
--> (2x-5)(x-4)=0 , thus x =5/2 or 4 .
Since we had x on both sides of the original equation Eqn1 , lets plug back the values to check for any extraneous solution . If we plug x=5/2 in the original equation we see LHS = RHS ( |5/2 − 1| = 3 |5/2 − 3| ) , similarly if we plug x=4 in the original equation we see LHS = RHS , thus both the solutions for x is valid
Now given Quantity B = 2, which is less than both 5/2 and 4 , thus answer A
we can write √x^2 = |x| when the power of root is even
so keeping that in mind we can write as √(x-1)^2 = 3 * √(x-3)^2
Squaring both the sides , we get , (x-1)^2 = 9(x-3)^2 --> x^2 -2x+1 = 9(x^2 -6x +9) --> x^2 -2x+1 = 9x^2 -54x+81
--> 8x^2 -52x + 80 =0 , Dividing both sides by 4 we get --> 2x^2 -13x +20 = 0 --> 2x^2 -8x -5x +20=0
--> (2x-5)(x-4)=0 , thus x =5/2 or 4 .
Since we had x on both sides of the original equation Eqn1 , lets plug back the values to check for any extraneous solution . If we plug x=5/2 in the original equation we see LHS = RHS ( |5/2 − 1| = 3 |5/2 − 3| ) , similarly if we plug x=4 in the original equation we see LHS = RHS , thus both the solutions for x is valid
Now given Quantity B = 2, which is less than both 5/2 and 4 , thus answer A
gmatclubot
Re: |x 1| = 3 |x 3| [#permalink]
21 Nov 2023, 22:52
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