What is x? (1) |2x| = 6x 4 (2) |x|

Question

What is x?

(1) |2x| = 6x – 4
(2) |x| < 2

Bunuel · Answer

Are you sure you copied the question correctly? Is it real MGAMT question?

From (1) x = 1 and from (2) |x| < 1. The statements contradict each other. Also, you gave the OA as D, while (2) is not sufficient on its own.

WarriorWithin · Answer

Hi @Banuel

This was written in my notes, but after reviewing it - it is |x| < 2 and the answer is only A is sufficient. Sorry of this mistake. I will correct it.

Kinshook · Answer

Asked: What is x?

(1) |2x| = 6x – 4
Case 1: x>0
2x = 6x - 4
4x = 4
x = 1; Feasible since x>0
Case 2: x<0
-2x = 6x - 4
8x = 4
x = 1/2 : Not feasible since x<0
x = 1 is the only solution
SUFFICIENT

(2) |x| < 1
-1 < x < 1
This gives a range of x. No unique value of x
NOT SUFFICIENT

IMO A

Bunuel · Answer

Got it. Thank you!

For the corrected version the answer is A indeed. From (1) x cannot be negative since in this case RHS (6x – 4) will be negative and LHS, which is an absolute value (|2x|), cannot equal to a negative number. So, x must be positive. This means that |2x| = 2x, and thus 2x = 6x – 4, which gives x = 1. (2) is clearly insufficient and the answer is A.

Hope it helps.

wali786 · Answer

From statement 1 we x=4 or 1/2. Do one always need to plug in the the numbers in the equation such as in statement 1? Or is there a shortcut or trick?

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What is x? (1) |2x| = 6x 4 (2) |x| < 2

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