If |x - 3| - |x - 4| = |x - 6|, what is the value of x?

Question

(1) x^2 = 25
(2) x^2 - 8x + 15 = 0

AndrewN · Answer

Provided the question has been transcribed correctly, it could not appear on the GMAT™ as such. The GMAT™ will always provide consistent information about an unknown between the two statements . Since Statement (1) looks like an easier entry point, how about we start there? Statement (1) x^2 = 25 |x| = 5 x = 5 or -5 Only one of these solutions is valid. |(5) - 3| - |(5) - 4| = |(5) - 6| |2| - |1| = |-1| 2 - 1 = 1 √ |(-5) - 3| - |(-5) - 4| = |(-5) - 6| |-8| - |-9| = |-11| 8 - 9 = 11 X So, Statement (1) is SUFFICIENT , since x can only equal 5. But when we look at Statement (2) , we can see pretty quickly that x will not be equal to 5: x^3 - 8x + 15 = 0 (5)^3 - 8(5) + 15 = 0 125 - 40 + 15 = 0 100 = 0 X The point of a well written DS question is to provide consistent information between statements, to see if they reveal enough overlapping information to answer the question on their own. It cannot be true that x can equal 5 in one case and not 5 in another. The other statement might not allow us to figure out that x = 5, but we should never see conflicting information. The graph of the polynomial in Statement (2) shows that the solution is around -3.5. Screen Shot 2022-07-11 at 14.34.47.png As I said before, either this question was not transcribed correctly, or it is not a GMAT™-like DS question. - Andrew

kntombat · Answer

aarish2102 , could you respond as soon as possible to what  AndrewN  posted on top.

It would be much appreciated.

AndrewN · Answer

Thank you,   kntombat  . I am next to positive that Statement (2) should read

x^2 - 8x + 15 = 0

Solving then yields one solution that overlaps with the one valid solution from Statement (1).

(x - 3)(x - 5) = 0

x = 3 or 5

Since we know from Statement (1) that 5 is a valid solution, we only need to consider 3 in the original equation.

|(3) - 3| - |(3) - 4| = |(3) - 6|

|0| - |-1| = |-3|

0 - 1 = 3   X

Hence, 3 cannot be a valid solution, and only 5 remains. The answer should, in fact, be (D), but only if the original Statement (2) shows  x  squared rather than cubed.

- Andrew

kntombat · Answer

AndrewN , I agree with you 100%.

AndrewN · Answer

Well, it looks like   Bunuel   took care of the issue for us. Thank you,   Bunuel  . (I have no idea how you manage to peek into these corners of the site when the World Cup competition is going on, but your efforts are much appreciated.)

- Andrew

If |x - 3| - |x - 4| = |x - 6|, what is the value of x?

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