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# For which of the following values of k does the equation (x - 1)(x - 2

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Math Expert
Joined: 02 Sep 2009
Posts: 59074
For which of the following values of k does the equation (x - 1)(x - 2  [#permalink]

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19 Mar 2019, 00:22
00:00

Difficulty:

65% (hard)

Question Stats:

42% (01:51) correct 58% (01:36) wrong based on 31 sessions

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For which of the following values of k does the equation $$\frac{x-1}{x-2} = \frac{x-k}{x-6}$$ have no solution for x?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3141
Re: For which of the following values of k does the equation (x - 1)(x - 2  [#permalink]

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19 Mar 2019, 00:58
1

Solution

Given:
• An equation: (x−1)/(x−2) = (x−k)/(x−6)

To find:
• The value of k, for which the equation does have no solution.

Approach and Working:
Simplifying the equation, we get:
• (x−1)/(x−2) = (x−k)/(x−6)
Or, (x – 1) (x – 6) = (x – 2) (x – k)
Or, x^2 – 7x + 6 = x^2 – x (2 + k) + 2k
Or, 7x – 6 = (2 + k) x – 2k
Or, x (7 – 2 – k) = 6 – 2k
Or, x = (6 – 2k)/(5 – k)

For no solution of this equation, 5 – k = 0, implies k = 5

Hence, the correct answer is option E.

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Re: For which of the following values of k does the equation (x - 1)(x - 2   [#permalink] 19 Mar 2019, 00:58
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