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# If k is an integer then find the value of (5^124*k−4)/(125^41*k+3)

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If k is an integer then find the value of (5^124*k−4)/(125^41*k+3)  [#permalink]

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11 Apr 2019, 23:07
00:00

Difficulty:

65% (hard)

Question Stats:

17% (02:16) correct 83% (02:45) wrong based on 6 sessions

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If k is an integer then find the value of $$\frac{5^{124k−4}}{125^ {41k+3}}$$

(1)$$(2k)* (2r-k – 1) = 26 x 1$$, where r is an integer

(2) $$13 + 2k = 3k + r$$, where r is an integer

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Re: If k is an integer then find the value of (5^124*k−4)/(125^41*k+3)  [#permalink]

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12 Apr 2019, 07:56
If k is an integer then find the value of 5124k−412541k+35124k−412541k+3

(1)(2k)∗(2r−k–1)=26x1(2k)∗(2r−k–1)=26x1, where r is an integer

(2) 13+2k=3k+r13+2k=3k+r, where r is an integer

Sol: The question stem basically asks what is the value of K?

statement 1:

(2k)∗(2r−k–1)=26x1(2k)∗(2r−k–1)=26x1, where r is an integer

Clearly k is not equal to 0.Because if k = 0 ,L.H.S is not equal to R.H.S

Let k=1
Then statement 1 will be reduced to 21*(2r)=26x1
The units digit of RHS is 1. This is possible when r=1. r cannot take any other value. At this point I am least concerned about x.

Note: To maintain L.H.S to R.H.S,k and r cannot take any other value except 1

Sufficient.

Statement2:

13+2k=3k+r, where r is an integer

Upon rearranging we have
k=13-r
Given r is an integer. We can have a unique value for k.
Insufficient.

Hope i arrived at the correct solution.

Cheers. Kudos if you like my post.
Re: If k is an integer then find the value of (5^124*k−4)/(125^41*k+3)   [#permalink] 12 Apr 2019, 07:56
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