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If r and s are positive integers, each greater than 1, and if 11(s - 1

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If r and s are positive integers, each greater than 1, and if 11(s - 1  [#permalink]

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New post 08 Mar 2019, 01:35
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Question Stats:

52% (02:05) correct 48% (01:41) wrong based on 21 sessions

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If r and s are positive integers, each greater than 1, and if 11(s - 1) = 13(r - 1), what is the least possible value of r + s?

A. 2
B. 11
C. 22
D. 24
E. 26

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Re: If r and s are positive integers, each greater than 1, and if 11(s - 1  [#permalink]

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New post 08 Mar 2019, 03:59
Bunuel wrote:
If r and s are positive integers, each greater than 1, and if 11(s - 1) = 13(r - 1), what is the least possible value of r + s?

A. 2
B. 11
C. 22
D. 24
E. 26


13*11= 143
so at s= 14 and r =12
we get 11(s - 1) = 13(r - 1)
IMO E ; 26
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Re: If r and s are positive integers, each greater than 1, and if 11(s - 1  [#permalink]

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New post 08 Mar 2019, 05:31
Bunuel wrote:
If r and s are positive integers, each greater than 1, and if 11(s - 1) = 13(r - 1), what is the least possible value of r + s?

A. 2
B. 11
C. 22
D. 24
E. 26



11(s - 1) = 13( r - 1 )

13 is not divisible by 11. So, r - 1 is divisible by 13. Least value of r = 14. Therefore (14 - 1) becomes multiple of 13.

The same way as above, 11 is not divisible by 13 .Therefore, s - 1 is a multiple of 11. Least value of s =12.

r = =14

s = 12

r + s = 14 + 12 = 26.

E is the correct answer.
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Re: If r and s are positive integers, each greater than 1, and if 11(s - 1   [#permalink] 08 Mar 2019, 05:31
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If r and s are positive integers, each greater than 1, and if 11(s - 1

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