Bunuel wrote:

The number 2135, when divided by a positive integer n, leaves a remainder r. What is the value of n?

(1) The number 2315, when divided by n, also leaves the same remainder r .

(2) The number 2585, when divided by n, also leaves the same remainder r .

Bunuel wrote:

The number 2135, when divided by a positive integer n, leaves a remainder r. What is the value of n?

(1) The number 2315, when divided by n, also leaves the same remainder r .

(2) The number 2585, when divided by n, also leaves the same remainder r .

2135

If

n= 2 then r = 1

n= 3 then r = 2

n= 4 then r = 3

n= 6 then r = 5

n= 8 then r = 1

n= 9 then r = 2

(1) 2315 = pn + r

if

n= 2 then r = 1

n= 3 then r = 2

n= 4 then r = 3

Not sufficient

(2) 2585

if

n=2 then r = 1

n=3 then r = 2

Not sufficient

On combining also not sufficient

E

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