Question

K is a 3 digit number .K1, K2, K3 are numbers obtained when K is in base 5,7 and 9 respectively. The units place in K1, K2, K3 is 2. How many such possible K values are there
a) 0 b) 1 c) 2 d) 3

Answer 1

it is b)1

hope it is correct

Answer 2

The correct option is d because there are 3 possible values of K.

Given,

K is a 3 digit number .

K1, K2, K3 are numbers obtained when K is in base 5,7 and 9 respectively.

The units place is 2 .

To Find,

possible values of K.

Solution,

firstly we have to take the L.C.M of the given bases

L.C.M of 5,7 and 9 = 315.

let the possible values be x.

number = 315•x+2.

let x=1,

315×1+2=317.

let x=2,

315×2+2=632.

let x=3,

315×3+2=947.

only 317,632and947 is possible in 3 digit numbers.

The correct option is d because there are 3 possible values of K.

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