Question

When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then
mainder is 9. What is the number?
B.
349
339
A
D.
Data inadequate
369
c.

Answer 1

Let Z be the number

Z = 13x + 11 where x is the quotient when Z is divided by 13

Z = 17y + 9 where y is the quotient when Z is divided by 17

13x + 11 = 17y + 9

13x + 2 = 17y since x and y are quotients they should be whole numbers . Since y has to be a whole number the left hand side should be multiple of 17

The least possible value of x satisfying the condition is 9 and y will be 7

The answer is 13*9 + 11 = 128 or it is 17*7 + 9 = 128

This is the least number possible. There will be multiple answers and will increase in multiples 17*13 = 221 like 349 , 570, etc