What is the value of the positive integer k?

Statement 1

K is an integer of the form 3x + 2. But there are infinite such integers possible (2, 5, 8, 11, 14, 17, 20, 23, 26... ). Not sufficient.


Statement 2

K is an integer of the form 5y + 1. But there are infinite such integers possible (1, 6, 11, 16, 21, 26,...). Not sufficient.


Combining the two statements

K = 3x + 2 = 5y + 1.
So k is an integer which leaves remainder '2' when divided by '3', and also leaves remainder '1' when divided by '5'. We can see from the analysis of two statements that '11' is the first such number which satisfies both these conditions.

To find general formula for such kind of numbers, one method is to find LEAST such number by trial/error method. Once we have identified the least number, there is a general formula for such number which is:
K = (Least number identified) + (LCM of divisors)*z, where 'z' is any non negative integer.

So for our given question, once we have identified least value of K to be 11, we can write a general formula for K as:
K = 11 + (LCM of 3&5)*z or 11 + 15*z

But since z can take infinite values, our number K can also take infinite values. Eg., 11, 26, 41, 56, ...
Thus combined also the statements are not sufficient to answer the question.


Hence E answer