If k is a positive two-digit integer, what is the tens digit of k ?
1) the sum of the tens digit of k and the units digit of k is 5. 2) the tens digit of k + 6 is 3.

The required positive two digit integer is 32.

Step-by-step explanation:

Given : If k is a positive two-digit integer.

1) The sum of the tens digit of k and the units digit of k is 5.

2) The tens digit of k + 6 is 3.

To find : What is the tens digit of k ?

Solution :

Let the two digit integer be

According to question,

By 1, The sum of the tens digit of k and the units digit of k is 5.

i.e.

The possible cases from counting are,

14, 41, 23, 32, 50  whose sum is 5.

By 2, The tens digit of k + 6 is 3.

Which means take number which is added by 6 and give tens digit as 3.

The only possible case is when k=32

As 32+6=38 where tens digit is 3.

Therefore, The required positive two digit integer is 32.