1.

What is the 'tens' digit of 2013^2-2013? (^ as in raised in power)(If you could explain too what the 'tens digit is because I'm not a native speaker and cannot understand it. I would really appreciate it! )

Answer»

Understanding

First, we are in BASE 10. Each digit value we write has powers of 10 multiplied to it.

For example, 123=10^2+2\times10^1+<klux>3</klux>\times10^0. If 10 is multiplied, it is the TENS digit. Here tens digit value is 2.

Sol.

Now let's solve our problem.

When we find a product of two integers, the first digit comes from below the tens digit.

Similarly, the tens digit comes from below the hundreds digit.

13^2-13

=169-13

=156

Hence the tens digit is 5.

Question

(I'm REALLY SORRY for leaving the wrong answer to your question.)

The numbers p,q,r, and s satisfy the following equations:

  • p+2q+3r+4s=k
  • 4p=3q=2r=s  

What is the smallest value of 'k' for which p,q,r and are all positive integers?

Sol.

Here, s is a multiple of 12 because of factors 4, 3, 2.

The least value of s=12, hence other values are p=3, q=4, r=6.

\therefore k=3+8+18+48=77

(A-20//B-24//C-25//D-77//E-154)

Hope you understood!



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