Categories
I.S.I. and C.M.I. Entrance

Hundred Integers | ISI-B.Stat Entrance | TOMATO 82

Try this beautiful Hundred Integers problem on Number system from TOMATO useful for ISI B.Stat Entrance. You may use sequential hints to solve the problem.

Try this beautiful hundred integers problem based on Remainder useful for ISI B.Stat Entrance.

Hundred Integers | ISI B.Stat Entrance | Problem-82


Let \(x_1,x_2,……,x_100\) be hundred integers such that the sum of any five of them is 20. Then..

  • the largest \(x_i\) equals 5
  • the smallest \(x_i\) equals to 3
  • \(x_{17} = x_{83}\)
  • none of the foregoing statements is true

Key Concepts


Number theory

Divisor

integer

Check the Answer


But try the problem first…

Answer:\(x_{17} = x_{83}\)

Source
Suggested Reading

TOMATO, Problem 82

Challenges and Thrills in Pre College Mathematics

Try with Hints


First hint

Let us take the numbers be \(x_i , x_j , x_k ,x_l , x_m \)

Now \(x_i + x_j + x_k + x_l + x_m = 20\) and again \(x_i + x_j + x_k + x_l + x_n = 20\)

Can you now finish the problem ……….

Second Hint

From the above relation there are three case arise that….

1)\(x_m = x_n\)

2)All the integers are equal.

3)\(x_{17} =x_{83}\)

So the correct answer is \(x_{17} =x_{83}\)

Subscribe to Cheenta at Youtube


Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.