INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

March 24, 2020

Number and Series | Number Theory | AIME I, 2015

Try this beautiful problem from the American Invitational Mathematics Examination, AIME 2015 based on Number Theory and Series.

Number Theory and Series - AIME 2015


The expressions A = \((1 \times 2)+(3 \times 4)+....+(35 \times 36)+37\) and B = \(1+(2 \times 3)+(4 \times 5)+....+(36 \times 37)\) are obtained by writing multiplication and addition operators in an alternating pattern between successive integers. Find the positive difference between integers A and B.

  • is 107
  • is 648
  • is 840
  • cannot be determined from the given information

Key Concepts


Series

Theory of Equations

Number Theory

Check the Answer


Answer: is 648.

AIME, 2015, Question 1

Elementary Number Theory by David Burton

Try with Hints


First hint

B-A=\(-36+(2 \times 3)+....+(2 \times 36)\)

Second Hint

=\(-36+4 \times (1+2+3+....+18)\)

Final Step

=\(-36+(4 \times \frac{18 \times 19}{2})\)=648.

Subscribe to Cheenta at Youtube


Leave a Reply

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

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com