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Algebra Arithmetic Math Olympiad PRMO

Rational Number and Integer | PRMO 2019 | Question 9

Try this beautiful problem from the Pre-RMO, 2019 based on Lines and Angles. You may use sequential hints to solve the problem.

Try this beautiful problem from the PRMO, 2019 based on Rational Number and Integer.

Rational Number and Integer – PRMO 2019


let the rational number \(\frac{p}{q}\) be closest to but not equal to \(\frac{22}{7}\) among all rational numbers with denominator < 100, find p-3q.

  • is 107
  • is 14
  • is 840
  • cannot be determined from the given information

Key Concepts


Rational number

Algebra

Integer

Check the Answer


Answer: is 14.

PRMO, 2019, Question 9

Higher Algebra by Hall and Knight

Try with Hints


First hint

|\(\frac{22}{7}-\frac{p}{q}\)|=|\(\frac{22q-7p}{7q}\)| then |22q-7p|=1 for smallest value

Second Hint

and q=99 then p=311

Final Step

p-3q=311-(3)(99)=311-297=14.

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