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Lines and Angles | PRMO 2019 | Question 7

Try this beautiful problem from the PRMO, 2019 based on Lines and Angles.

Lines and Angles - PRMO 2019


On a clock, there are two instants between 12 noon and 1 pm when the hour hand and the minute hand are at right angles. the difference in minutes between these two instants written as a+\frac{b}{c} where a b c are positive integers with b\lt c and \frac{b}{c} in the reduced form. find a+b+c.

  • is 107
  • is 51
  • is 840
  • cannot be determined from the given information

Key Concepts


Lines

Algebra

Angles

Check the Answer


Answer: is 51.

PRMO, 2019, Question 7

Higher Algebra by Hall and Knight

Try with Hints


Minute hand turns 6 (in degrees) in 1 min and hour hand turns half (in degree) in 1 min

x min after 12 is 6x -\frac{x}{2}=90 or 270 (in degrees) then x =16\frac{4}{11} or 49\frac{1}{11}

Difference 32\frac{8}{11} then a+b+c=32+8+11=51.

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Try this beautiful problem from the PRMO, 2019 based on Lines and Angles.

Lines and Angles - PRMO 2019


On a clock, there are two instants between 12 noon and 1 pm when the hour hand and the minute hand are at right angles. the difference in minutes between these two instants written as a+\frac{b}{c} where a b c are positive integers with b\lt c and \frac{b}{c} in the reduced form. find a+b+c.

  • is 107
  • is 51
  • is 840
  • cannot be determined from the given information

Key Concepts


Lines

Algebra

Angles

Check the Answer


Answer: is 51.

PRMO, 2019, Question 7

Higher Algebra by Hall and Knight

Try with Hints


Minute hand turns 6 (in degrees) in 1 min and hour hand turns half (in degree) in 1 min

x min after 12 is 6x -\frac{x}{2}=90 or 270 (in degrees) then x =16\frac{4}{11} or 49\frac{1}{11}

Difference 32\frac{8}{11} then a+b+c=32+8+11=51.

Subscribe to Cheenta at Youtube


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