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August 1, 2020

Nearest value | PRMO 2018 | Question 14

Try this beautiful problem from the PRMO, 2018 based on Nearest value.

Nearest Value - PRMO 2018

If x=cos1cos2cos3.....cos89 and y=cos2cos6cos10....cos86, then what is the integer nearest to \(\frac{2}{7}log_2{\frac{y}{x}}\)?

  • is 107
  • is 19
  • is 840
  • cannot be determined from the given information

Key Concepts




Check the Answer

Answer: is 19.

PRMO, 2018, Question 14

Higher Algebra by Hall and Knight

Try with Hints

First hint



[ since cos\(\theta\)=sin(90-\(\theta\)) from cos 46 upto cos 89 and 2sin\(\theta\)cos\(\theta\)=sin2\(\theta\)]

Second Hint


[ since sin\(\theta\)=cos(90-\(\theta\))]


[ since cos\(\theta\)=sin(90-\(\theta\))]

Final Step


[since \(cos4cos8cos12...cos88\)










\(\frac{2}{7}log_2{\frac{y}{x}}\)=\(\frac{2}{7} \times \frac{133}{2}\)=19.

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