As easy as A-B-C!

Algebra Level 4

Consider the real numbers A , B , C . . . . . . . . . . . . Z A,B,C............Z such that: E V I L EVIL = 5 31 \frac{5}{31} , L O V E LOVE = 6 29 \frac{6}{29} and I M O IMO = 7 3 \frac{7}{3} .

If O M O OMO = m n \frac{m}{n} where m m and n n are relatively prime positive integers. Find the value of m + n m+n .


The answer is 579.

Yash Singhal by Yash Singhal , 22, India

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2 solutions

From ratio EVIL / LOVE = (5/31)/(6/29) = 145/186 = I/O implies that I = 145O/186 giving IMO = (145/186)OMO = 7/3. Here, OMO = (7/3)(186/145) = 434/145 giving 434+145 = 579.

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Efren Medallo
May 15, 2015

You can easily get O M O OMO by doing

LOVE x IMO / EVIL

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