Question

given that the 4 letters O,L,Y,M represent 4 different digits and the sum of the 4 numbers OLYM,LOMY,YMOL,MYLO, is equals to 29997.What is the value of the sum O+L+Y+M? (a)10 ,(b) 15, (c) 20, (d) 27 , (e) 30

Answer 1

Answer: (d) 27

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Reason:

The four numbers are OLYM, LOMY, YMOL, and MYLO.

The units digits of each of those are M, Y, L, and O in that order.

Adding those units digits will produce either a one or two digit number. Either way, the result will involve a units digit that matches the units digit of the sum 29997. In that case it's 7.

Therefore, the answer must have a units digit of 7. The only answer choice possible is choice (d).

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Examples:

OLYM + LOMY + YMOL + MYLO = 3798+7389+9837+8973 = 29997

O + L + Y + M = 3 + 7 + 9 + 8 = 27

and

OLYM + LOMY + YMOL + MYLO = 4698+6489+9846+8964 = 29997

O + L + Y + M = 4 + 6 + 9 + 8 = 27

and

OLYM + LOMY + YMOL + MYLO = 5796+7569+9657+6975 = 29997

O + L + Y + M = 5 + 7 + 9 + 6 = 27

I used computer software to generate these examples. There are others.