Project ForgeWhat is the sum of the missing digits in the subtraction problem below?
5 _ _ _ _ - 4 8 _ 8 9 --------- 1 1 1 1
- A8
- B10
- C11
- Cannot be determined
Explanation
Working the standard column subtraction with borrows from the units place leftward, the units and tens columns force the minuend's last two missing digits to 0 (with borrows propagating left), and the ten-thousands column (5-4-borrow=0) forces a borrow out of the thousands column, which forces the thousands digit to 0 and forces the hundreds column to also borrow — but that hundreds-column borrow condition (subtrahend's hundreds digit minus minuend's hundreds digit = 8, i.e. e = b + 8) has TWO valid single-digit solutions: b=0,e=8 (giving minuend 50000, subtrahend 48889, missing-digit sum 8) and b=1,e=9 (giving minuend 50100, subtrahend 48989, missing-digit sum 10). Since both fully satisfy the printed subtraction with no further constraint to break the tie, the sum genuinely cannot be uniquely determined from the given information.
Source: GATE ME 2017 Session 1 (ME-1) (2017)
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