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Subtracting a Number with Reversed Digits

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June 8, 2009
geometry3D geometry

Problem Statement

From a two-digit number N N we subtract the number with the digits reversed and find that the result is a positive perfect cube. Then: <spanclass=′latex−bold′>(A)</span> N cannot end in 5<spanclass=′latex−bold′>(B)</span> N can end in any digit other than 5<spanclass=′latex−bold′>(C)</span> N does not exist<spanclass=′latex−bold′>(D)</span> there are exactly 7 values for N<spanclass=′latex−bold′>(E)</span> there are exactly 10 values for N <span class='latex-bold'>(A)</span>\ {N}\text{ cannot end in 5}\qquad\\ <span class='latex-bold'>(B)</span>\ {N}\text{ can end in any digit other than 5}\qquad \\ <span class='latex-bold'>(C)</span>\ {N}\text{ does not exist}\qquad \\ <span class='latex-bold'>(D)</span>\ \text{there are exactly 7 values for }{N}\qquad \\ <span class='latex-bold'>(E)</span>\ \text{there are exactly 10 values for }{N}
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