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Which is larger? (Posted on 2008-06-30) Difficulty: 2 of 5
Which is larger, where n is a natural number:
     99n + 100n   or   101n ?

See The Solution Submitted by pcbouhid    
Rating: 4.0000 (4 votes)

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Solution Solution | Comment 3 of 7 |

99n + 100n > 101n where natural number n < 49, and
99n + 100n < 101n where natural number n >= 49

9948 + 10048 =
1617290140942288185336108527714065
4376666780078410155984946941482067
05262569099287208400715275201

and 10148 =
1612226077682464366162063721580560
4379588397845435231244069431329964
71824157105135854515307284801

As can be seen, 9948 + 10048  > 10148 

9949 + 10049 =
1611117239532865303482747442436924
7832900112277626054425097472067246
3820994340829433631670812244899

and 10149 =
1628348338459289009823684358796366
0423384281823889583556510125643264
3654239867618721306046035764901

As can be seen, 9949 + 10049  < 10149 


  Posted by Dej Mar on 2008-06-30 11:23:46
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