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gina runs every 4 days, cycles every 32 days and jogs every 12 days. if she did all three activities on tuesday, in how many days and on what day of the week will she do all three activities again on the same day?

Answer :

FICHOHGO

Gina will perform all 3 activities again on the same day after 96 days which will be on a Sunday.

  • Running days = 4
  • Cycling days = 32
  • Jogging days = 12

To obtain the number of days after which all three activities will be done on the same day, we obtain the lowest common multiple of 4, 32 and 12 :

Multiples of :

  • 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104

  • 32 = 32, 64, 96, 128

  • 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108

The lowest mutlple common of 4, 32 and 12 is 96 ;

Therefore, Gina will perform all the three activities together after 96 days, which will be on a Sunday

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