Kogarashiid
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A box contains only green, red, blue and yellow counters. There is always at least one green counter amongst any 27 counters chosen from the box; always at least one red counter amongst any 25 counters chosen; always at least one blue amongst any 22 counters chosen and always at least one yellow amongst any 17 counters chosen. What is the largest number of counters that could be in the box?

(A) 27 (B) 29 (C) 51 (D) 87 (E) 91

Don't you dare say 91.

Sagot :

Francocanacariid

The largest number of counters that could be in the box is 91.

Since a box contains only green, red, blue and yellow counters, and there is always at least one green counter amongst any 27 counters chosen from the box; always at least one red counter amongst any 25 counters chosen; always at least one blue amongst any 22 counters chosen and always at least one yellow amongst any 17 counters chosen, to determine what is the largest number of counters that could be in the box among the options in the list, the following calculation must be performed :

  • 27/27 = 1
  • 29/27 = 1.07
  • 51/27 = 1.88
  • 87/27 = 3.22
  • 91/27 = 3.37

Therefore, the largest number of counters that could be in the box is 91.

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