PSLE Letters Q, K and U formed a patten as shown below.
Q K Q U Q Q K Q U Q Q K Q U Q . . .
If there are 61 'Q', what is the greatest possible number of letters in the pattern?
Number of letters in 1 set of Q K Q U Q = 5
Number of letters 'Q' in 1 set of Q K Q U Q = 3
Number of sets of 3 'Q' if there are 61 'Q'
= 61 ÷ 3
= 20 r 1
If the remainder is 1, there is 1 'Q' and the largest possible number of letters is the final incomplete set is 2. (Q K)
If the remainder is 2, there are 2 'Q' and the largest possible number of letters is the final incomplete set is 4. (Q K Q U)
Greatest possible number of letters
= 20 x 5 + 2
= 100 + 2
= 102
Answer(s): 102