Sequence and progression
Algebra
Level
pending
A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of the numbers on the remaining cards is 1224. If the smaller to the numbers on the removed cards is K, then K-20 is equal to?
The answer is 5.
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1 solution
1224=n(n+1)/2 - (2K+1)..........(main equation)
If we choose two cards with lowest sum possible then:
n(n+1)/2 - 3 > or equal to 1224 n(n+1)> or equal to 2454 n> or equal to 50..........(1)
If we choose two cards with highest sum possible then: n(n+1)/2 - (2n-1)< or equal to 1224 n^2 - 3n < or equal to 2446 n< or equal to 50.............(2)
From (1) and (2) n=50 By putting value of n in main equation K=25 Hence, K-20=5