cards are always tricky!!
Algebra
Level
1
A pack contains n cards numbered from 1 to n. Two consecutive cards are removed from the pack and the sum of the numbers of the remaining cards is 1224. If the smaller of the numbers on the removed cards is k, then k-20=
The answer is 5.
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1 solution
no. of cards = n cards taken out --> k , k+1 (n² + n)/2 – (2k + 1) = 1224, n² + n – 4k = 2450, k = (n² + n – 2450)/4, ————— (1)
But since 1 ≤ k ≤ n – 1, 1 ≤ (n² + n – 2450)/4 ≤ n – 1 Simplify the inequality and getting : 49 < n < 51, which imply n = 50 Substitute to (1) and getting k = 25, so k – 20 = 5