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← JEE Main 2022 · 29 Jul · Shift 1
MathematicsInteger+4 / -1Question 29 of 90

JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 29

Let S = {4, 6, 9} and T = {9, 10, 11, ..., 1000}. If A = {a1+a2+⋯+aka_1+a_2+\dots+a_k : k ∈ N, a1,a2,a3,…,aka_1,a_2,a_3,\dots,a_k ∈ S}, then the sum of all the elements in the set T − A is equal to _______.

Answer and worked solution

Official answer: 11

Even numbers. Fours and sixes make every even number from 4 up.

Odd numbers need an odd number of 9s: 99, then 9+4=139+4=13, 9+6=159+6=15, and every odd number from 13 on. In T, only 11 is missed.

Answer: 11