JEE Main 2021 · 24 Feb · Shift 1 · Mathematics Q85

MathematicsInteger+4 / -1Question 85 of 90

Let A = {n ∈ ℕ : n is a 3-digit number}

B = {9k + 2 : k ∈ ℕ}

and C = {9k + l : k ∈ ℕ} for some l (0 < l < 9)

If the sum of all the elements of the set A ∩ (B ∪ C) is 274 × 400, then l is equal to _______.

Your answer

Answer and worked solution

Official answer: 5

B part. Three-digit numbers $\equiv2\pmod9$ : 101 to 992, 100 terms, sum 54650.

C part must add $109600-54650=54950$ with no overlap ( $l\ne2$ ). For $l=5$ : 104 to 995, 100 terms, sum $50\times1099=54950$ .

Answer: 5

JEE Main 2021 · 24 Feb · Shift 1, Mathematics question 85