What is the value of x for which the 7-digit number 7583x24 is divisible by 44?

A number divisible by 44 must be divisible by both 4 and 11. 1️⃣ Divisibility by 4: Last two digits = 24, which is divisible by 4 ✅ 2️⃣ Divisibility by 11: Rule → (Sum of odd-place digits) − (Sum of even-place digits) = multiple of 11. Digits: 7 5 8 3 x 2 4 Odd places (1st, 3rd, 5th, 7th): 7 + 8 + x + 4 = 19 + x Even places (2nd, 4th, 6th): 5 + 3 + 2 = 10 → (19 + x) − 10 = 9 + x For divisibility by 11 → 9 + x = 0, 11, 22... So x = 2 makes (9 + 2 = 11), divisible by 11 ✅