Question

The mean of all 4 -digit even natural numbers of the form 'aabb', where a >0, is

• A. 5050
• B. 4466
• C. 5544
• D. 4864

Answer 1

Answer: (C)

5544

Answer 2

The correct answer is (C): $5544$

The sum of possible even digit numbers in the form aabb is $1100 + 1122 + 1144 1166 + 1188 + 2200 + 2222 + 2288 +$ .......$9900 + 9922 + 9988$ i.e. ($45$ numbers)

⇒ 1100+1100+1100+1100+1100+22+44+66+88+2200+2200+2200+2200+2200+22+44+66+88+…$$+9900+9900+9900+990+9900+22+44+66+88

$⇒ 5(1100+2200+.....9900)+9(22+44+66+88)5×1100(1+2+....9)+9×22(1+2+3+4)$

$⇒ 5500(45) + 45 × 44 = 45(5544)$

Hence mean = $5544$