CAT 2020 Exam Shift 1 Solved Paper

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Question : 64 of 76

Marks: +1, -0

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

a>0

, is

5050
4466
5544
4864

Solution:

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

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