Because of an error, a printing machine cannot print 6 and 8. The machine is used to print page numbers on a volume of an encyclopedia. What number is printed on the 503rd page of the encyclopedia? (747, 979, 959, 757)

3 years, 6 months ago

From 1-99, there are 19 numbers that have digit 6 and 19 numbers that have digit 8. While adding these two, we are counting the numbers '68' and '86' twice. So the number of numbers from 1 to 99 that have the digits either 6 or 8 are 19+19-2 = 36. Similarly, from 101-200 also there are 36 such numbers and so on.

So, until 503, there are 36*5 = 180 such numbers.

=> From 504-599, there are 97 numbers out of which 36 numbers contain either 6 or 8. Therefore 97-36 = 61 numbers are printed from 504-599.

=> 180 - 61 = 119 more are left. Number from 600-699 are not printed and hence 64 numbers are printed from 700 to 799. 119-64 = 55 more are left.

Again numbers from 800 to 899 are nor printed.

In 900s, numbers that are not printed are 906,908,916,918,926,928,936,938,946,948,956,958, all numbers from 960 to 969, 976,978, all numbers from 980 to 989, 996 and 998. We can see that until 979, 25 numbers are not printed, so 80-25 = 55 and we had 55 numbers left to be printed.

Hence 979 is the answer.

1 year, 11 months ago

As @Shreya Reddyhas answered well, I suggest you to practice more questions from **Cracku's CAT Quotient. **Also Download formulas pdf for CAT**.**