all numbers greater than 1000 formed by using the digits 1, 3, 5, 7, no digit repeated in any number is A. 106656 B. 101276 C. 82171 D. 81273

as per the options, the question should have been the sum of numbers greater than 1000 formed by the digits 1, 3, 5 and 7 when no repetition is allowed.

The numbers formed using teh digits 1, 3, 5 and 7 will be

1357

1375

1573

1537

….…

In total, there would be 4! = 24 numbers to add.

Each vertical column would have an equal numbver of 1’s, 3’s, 5’s and 7’s.

Hence, since 24/4 = 6, the sum of each column would be 6 * (1+3+5+7) = 96.

Hence, the required sum is

96*1000 + 96*100 + 96*10 + 96*1

= 106656.

Hence, the correct option is (A).

Thanks & Regards

Latika Leekha

askIITians Faculty