## Sunday, 30 October 2011

### Numbers-9 (XAT-2011) (5-Marks)

Let an = 111111…1, where 1 occurs n number of times. Then,
(i) a741 is not a prime
(ii) a534 is not a prime
(iii) a123 is not a prime
(iv) a77 is not a prime
(1) (i) is correct
(2) (i) and (ii) correct
(3) (ii) and (iii) correct
(4) All of them are correct
(5) None of them is correct
For Answer Click on "Read more" below:
Solution:
a741 has 741 number of 1’s => sum of all digits = 7+4+1 = 12 being multiple of 3, it is not a prime => option (i) is correct

a534 has 534 number of 1’s => even number of 1’s
=> sum of alternate digits starting with 1st digit = sum of alternate digits starting with 2nd digit (rather we can say, sum of digits in all even places = sum of digits in all odd places)
=> it is a multiple of 11 => it is not a prime => option (ii) is also correct

a123 has 123 number of 1’s => sum of all digits = 1+2+3 = 6 being multiple of 3, it is not a prime => option (iii) is also correct

Being (i),(ii),(iii) options correct we can eliminate the answer options (1),(2),(3) and safely assume that a77 is also not a prime.
Answer (4)