Question

The sum of all 2 – digit numbers divisible by 19 will be __________

(a) 345

(b) 245

(c) 275

(d) 285

I got this question during an interview for a job.

Enquiry is from Sum of N Terms of Arithmetic Progression topic in division Arithmetic Progressions of Mathematics – Class 10

Answer 1

The correct option is (c) 275

For explanation I would say: The AP according to the given data will be 19, 38, 57, …, 95

Here a = 19 and d = 19

Tn = a + (n – 1)d = 95

19 + (n – 1)19 = 95

19 + 19n – 19 = 95

19n = 95

n = 5

We know that, Sn = \(\frac {n}{2}\) (a + l)

Sn = \(\frac {5}{2}\) ((19) + 95)

Sn = 285