Kalyn writes down all of the integers from 1 to 1000 that have 4 as the sum of their digits. If $\frac{a}{b}$ (in lowest terms) is the fraction of these numbers that are prime, then $a+b$ is
(A) 5
(B) 4
(C) 15
(D) 26
(E) 19
Kalyn writes down all of the integers from 1 to 1000 that have 4 as the sum of their digits. If $\frac{a}{b}$ (in lowest terms) is the fraction of these numbers that are prime, then $a+b$ is
(A) 5
(B) 4
(C) 15
(D) 26
(E) 19

## Solution

The numbers between 1 and 1000 that have 4 as the sum of their digits are 4, (13), 22, (31), 40, (103), 112, 121, 130, 202, (211), 220, 301, 310, 400 .

The circled numbers are prime which means that 4 out of the 15 are prime and $a+b=19$.

ANSWER: (E)