The number 3798125P369 is divisible by 7. What is the value of the digit P?
The number 3798125P369 is divisible by 7. What is the value of the digit P?
1
6
7
9
Solution
Group the digits into triplets from the right: (37)(981)(25P)(369). The alternating sum for divisibility by 7 gives $369 - 25P + 981 - 37 = 1313 - 25P$. For this to be divisible by 7, with 25P between 250 and 259, we need 25P = 256, which makes $1313 - 256 = 1057 = 7 \times 151$. Hence P = 6.