Let n be the largest integer for which 14n has exactly 100 digits. Counting from right to left, what is the 68th digit of n? (Hint: (1) the largest integer of q digits must be 10q-1, (2) using the concept of rational number with repeating decimal) (A) 1 (B) 2 (C) 4 (D) 5 (E) 8

a

step-by-step explanation:

given the 2 equations

- x + y = - 2 → (1)

2x - 3y = 4 → (2)

multiplying (1) by 2 and adding to (2) will eliminate the x- term

- 2x + 2y = - 4 → (3)

add (2) and (3) term by term

(2x - 2x) + (- 3y + 2y) = (4 - 4), simplifying gives

- y = 0 ⇒ y = 0

substitute y = 0 in either of the 2 equations for corresponding value of x

substituting in (2) gives

2x = 4 ( divide both sides by 2 )

x = 2

solution is (2, 0 ) → a

the answer is 25 because they're both the same