Re: How many positive integers \(n\) have the property that both \(3n\) and \(\dfrac{n}3\) are 4-digit integers?

1000 < =3n <= 9999 o 1000/3 <= n < = 9999/3 o 333.33 < = n < 3333-----(1) • 1000 < =n/3 <= 9999 o 3000 < = n < 9999*3---------(2) • Combining both 1 and 2, we get o 3000 <= n < 3333 o As n/3 is an integer, n has to be a multiple of 3. o (3333-3000)/3 +1 = 112 Hence, n can have 112 values. Thus, opti...