1. Person A needs a $30. ATMs dispenses either$30, $40 or$70 notes. What is the largest amount he can withdraw to be certain that he has at least one $30 note? 2. A certain positive integer X greater than 100 is displayed. But when its two rightmost digits are erased, the number left is X/154. Find all possible numbers of X. 2. Hello, delicate_tears! Maybe I'm reading it wrong, but I don't understand #1 . . . 2. A certain positive integer $X$ greater than 100 is displayed. But when its two rightmost digits are erased, the number left is $\frac{X}{154}.$ Find all possible values of $X$. We have the number: . $X \;=\;"abc" \;=\;100a + 10b + c$ . . where $b\text{ and }c$ are digits . . . and $a$ is any positive integer. If the two rightmost digits are erased, the number becomes: . $a$ . . which equals $\frac{X}{154}$ So we have: . $a \;=\;\frac{100a + 10b + c}{154} \quad\Rightarrow\quad 54a \:=\:10b + c$ Since $10b + c$ is a two-digit number, the only solution is: . $a = 1,\:b = 5,\:c = 4$ Therefore: . $X \;=\;154$ 3. Hi Delicate_Tears, I can only imagine the solution to be$870. The Least Common Multiple of 30, 40, and 70 is $840. An ATM dispenser machine may give you$840 in bills of 30s only, 40s only, 70s only, or a mix between them. The only way to make sure that the bill has to give you a 30 dollar bill is to add 30 to the LCM.