let passport card = p ; everywhere card = e , and American card = a

Target question= Does he get owe the greatest balance on everywhere card.
$$i.e\ e>a\ and\ e>p\ ?$$

Statement 1
The sum of the balances on his everywhere cared and American card is $1350 and 3times the balances on his passport card.

eta=$350 and $1350=3p $$p=\frac{1350}{3}=450$$
if e=1000 and a=350 then e is the greatest of all definite value of e and a is unknown some target question cannot be evaluated statement 1 is NOT SUFFICIENT.


Statement 2
The balance on his everywhere card is 4/3 of the balance on his passport and 4/5 of the balance on his American Local card.

i.e e is 4 out of 3p's = e>p
e is 4 out of 5a's = e<a

$$p<e<a,\ David\ owe\ the\ greatest\ \ balance\ on\ the\ America\ local\ \ \ card\ \ and\ not\ on\ the\ \ everywhere\ card\ and\ Statement\ 2\ \ alone\ is\ SUFFICIENT$$

let passport card = p ; everywhere card = e , and American card = a

Target question= Does he get owe the greatest balance on everywhere card.
$$i.e\ e>a\ and\ e>p\ ?$$

Statement 1
The sum of the balances on his everywhere cared and American card is $1350 and 3times the balances on his passport card.

eta=$350 and $1350=3p $$p=\frac{1350}{3}=450$$
if e=1000 and a=350 then e is the greatest of all definite value of e and a is unknown some target question cannot be evaluated statement 1 is NOT SUFFICIENT.


Statement 2
The balance on his everywhere card is 4/3 of the balance on his passport and 4/5 of the balance on his American Local card.

i.e e is 4 out of 3p's = e>p
e is 4 out of 5a's = e<a

$$p<e<a,\ David\ owe\ the\ greatest\ \ balance\ on\ the\ America\ local\ \ \ card\ \ and\ not\ on\ the\ \ everywhere\ card\ and\ Statement\ 2\ \ alone\ is\ SUFFICIENT$$

$$Answer\ is\ Option\ B$$