1000 dollars were converted into pounds

[NandishSS]

1000 dollars were converted into pounds and then the pounds were converted back into dollars at the same exchange rate of x% pounds per dollar. If a commission of y% is levied on any exchange operation, what dollar amount was left after the exchanges?

A)x = 0.6
B)y = 5

OA: B

[DavidG@VeritasPrep]

1000 dollars were converted into pounds and then the pounds were converted back into dollars at the same exchange rate of x pounds per dollar. If a commission of y% is levied on any exchange operation, what dollar amount was left after the exchanges?

A)x = 0.6
B)y = 5

OA: B

I'm assuming the exchange rate is x pounds per dollar, rather than x%, so I adjusted the question accordingly.

This can be treated as a pure logic problem. If the dollars are being converted into pounds and then back into dollars, the exchange rate doesn't matter. Imagine the exchange rate is 1 dollar for 2 pounds. If I have 100 dollars, and change it to pounds, I'd then have 200 pounds. And if I go back to dollars, of course, I'd still have 100 dollars. If the exchange rate were 1 dollar for 3 pounds, that 100 dollars will briefly become 300 pounds before becoming 100 dollars, post exchange. All that matter is the fee percentage.

The rephrased question: what is the value of y? Well, not so challenging now. The answer is B

[DavidG@VeritasPrep]

1000 dollars were converted into pounds and then the pounds were converted back into dollars at the same exchange rate of x pounds per dollar. If a commission of y% is levied on any exchange operation, what dollar amount was left after the exchanges?

A)x = 0.6
B)y = 5

OA: B

(You could also test some numbers to prove that S2 is alone sufficient. Say that the exchange rate is 1 dollar: 2 pounds. Initially, that $1000 will be charged a 5% fee when changed to 2000 pounds, reducing the amount to 1900 pounds. Then we'll go back to dollars, so we'll have 950 dollars, but another 5% will be charged on the transaction, reducing the 950 dollars by 47.5, and leaving us with $902.5.)

Now say the exchange rate is 1 dollar: 3 pounds. Initially, that $1000 will be charged a 5% fee when changed to 3000 pounds, reducing the amount to 2850 pounds. Then we'll go back to dollars, so we'll have 2850/3 = 950 dollars. (No need to go any further, because we did this in the first instance, but another 5% will be charged on the transaction, reducing the 950 dollars by 47.5, again leaving us with $902.5.)

Better to see the logic. Though the logic of the person making this expensive and seemingly pointless exchange eludes me