Hard Problem Solving Question

Today I would like to provide an example of a hard “problem solving” question that could show up on the revised SAT. You can use your calculator for this one.

Level 5 – Problem Solving

John, a United States resident, is on vacation in Spain and is trying to decide if he should use his own credit card from the U.S., or to purchase a prepaid credit card for 500 euros in Spain.

The bank that issues John’s U.S. credit card converts all purchase prices at the foreign exchange rate for that day, and an additional fee of 6% of the converted cost is applied before the bank posts the charge.

If John decides to purchase the prepaid card, he can use this card spending dollars at the exchange rate for that day with no fee, but he loses any money left unspent on the card.

Suppose that John does decide to buy the prepaid card. What is the least number of the 500 euros John must spend for the prepaid card to have been the cheaper option? Round your answer to the nearest whole number of euros.

Please feel free to post your solutions or attempted solutions in the comments below and we can discuss the best way to solve the problem. I will post a solution to this problem tomorrow.

More Hard SAT Math Practice Problems

For many more hard SAT math problems like these, each with several fully explained solutions, check out New SAT Math Problems arranged by Topic and Difficulty Level. Click on the picture below for more information about this book.

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Speak to you soon!

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