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$ 1 9 7
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$ 9 8 ) Clue
THE PROBLEM IS THAT THE QUESTION IS CLEVERLY PHRASED TO CAUSE CONFUSION. THE BALANCE TOTAL DOES NOT NEED TO BE EQUAL TO THE WITHDRAWAL TOTAL. AND IN THIS CASE, THE BALANCE TOTAL WILL NOT ADD UP TO SOMETHING MEANINGFUL. LET'S SAY YOU HAVE $100 IN YOUR BANK ACCOUNT AND YOU MAKE 2 WITHDRAWALS OF $1 EACH. THE WITHDRAWAL TOTAL IS $2 ($1 + $1). BUT THE BALANCE TOTAL IS $197 ($99 + $98) THE PROBLEM IS THAT THE QUESTION IS CLEVERLY PHRASED TO CONCEAL WHAT IS REALLY GOING ON. LET'S LOCATE ALL THAT MONEY. THERE ARE TWO WAYS TO THINK ABOUT HOW MUCH MONEY IS OUT THERE TO BE FOUND.THE WAY THAT THIS QUESTION IS TRICKY IS THAT IT COMBINES THAT TWO WAYS. THE FIRST WAY IS THIS. HOW MUCH MONEY DID MOM AND DAD PAY ORIGINALLY? THE SECOND WAY IS THIS. HOW MUCH MONEY DID THEY END UP PAYING? SO IF IT IS THE FIRST WAY, THEN CLEARLY THE TOTAL WE NEED TO ACCOUNT FOR IS THE $100. SO LET'S SEE WHAT HAPPENS TO THAT $100. THE SHIRT COSTS $97, THE BOY KEEPS $1 AND MOM AND DAD GET $1 BACK. THAT ADDS UP FINE. NOW LET'S LOOK AT THE SECOND WAY. HOW MUCH MONEY DID THEY END UP PAYING? WELL $98 DOLLARS, AND $97 OF IT WENT FOR THE SHIRT AND $1 TO THE BOY. NOW, THAT ADDS UP TOO. THE PROBLEM WITH THE QUESTION IS THAT THE THE $1 THAT THE BOY KEEPS IS CONTAINED IN THE $98 THAT THEY END UP PAYING SO WE SHOULDN'T EXPECT THEM TO ADD TO ANYTHING MEANINGFUL IF YOU LOOK AT THE AVERAGE PRICE OF THE APPLES ON THE FIRST DAY, IT IS $25 DIVIDED BY 60, OR 412⁄3 CENTS PER APPLE. WHEN THE WOMEN SELL THE APPLES AT 5 FOR $2 ON THE SECOND DAY, THEY ARE ONLY CHARGING 40 CENTS PER APPLE. THE DECREASE IN PRICE OF 12⁄3 CENTS PER APPLE FOR 60 APPLES ACCOUNTS FOR THE MISSING DOLLAR. HERE IS A ANOTHER WAY TO LOOK AT THIS. ON THE SECOND DAY, EVERY TIME 5 APPLES ARE SOLD FOR $2, LET US ASSUME THAT THE FIRST WOMAN TAKES $1 AND GIVES 2 APPLES AND THE SECOND WOMAN TAKES $1 AND GIVES 3 APPLES. THIS WAY THE FIRST WOMAN SELLS 24 APPLES AND SECOND ONE SELLS 36 APPLES FOR $12 EACH. THIS MEANS THAT THE 6 APPLES OF THE FIRST WOMAN HAVE BEEN TRANSFERRED TO THE SECOND WOMAN AT A LOSS OF $1. IF THE FIRST WOMAN SOLD THE 6 APPLES, SHE WOULD HAVE MADE $3. BUT SINCE THE SECOND WOMAN SOLD THE 6 APPLES, SHE WOULD HAVE ONLY MADE $2. $3 - $2 = $1, THE LOSS THEY INCURRED COMPARED TO BEFORE THE FOUR WEIGHTS ARE: 1, 3, 9 AND 17. THE FOURTH WEIGHT IS NOT 27 BECAUSE BY USING A 27 POUND WEIGHT, WE WOULD ABLE TO MEASURE UP TO 40 POUNDS. BUT SINCE WE NEED TO MEASURE ONLY UP TO 30 POUNDS, WE CAN SUBTRACT 10 FROM 27 TO GET 17. LET A=1, B=3, C=9 AND D=17. 1LBS = A 2LBS + A = B 3LBS = C 4LBS = A + B 5LBS + A + B = C 6LBS + B = C 7LBS + B = A + C 8LBS + A = C 9LBS = C 10LBS = A + C ... 20LBS = B + D ... 30LBS = A + B + C + D