Mark has twice as many oranges as George. Tony has 10 less than twice the sum of George and Mark’s oranges. If Tony were to give 15 oranges to George and 5 oranges to Mark, George and Mark would each have half the number of oranges Tony had originally. How many oranges did George have originally?
Use PITA here. If you start with choice (C), George has 20 oranges, which means Mark has 40 and Tony has 110. If we add 15 to George, he’d have 35, and Mark would get 5, so he’d have 45. These values aren’t equal—in fact, the difference between them is too large, so that’s a clue that we should try using smaller numbers. If you try choice (B), Mark now has 30, Tony has 80, and after Tony gives 15 to George and 5 to Mark, George has 30 and Mark has 35. The difference is smaller, so we know we are going in the right direction. The answer must be choice (A). If you try choice (A), George has 10, Mark has 20, and Tony has 50 to start. After the exchange, George and Mark both have 25, which is half of 50.
- 10
- 15
- 20
- 25
- 50
Use PITA here. If you start with choice (C), George has 20 oranges, which means Mark has 40 and Tony has 110. If we add 15 to George, he’d have 35, and Mark would get 5, so he’d have 45. These values aren’t equal—in fact, the difference between them is too large, so that’s a clue that we should try using smaller numbers. If you try choice (B), Mark now has 30, Tony has 80, and after Tony gives 15 to George and 5 to Mark, George has 30 and Mark has 35. The difference is smaller, so we know we are going in the right direction. The answer must be choice (A). If you try choice (A), George has 10, Mark has 20, and Tony has 50 to start. After the exchange, George and Mark both have 25, which is half of 50.
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