Question 1192360
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Apparently the other tutor misread the problem, or didn't understand it.<br>
(Note: I see the other tutor apparently saw that her original response was incorrect and replaced it with a valid answer.)<br>
The solution is rather simple.<br>
For each number x that James wrote down, Jia wrote down the number (7-x); the sum of those two numbers is 7.<br>
James's total was 22, and Jia's total was 34; that means the sum of all of their numbers was 22+34=56. Then, since the sum of each pair of numbers is 7, there must have been 56/7=8 pairs of numbers.<br>
ANSWER: James wrote down 8 numbers.<br>
It's easy to verify by example that the described problem CAN occur.  Simply write down 8 numbers each less than 7 that have a sum of 22 to be James's numbers; then find Jia's corresponding numbers and see that their sum is 34.<br>