Xander, Yolanda, and Zelda each have at least one hat. Zelda

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The case when x=1, y=4, and z=7 does not satisfy the first statement, which says that \(z-x\leq{5}\) (Zelda has no more than 5 hats more than Xander). Also notice that there are some cases missing for (1) and (2) in fluke's solution.

Complete solution:

Xander, Yolanda, and Zelda each have at least one hat. Zelda has more hats than Yolanda, who has more than Xander. Together, the total number of hats the three people have is 12. How many hats does Yolanda have?

Given: x<y<z and x+y+z=12. Question: y=?

Now, only following 7 cases are possible;

X-Y-Z
1-2-9
1-3-8
1-4-7
1-5-6
2-3-7
2-4-6
3-4-5

(1) Zelda has no more than 5 hats more than Xander --> \(z-x\leq{5}\) --> first 3 cases are out and only following cases are left: {1, 5, 6}, {2, 3, 7}, {2, 4, 6}, and {3, 4, 5}. Not sufficient.

(2) The product of the numbers of hats that Xander, Yolanda, and Zelda have is less than 36 --> last 3 cases are out and only following cases are left: {1, 2, 9}, {1, 3, 8}, {1, 4, 7}, and {1, 5, 6}. Not sufficient.

(1)+(2) There is only one case common for (1) and (2): {1, 5, 6}, so z=6. Sufficient.

Answer: C.

Hope it's clear.