j_shreyans wrote: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?
(1) Zelda has no more than 5 hats more than Xander.
(2) The product of the numbers of hats that Xander, Yolanda, and Zelda have is less than 36.
OAC
x+y+z = 12 and x<y<z.
Only the following options for x, y and z are possible:
1, 2, 9
1, 3, 8
1, 4, 7
1, 5, 6
2, 3, 7
2, 4, 6
3, 4, 5.
Statement 1: z-x ≤ 5
From the list above, the following cases are possible:
1, 5, 6
2, 3, 7
2, 4, 6
3, 4, 5.
Since y can be different values, INSUFFICIENT.
Statement 2: xyz < 36
From the list above, the following cases are possible:
1, 2, 9
1, 3, 8
1, 4, 7
1, 5, 6.
Since y can be different values, INSUFFICIENT.
Statements combined:
From the list above, only one case satisfies both statements:
1, 5, 6.
Thus, y=5.
SUFFICIENT.
The correct answer is
C.
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