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07 Oct 2011, 22:23
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
56% (02:57) correct
44%
(03:09)
wrong
based on 559
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Not Attempted Yet
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.
(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.
22 Apr 2012, 21:44
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anushapolavarapu
Welcome to GMAT Club. Below is an answer to your doubt.
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.
General Discussion
08 Oct 2011, 00:35
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kkalyan
kkalyan: Please tag the source correctly. It is a Manhattan GMAT question, not a GMAT Prep question. Also, please try to give a unique name for the subject.
MGMAT DS: Hats owned by Xander, Yolanda, and Zelda
Z>Y>X
Z+Y+X=12
1) Z-X<=5
1, 5, 6
2, 4, 6
Not Sufficient.
2) X.Y.Z<36
1, 5, 6
1, 2, 9
Not Sufficient.
Combined;
{1, 5, 6}
Y=5
Ans: "C"
