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
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Yolanda
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j_shreyans
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x+y+z = 12 and x<y<z.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
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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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gmatcracker0123
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How would the question be solved if the sum of the hats was a bigger number... Listing down all the possible answers would've be a feasible approach then right?GMATGuruNY wrote:x+y+z = 12 and x<y<z.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
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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Hi gmatcrack0123,
This DS prompt is based on limited possibilities. When this type of situation occurs, it helps to quickly list out all of the options so that you can physically "see" them on the pad (and reference them as needed). The effort to do that work up-front will save you LOTS of time later when dealing with the two Facts.
In the event that the options are NOT that limited, then you would essentially TEST Values on a Fact-by-Fact basis.
For example, if we were told that the total number of hats was 100, then you couldn't realistically list out all of the possibiltiies. When it comes to dealing with the Facts though, you would come up with individual TESTS to prove that a Fact was insufficient.
eg. X < Y < Z and X + Y + Z = 100
Fact 1: Zelda has no more than 5 hats more than Xander.
This would mean that X, Y and Z are fairly "close" together. With a sum of 100, each of the 3 would be close to 33.
X = 32
Y = 33
Z = 35
OR
X = 31
Y = 34
Z = 35
With 2 different values for Y, Fact 1 would be INSUFFICIENT.
GMAT assassins aren't born, they're made,
Rich
This DS prompt is based on limited possibilities. When this type of situation occurs, it helps to quickly list out all of the options so that you can physically "see" them on the pad (and reference them as needed). The effort to do that work up-front will save you LOTS of time later when dealing with the two Facts.
In the event that the options are NOT that limited, then you would essentially TEST Values on a Fact-by-Fact basis.
For example, if we were told that the total number of hats was 100, then you couldn't realistically list out all of the possibiltiies. When it comes to dealing with the Facts though, you would come up with individual TESTS to prove that a Fact was insufficient.
eg. X < Y < Z and X + Y + Z = 100
Fact 1: Zelda has no more than 5 hats more than Xander.
This would mean that X, Y and Z are fairly "close" together. With a sum of 100, each of the 3 would be close to 33.
X = 32
Y = 33
Z = 35
OR
X = 31
Y = 34
Z = 35
With 2 different values for Y, Fact 1 would be INSUFFICIENT.
GMAT assassins aren't born, they're made,
Rich
