Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Xander, Yolanda, and Zelda each have at least one hat. Zelda [#permalink]
07 Oct 2011, 21:23

1

This post received KUDOS

00:00

A

B

C

D

E

Difficulty:

85% (hard)

Question Stats:

53% (02:35) correct
47% (01:35) wrong based on 106 sessions

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.

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.

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

what about the combination {1,4,7}. even this satisfies the 2 conditions right. 1+4+7=12(x<y<z) and 1*4*7=28 which is < 36

So, I think answer should be E. Can you please help.

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.

Xander, Yolanda, and Zelda each have at least one hat. Zelda [#permalink]
23 Apr 2012, 09:37

Expert's post

aalba005 wrote:

anushapolavarapu wrote:

Hi fluke,

what about the combination {1,4,7}. even this satisfies the 2 conditions right. 1+4+7=12(x<y<z) and 1*4*7=28 which is < 36

So, I think answer should be E. Can you please help.

{1,4,7}. Z has more than 5 hats than X does. Again great explanation above.

Do you suggest during these type of questions to spend time writing out all combination possibilities at the start?

It depends how many possible combinations are there. Luckily there are only 7 for this question, so it's not hard to write them all down. In this case everything will be in front of you so you won't miss any case while solving. _________________

what about the combination {1,4,7}. even this satisfies the 2 conditions right. 1+4+7=12(x<y<z) and 1*4*7=28 which is < 36

So, I think answer should be E. Can you please help.

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.

Yes, It was slightly time consuming question. _________________

Re: Xander, Yolanda, and Zelda each have at least one hat. Zelda [#permalink]
21 Aug 2014, 04:52

Hi Bunuel, I took 3 minutes to solve this problem.I took time to list down all the values XYZ with both constraints ie , XYZ <36 and X+Y+Z=12. how can i speed up in solving such problems? Is there a better way and while listing I get tensed too as i might miss some cases.

Re: Xander, Yolanda, and Zelda each have at least one hat. Zelda [#permalink]
21 Aug 2014, 10:09

Bunuel wrote:

aalba005 wrote:

anushapolavarapu wrote:

Hi fluke,

what about the combination {1,4,7}. even this satisfies the 2 conditions right. 1+4+7=12(x<y<z) and 1*4*7=28 which is < 36

So, I think answer should be E. Can you please help.

{1,4,7}. Z has more than 5 hats than X does. Again great explanation above.

Do you suggest during these type of questions to spend time writing out all combination possibilities at the start?

It depends how many possible combinations are there. Luckily there are only 7 for this question, so it's not hard to write them all down. In this case everything will be in front of you so you won't miss any case while solving.

What do you suggest if we weren't able to write down all possible answers ?! For this particular question...

gmatclubot

Re: Xander, Yolanda, and Zelda each have at least one hat. Zelda
[#permalink]
21 Aug 2014, 10:09

Great to know you are joining Kellogg. A lot was being talked about your last minute interview on Pagalguy (all good though). It was kinda surprise that you got the...