Find all School-related info fast with the new School-Specific MBA Forum

It is currently 13 Jul 2014, 06:03

Close

GMAT Club Daily Prep

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Fresh Meat!!!

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
15 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18519
Followers: 3196

Kudos [?]: 21393 [15] , given: 2546

Fresh Meat!!! [#permalink] New post 17 Apr 2013, 05:11
15
This post received
KUDOS
Expert's post
14
This post was
BOOKMARKED
The next set of PS questions. I'll post OA's with detailed explanations after some discussion. Please, post your solutions along with the answers.

1. The length of the diagonal of square S, as well as the lengths of the diagonals of rhombus R are integers. The ratio of the lengths of the diagonals is 15:11:9, respectively. Which of the following could be the difference between the area of square S and the area of rhombus R?

I. 63
II. 126
III. 252


A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

Solution: fresh-meat-151046-80.html#p1215318


2. Set S contains 7 different letters. How many subsets of set S, including an empty set, contain at most 3 letters?

A. 29
B. 56
C. 57
D. 63
E. 64

Solution: fresh-meat-151046-100.html#p1215323

3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Solution: fresh-meat-151046-100.html#p1215329


4. The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of positive perfect squares less than n and g(n) is the number of primes numbers less than n. If f(x) + g(x) = 16, then x is in the range:

A. 30 < x < 36
B. 30 < x < 37
C. 31 < x < 37
D. 31 < x < 38
E. 32 < x < 38

Solution: fresh-meat-151046-100.html#p1215335


5. Which of the following is a factor of 18!+1?

A. 15
B. 17
C. 19
D. 33
E. 39

Solution: fresh-meat-151046-100.html#p1215338


6. If the least common multiple of a positive integer x, 4^3 and 6^5 is 6^6. Then x can take how many values?

A. 1
B. 6
C. 7
D. 30
E. 36

Solution: fresh-meat-151046-100.html#p1215345


7. The greatest common divisor of two positive integers is 25. If the sum of the integers is 350, then how many such pairs are possible?

A. 1
B. 2
C. 3
D. 4
E. 5

Solution: fresh-meat-151046-100.html#p1215349


8. The product of a positive integer x and 377,910 is divisible by 3,300, then the least value of x is:

A. 10
B. 11
C. 55
D. 110
E. 330

Solution: fresh-meat-151046-100.html#p1215359


9. What is the 101st digit after the decimal point in the decimal representation of 1/3 + 1/9 + 1/27 + 1/37?

A. 0
B. 1
C. 5
D. 7
E. 8

Solution: fresh-meat-151046-100.html#p1215367


10. If x is not equal to 0 and x^y=1, then which of the following must be true?

I. x=1
II. x=1 and y=0
III. x=1 or y=0


A. I only
B. II only
C. III only
D. I and III only
E. None

Solution: fresh-meat-151046-100.html#p1215370


Kudos points for each correct solution!!!
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Kaplan Promo CodeKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
Intern
Intern
avatar
Joined: 22 May 2013
Posts: 48
Concentration: General Management, Technology
GPA: 3.9
WE: Information Technology (Computer Software)
Followers: 0

Kudos [?]: 8 [0], given: 8

GMAT ToolKit User
Re: Fresh Meat!!! [#permalink] New post 21 Jun 2013, 20:56
Hi Bunuel,
this seemed like a great way to earn kudos points,
Would you be having more questionaires like this in future also? as it sorta helps to boost up the kudos for people who have recently joined the forum and want to make it in time to get to the gmatclub tests by earning kudos.
_________________

PS: Like my approach? Please Help me with some Kudos. :-)

Intern
Intern
avatar
Joined: 23 Apr 2013
Posts: 6
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Fresh Meat!!! [#permalink] New post 01 Jul 2013, 09:12
Hello.. Can someone please explain why "x" ( 15x:11x:9x) needs to be an integer? Why not 1.5?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18519
Followers: 3196

Kudos [?]: 21393 [0], given: 2546

Re: Fresh Meat!!! [#permalink] New post 01 Jul 2013, 09:23
Expert's post
CIyer wrote:
Hello.. Can someone please explain why "x" ( 15x:11x:9x) needs to be an integer? Why not 1.5?


We are told that the length of the diagonals are integers and their ratio is 15:11:9. This means that the lengths are multiples of 15, 11 and 9. If x=1.5, then the lengths won't be integers.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 29 Aug 2012
Posts: 31
WE: General Management (Consulting)
Followers: 0

Kudos [?]: 11 [0], given: 6

GMAT ToolKit User
Re: Fresh Meat!!! [#permalink] New post 07 Jul 2013, 06:56
Bunuel wrote:
3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Consider the set without 0: {1, 2, 3, 4, 5}. Each out of 5 elements of the set {1, 2, 3, 4, 5} has TWO options: either to be included in the subset or not, so total number of subsets of this set is 2^5=32. Now, each such set will be a subset of {0, 1, 2, 3, 4, 5} and won't include 0.

Answer: D.



Hi Bunuel,

I did this exercise as follows:

I eliminate the 0, so i have the following set: (1,2,3,4,5). Now, i use combinatorics.

Set containing 5 elements: 5C5=1
Set containing 4 elements: 4C5=5
Set containing 3 elements: 3C5=10
Set containing 2 elements: 2C5=10
Set containing 1 elements: 1C5=5

So, the total of posibilites are 31. What am I missing here¿??

Thanks in advance
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18519
Followers: 3196

Kudos [?]: 21393 [0], given: 2546

Re: Fresh Meat!!! [#permalink] New post 07 Jul 2013, 07:03
Expert's post
jacg20 wrote:
Bunuel wrote:
3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Consider the set without 0: {1, 2, 3, 4, 5}. Each out of 5 elements of the set {1, 2, 3, 4, 5} has TWO options: either to be included in the subset or not, so total number of subsets of this set is 2^5=32. Now, each such set will be a subset of {0, 1, 2, 3, 4, 5} and won't include 0.

Answer: D.



Hi Bunuel,

I did this exercise as follows:

I eliminate the 0, so i have the following set: (1,2,3,4,5). Now, i use combinatorics.

Set containing 5 elements: 5C5=1
Set containing 4 elements: 4C5=5
Set containing 3 elements: 3C5=10
Set containing 2 elements: 2C5=10
Set containing 1 elements: 1C5=5

So, the total of posibilites are 31. What am I missing here¿??

Thanks in advance


You are missing 1 empty set, which is a subset of the original set and also does not contain 0.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 29 Aug 2012
Posts: 31
WE: General Management (Consulting)
Followers: 0

Kudos [?]: 11 [0], given: 6

GMAT ToolKit User
Re: Fresh Meat!!! [#permalink] New post 07 Jul 2013, 07:06
Bunuel wrote:
jacg20 wrote:
Bunuel wrote:
3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Consider the set without 0: {1, 2, 3, 4, 5}. Each out of 5 elements of the set {1, 2, 3, 4, 5} has TWO options: either to be included in the subset or not, so total number of subsets of this set is 2^5=32. Now, each such set will be a subset of {0, 1, 2, 3, 4, 5} and won't include 0.

Answer: D.



Hi Bunuel,

I did this exercise as follows:

I eliminate the 0, so i have the following set: (1,2,3,4,5). Now, i use combinatorics.

Set containing 5 elements: 5C5=1
Set containing 4 elements: 4C5=5
Set containing 3 elements: 3C5=10
Set containing 2 elements: 2C5=10
Set containing 1 elements: 1C5=5

So, the total of posibilites are 31. What am I missing here¿??

Thanks in advance


You are missing 1 empty set, which is a subset of the original set and also does not contain 0.

Hope it's clear.


Ouch, tricky.. Thanks so much!
Intern
Intern
avatar
Joined: 23 Apr 2013
Posts: 6
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Fresh Meat!!! [#permalink] New post 08 Jul 2013, 08:03
1 useful formula: 2^n=nc0 + nc1+ ..... + ncn; here n=5, ans= 2^5= 32
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18519
Followers: 3196

Kudos [?]: 21393 [0], given: 2546

Re: Fresh Meat!!! [#permalink] New post 08 Jul 2013, 09:46
Expert's post
Intern
Intern
avatar
Joined: 06 Jun 2013
Posts: 27
Concentration: Finance, Economics
Schools: AGSM '16
Followers: 0

Kudos [?]: 0 [0], given: 11

Re: Fresh Meat!!! [#permalink] New post 08 Jul 2013, 10:26
Bunuel wrote:
SOLUTIONS:

1. The length of the diagonal of square S, as well as the lengths of the diagonals of rhombus R are integers. The ratio of the lengths of the diagonals is 15:11:9, respectively. Which of the following could be the difference between the area of square S and the area of rhombus R?

I. 63
II. 126
III. 252


A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

Given that the ratio of the diagonal is d_s:d_1:d_2=15x:11x:9x, for some positive integer x (where d_s is the diagonal of square S and d_1 and d_2 are the diagonals of rhombus R).

area_{square}=\frac{d^2}{2} and area_{rhombus}=\frac{d_1*d_2}{2}.

The difference is area_{square}-area_{rhombus}=\frac{(15x)^2}{2}-\frac{11x*9x}{2}=63x^2.

If x=1, then the difference is 63;
If x=2, then the difference is 252;
In order the difference to be 126 x should be \sqrt{2}, which is not possible.

Answer: D.


Hi Bunuel,

This is probably a stupid question. But why can't x be \sqrt{2}?
Intern
Intern
avatar
Joined: 06 Jun 2013
Posts: 27
Concentration: Finance, Economics
Schools: AGSM '16
Followers: 0

Kudos [?]: 0 [0], given: 11

Re: Fresh Meat!!! [#permalink] New post 08 Jul 2013, 10:28
Aho92 wrote:
Bunuel wrote:
SOLUTIONS:

1. The length of the diagonal of square S, as well as the lengths of the diagonals of rhombus R are integers. The ratio of the lengths of the diagonals is 15:11:9, respectively. Which of the following could be the difference between the area of square S and the area of rhombus R?

I. 63
II. 126
III. 252


A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

Given that the ratio of the diagonal is d_s:d_1:d_2=15x:11x:9x, for some positive integer x (where d_s is the diagonal of square S and d_1 and d_2 are the diagonals of rhombus R).

area_{square}=\frac{d^2}{2} and area_{rhombus}=\frac{d_1*d_2}{2}.

The difference is area_{square}-area_{rhombus}=\frac{(15x)^2}{2}-\frac{11x*9x}{2}=63x^2.

If x=1, then the difference is 63;
If x=2, then the difference is 252;
In order the difference to be 126 x should be \sqrt{2}, which is not possible.

Answer: D.


Hi Bunuel,

This is probably a stupid question. But why can't x be \sqrt{2}?

Okay. I got it. Stupid me. They have to be integers
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18519
Followers: 3196

Kudos [?]: 21393 [0], given: 2546

Re: Fresh Meat!!! [#permalink] New post 08 Jul 2013, 23:40
Expert's post
Intern
Intern
avatar
Joined: 16 Sep 2010
Posts: 12
Followers: 0

Kudos [?]: 13 [0], given: 0

Re: Fresh Meat!!! [#permalink] New post 22 Jul 2013, 08:08
hi Bunuel, thanks so much for your help - you're explanations to all kinds of problems have been invaluable to me in my studies thus far...

RE: the following question -

3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Solution:

Subset means selecting 0 or more from given set. since 0 should be excluded we have 5 numbers in set.

selecting 0 to n from given set is 2^n => 2^5= 32.

Ans: 32


Where do you get the 2 rom in 2*5?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18519
Followers: 3196

Kudos [?]: 21393 [0], given: 2546

Re: Fresh Meat!!! [#permalink] New post 22 Jul 2013, 08:17
Expert's post
tricialin wrote:
hi Bunuel, thanks so much for your help - you're explanations to all kinds of problems have been invaluable to me in my studies thus far...

RE: the following question -

3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Solution:

Subset means selecting 0 or more from given set. since 0 should be excluded we have 5 numbers in set.

selecting 0 to n from given set is 2^n => 2^5= 32.

Ans: 32


Where do you get the 2 rom in 2*5?


OE's are in the original post here: fresh-meat-151046-100.html#p1213230. OE for this question is here: fresh-meat-151046-100.html#p1215329

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 06 Jun 2012
Posts: 150
Followers: 0

Kudos [?]: 15 [0], given: 37

GMAT ToolKit User
Re: Fresh Meat!!! [#permalink] New post 27 Aug 2013, 06:16
Bunuel wrote:
3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Consider the set without 0: {1, 2, 3, 4, 5}. Each out of 5 elements of the set {1, 2, 3, 4, 5} has TWO options: either to be included in the subset or not, so total number of subsets of this set is 2^5=32. Now, each such set will be a subset of {0, 1, 2, 3, 4, 5} and won't include 0.

Answer: D.



Hi Bunuel,

I solved it as below and got the answer wrong. Can you let me know what i did wrong and please explain your approach in more detail.

Elements are {1, 2, 3, 4, 5}

Subset of 1: 5C1 = 5
Subset of 2: 5C2 = 10
Subset of 3: 5C3 = 10
Subset of 4: 5C4 = 5
Subset of 5: 5C5 = 1

Total of 31.
_________________

Please give Kudos if you like the post

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18519
Followers: 3196

Kudos [?]: 21393 [0], given: 2546

Re: Fresh Meat!!! [#permalink] New post 27 Aug 2013, 06:22
Expert's post
summer101 wrote:
Bunuel wrote:
3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?

A. 16
B. 27
C. 31
D. 32
E. 64

Consider the set without 0: {1, 2, 3, 4, 5}. Each out of 5 elements of the set {1, 2, 3, 4, 5} has TWO options: either to be included in the subset or not, so total number of subsets of this set is 2^5=32. Now, each such set will be a subset of {0, 1, 2, 3, 4, 5} and won't include 0.

Answer: D.



Hi Bunuel,

I solved it as below and got the answer wrong. Can you let me know what i did wrong and please explain your approach in more detail.

Elements are {1, 2, 3, 4, 5}

Subset of 1: 5C1 = 5
Subset of 2: 5C2 = 10
Subset of 3: 5C3 = 10
Subset of 4: 5C4 = 5
Subset of 5: 5C5 = 1

Total of 31.


All is fine except that you are forgetting an empty set which is also a subset and do not contain 0. As for my solution check this post it might help: how-many-subordinates-does-marcia-have-57169.html#p692676
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 28 Jun 2013
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Fresh Meat!!! [#permalink] New post 28 Aug 2013, 00:05
Bunuel wrote:
SOLUTIONS:

1. The length of the diagonal of square S, as well as the lengths of the diagonals of rhombus R are integers. The ratio of the lengths of the diagonals is 15:11:9, respectively. Which of the following could be the difference between the area of square S and the area of rhombus R?

I. 63
II. 126
III. 252


A. I only
B. II only
C. III only
D. I and III only
E. I, II and III

Given that the ratio of the diagonal is d_s:d_1:d_2=15x:11x:9x, for some positive integer x (where d_s is the diagonal of square S and d_1 and d_2 are the diagonals of rhombus R).

area_{square}=\frac{d^2}{2} and area_{rhombus}=\frac{d_1*d_2}{2}.

The difference is area_{square}-area_{rhombus}=\frac{(15x)^2}{2}-\frac{11x*9x}{2}=63x^2.

If x=1, then the difference is 63;
If x=2, then the difference is 252;
In order the difference to be 126 x should be \sqrt{2}, which is not possible.

Answer: D.


Thank you. I have a question - Why cant x be [square_root]2. Why cant we have sides of lengths 5*[square_root]2, 11*[square_root]2 and 9*[square_root]2?
Expert Post
1 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 626
Followers: 40

Kudos [?]: 528 [1] , given: 135

Premium Member
Re: Fresh Meat!!! [#permalink] New post 28 Aug 2013, 00:28
1
This post received
KUDOS
Expert's post
Gagan1983 wrote:
Bunuel wrote:
SOLUTIONS:

[b]1. The length of the diagonal of square S, as well as the lengths of the diagonals of rhombus R are integers. The ratio of the lengths of the diagonals is 15:11:9, respectively. Which of the following could be the difference between the area of square S and the area of rhombus R?

Given that the ratio of the diagonal is d_s:d_1:d_2=15x:11x:9x, for some positive integer x (where d_s is the diagonal of square S and d_1 and d_2 are the diagonals of rhombus R).

area_{square}=\frac{d^2}{2} and area_{rhombus}=\frac{d_1*d_2}{2}.

The difference is area_{square}-area_{rhombus}=\frac{(15x)^2}{2}-\frac{11x*9x}{2}=63x^2.

If x=1, then the difference is 63;
If x=2, then the difference is 252;
In order the difference to be 126 x should be \sqrt{2}, which is not possible.

Answer: D.


Thank you. I have a question - Why cant x be [square_root]2. Why cant we have sides of lengths 5*[square_root]2, 11*[square_root]2 and 9*[square_root]2?


Firstly, these are not the sides of the given square and rhombus. They are diagonal values, where 15x corresponds to the square(where the diagonals are equal) and the 11x and 9x correspond to the rhombus(which has unequal diagonals). Also, it is mentioned that they are all integers, thus, if x = \sqrt{2}, then the value of the diagonal of the square/rhombus will no longer be an integer.

Hope this helps.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Manager
Manager
avatar
Joined: 20 Nov 2011
Posts: 54
Followers: 0

Kudos [?]: 4 [0], given: 17

Re: Fresh Meat!!! [#permalink] New post 28 Aug 2013, 09:42
Thanx bunnel for this set of question. I learned many good stuffs. Cheers
Intern
Intern
avatar
Joined: 28 Jun 2013
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: Fresh Meat!!! [#permalink] New post 28 Aug 2013, 10:55
mau5 wrote:
Gagan1983 wrote:
Bunuel wrote:
SOLUTIONS:

[b]1. The length of the diagonal of square S, as well as the lengths of the diagonals of rhombus R are integers. The ratio of the lengths of the diagonals is 15:11:9, respectively. Which of the following could be the difference between the area of square S and the area of rhombus R?

Given that the ratio of the diagonal is d_s:d_1:d_2=15x:11x:9x, for some positive integer x (where d_s is the diagonal of square S and d_1 and d_2 are the diagonals of rhombus R).

area_{square}=\frac{d^2}{2} and area_{rhombus}=\frac{d_1*d_2}{2}.

The difference is area_{square}-area_{rhombus}=\frac{(15x)^2}{2}-\frac{11x*9x}{2}=63x^2.

If x=1, then the difference is 63;
If x=2, then the difference is 252;

In order the difference to be 126 x should be \sqrt{2}, which is not possible.

Answer: D.


Thank you. I have a question - Why cant x be [square_root]2. Why cant we have sides of lengths 5*[square_root]2, 11*[square_root]2 and 9*[square_root]2?


Firstly, these are not the sides of the given square and rhombus. They are diagonal values, where 15x corresponds to the square(where the diagonals are equal) and the 11x and 9x correspond to the rhombus(which has unequal diagonals). Also, it is mentioned that they are all integers, thus, if x = \sqrt{2}, then the value of the diagonal of the square/rhombus will no longer be an integer.

Hope this helps.


Thanks a bunch, Mau5, I did not read the given condition properly. Cheers.
Intern
Intern
avatar
Joined: 23 Oct 2012
Posts: 36
Followers: 2

Kudos [?]: 11 [0], given: 95

GMAT ToolKit User
Re: Fresh Meat!!! [#permalink] New post 31 Aug 2013, 09:50
Bunuel wrote:
6. If the least common multiple of a positive integer x, 4^3 and 6^5 is 6^6. Then x can take how many values?

A. 1
B. 6
C. 7
D. 30
E. 36

We are given that 6^6=2^{6}*3^{6} is the least common multiple of the following three numbers:

x;
4^3=2^6;
6^5 = 2^{5}*3^5;

First notice that x cannot have any other primes other than 2 or/and 3, because LCM contains only these primes.

Now, since the power of 3 in LCM is higher than the powers of 3 in either the second number or in the third, than x must have 3^{6} as its multiple (else how 3^{6} would appear in LCM?).

Next, x can have 2 as its prime in ANY power ranging from 0 to 6, inclusive (it cannot have higher power of 2 since LCM limits the power of 2 to 6).

Thus, x could take total of 7 values.

Answer: C.


Hi Bunuel,
x can take factor of 2 with power from 2 to 6 or no factor of 2. So the answer can be 6 too.
Please explain !
thanks
Re: Fresh Meat!!!   [#permalink] 31 Aug 2013, 09:50
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic A Fresh Start... nirajb 2 22 Feb 2014, 03:36
1 Dead Meat Syndrome - Interviews, Waitlists WishHorse 9 14 Mar 2011, 13:54
fresh potatoes watever 6 19 Feb 2006, 10:16
Here`s an appetizer for you SC beasts! Fresh meat for GMATT73 12 28 Jan 2006, 22:21
Fresh Start maxpowers 2 18 Nov 2005, 09:08
Display posts from previous: Sort by

Fresh Meat!!!

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page   Previous    1   2   3   4   5   6   7   8   9    Next  [ 175 posts ] 



GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.