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

It is currently 21 Aug 2014, 04:48

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: 19036
Followers: 3360

Kudos [?]: 24445 [15] , given: 2677

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 GMAT Prep Discount CodesKnewton GMAT Discount CodesVeritas Prep GMAT Discount Codes
1 KUDOS received
Manager
Manager
User avatar
Joined: 20 Apr 2012
Posts: 89
Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE: Education (Education)
Followers: 9

Kudos [?]: 99 [1] , given: 30

GMAT ToolKit User
Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 05:38
1
This post received
KUDOS
6. The problem states that lcm(x, 2^6, 2^5*3^5)=2^6*3^6.
When we calculate lcm we have to take the highest powers in prime factorizations of numbers.
If lcm contains 3^6 it must be in some number. So, x=3^6*y.
y could be any factor of 2^6. The possible values of x: 3^6, 3^6*2, 3^6*2^2, 3^6*2^3, 3^6*2^4, 3^6*2^5, 3^6*2^6.

The correct answer is C.
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos:)

1 KUDOS received
Manager
Manager
User avatar
Joined: 20 Apr 2012
Posts: 89
Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE: Education (Education)
Followers: 9

Kudos [?]: 99 [1] , given: 30

GMAT ToolKit User
Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 05:43
1
This post received
KUDOS
7. Let two numbers be 25n and 25m, where gcd(n,m)=1. Then 25n+25m=350 or n+m=14. So, our goal is to find pairs of numbers (n,m) such that gcd(n,m)=1 and n+m=14: (1,13), (3,11), (5, 9).

The correct answer is C.
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos:)

1 KUDOS received
Manager
Manager
User avatar
Joined: 20 Apr 2012
Posts: 89
Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE: Education (Education)
Followers: 9

Kudos [?]: 99 [1] , given: 30

GMAT ToolKit User
Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 05:51
1
This post received
KUDOS
8. We know that x*377,910/3,300=some positive integer. Let's simplify this fraction:
Divide numerator and denominator by 30: x*12,597/110.

12,597 is not divisible neither by 11 nor 2 nor 5. So, x must be divisble by 110. Then the least value of x is 110.

The answer is D.
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos:)


Last edited by smyarga on 19 Apr 2013, 06:05, edited 1 time in total.
1 KUDOS received
Manager
Manager
User avatar
Joined: 20 Apr 2012
Posts: 89
Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE: Education (Education)
Followers: 9

Kudos [?]: 99 [1] , given: 30

GMAT ToolKit User
Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 05:56
1
This post received
KUDOS
9. Just add: 1/3+1/9+1/27+1/37=(333+111+37+27)/999=508/999=0.(508).

101st digit after decimal point is 0, because we have period with 3 digits and 101=3*33+2.

The correct answer is A.
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos:)

1 KUDOS received
Manager
Manager
User avatar
Joined: 20 Apr 2012
Posts: 89
Location: Ukraine
GMAT 1: 690 Q51 V31
GMAT 2: 730 Q51 V38
WE: Education (Education)
Followers: 9

Kudos [?]: 99 [1] , given: 30

GMAT ToolKit User
Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 06:02
1
This post received
KUDOS
10. The answer is none. x could be -1. For example (-1)^2=1.
The correct answer is E.
_________________

I'm happy, if I make math for you slightly clearer
And yes, I like kudos:)

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 16 Dec 2011
Posts: 453
Followers: 9

Kudos [?]: 141 [1] , given: 70

Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 09:18
1
This post received
KUDOS
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


Let’s say diagonal of square is 15x and diagonals of rhombus are 11x and 9x where x is an integer.
Area of square = (1/2) * 15^2 * x^2 = (1/2) * 225 * x^2
Area of rhombus = (1/2) * 11*9 * x^2 = (1/2) * 99 * x^2
Difference of areas = (1/2) * 126 * x^2 = 63 * x^2
So, the different must be a multiple of 63.

I. Here x^2 = 1. Possible option.
II. 126 = 63*2. Here x^2 = 2. So, x is not integer. This option is not possible.
III. 252 = 63*4. Here x^2 = 4 --> x = 2. Possible option

Correct answer is D.
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 16 Dec 2011
Posts: 453
Followers: 9

Kudos [?]: 141 [1] , given: 70

Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 09:18
1
This post received
KUDOS
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

Number of subsets with 0 letter = 1
Number of subsets with 1 letter = 7C1 = 7
Number of subsets with 2 letters = 7C2 = 21
Number of subsets with 3 letters = 7C3 = 35
Total number of subsets with at most 3 letters = 1 + 7 + 21 + 35 = 64

Correct answer is E.
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 16 Dec 2011
Posts: 453
Followers: 9

Kudos [?]: 141 [1] , given: 70

Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 09:18
1
This post received
KUDOS
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

Here we need to find out the possible subsets with the numbers {1,2,3,4,5}.

In the short way:
Total number of subsets = 2^5 = 32

In the long way:
Number of subsets with 0 element (null set) = 1
Number of subsets with 1 element = 5C1 = 5
Number of subsets with 2 elements = 5C2 = 10
Number of subsets with 3 elements = 5C3 = 10
Number of subsets with 4 elements = 5C4 = 5
Number of subsets with 5 elements = 5C5 = 1
Total number of subsets = 1+ 5 + 10 + 10 + 5 + 1 = 32

Correct answer is D.
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 16 Dec 2011
Posts: 453
Followers: 9

Kudos [?]: 141 [1] , given: 70

Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 09:19
1
This post received
KUDOS
4. The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of 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

For x = 37, f(x) + g(x) = 5 + 12 = 17
For x = 36, f(x) + g(x) = 5 + 11 = 16
For x = 32, f(x) + g(x) = 5 + 11 = 16
For x = 31, f(x) + g(x) = 5 + 10 = 15
So, 31 < x < 37

Correct answer is C
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 16 Dec 2011
Posts: 453
Followers: 9

Kudos [?]: 141 [1] , given: 70

Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 09:19
1
This post received
KUDOS
5. Which of the following is a factor of 18!+1?

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

18! and 18!+1 are consecutive integers and so they do not have any common factor except 1.
15, 17, 33 (=3*11), and 39 (=3*13) are factors of 18! and none of those can be a factor of 18!+1.
So, only 19 can be a factor of 18!+1

Correct answer is C.
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 16 Dec 2011
Posts: 453
Followers: 9

Kudos [?]: 141 [1] , given: 70

Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 09:20
1
This post received
KUDOS
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

350 = 25 * 14
To have the GCD of two numbers to be 25, we need to split 14 into two co-prime numbers. Such pairs of numbers are: (1,13), (3,11), and (5,9).

Correct answer is C.
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 16 Dec 2011
Posts: 453
Followers: 9

Kudos [?]: 141 [1] , given: 70

Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 09:20
1
This post received
KUDOS
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

377,910 = 3 * 3 * 10 * 4199
3,310 = 3 * 10 *10 * 11
So, x must have 10 and 11 as factors.
--> Least value of x is 110.

Correct answer is D.
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 16 Dec 2011
Posts: 453
Followers: 9

Kudos [?]: 141 [1] , given: 70

Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 09:21
1
This post received
KUDOS
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

x^y=1 can be obtained by any of the following:
(a) y = 0 and x = any real number
(b) x = 1 and y = any real number
(c) x = -1 and y = any even number

I. For x=2 and y=0, x^y=1. So, this condition is not necessarily true.
II. For x=2 and y=0, x^y=1. For x=1 and y=5, x^y=1. So, this condition is not necessarily true.
III. For x=-1 and y=2, x^y=1. So, this condition is not necessarily true.

Correct answer is E.
1 KUDOS received
Manager
Manager
avatar
Status: Looking to improve
Joined: 15 Jan 2013
Posts: 177
GMAT 1: 530 Q43 V20
GMAT 2: 560 Q42 V25
GMAT 3: 650 Q48 V31
Followers: 1

Kudos [?]: 36 [1] , given: 65

Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 12:54
1
This post received
KUDOS
Q4). The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of 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:

Answer - C


g(x) --> Primes - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41
f(x) --> Squares - 1, 4, 9, 16, 25, 36

x = 32 ==> f(32) + g(32) = 5 + 11 = 16
_________________

KUDOS is a way to say Thank You

1 KUDOS received
Manager
Manager
avatar
Status: Looking to improve
Joined: 15 Jan 2013
Posts: 177
GMAT 1: 530 Q43 V20
GMAT 2: 560 Q42 V25
GMAT 3: 650 Q48 V31
Followers: 1

Kudos [?]: 36 [1] , given: 65

Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 13:51
1
This post received
KUDOS
Q8) The product of a positive integer x and 377,910 is divisible by 3,300, then the least value of x is:

Answer is D

3,300 factors are 3 * 11 * 5 ^2 * 2^ 2
377,910 factors are 3^2 * 2 * 5 * 13 * 17 * 19

3,300 can be factor of x * 377,910 only if x has 5 * 11 * 2 as the minimum factors. Hence x is 110
_________________

KUDOS is a way to say Thank You

1 KUDOS received
Manager
Manager
avatar
Joined: 26 Feb 2013
Posts: 54
Concentration: Strategy, General Management
GMAT 1: 660 Q50 V30
WE: Consulting (Telecommunications)
Followers: 0

Kudos [?]: 3 [1] , given: 16

Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 23:06
1
This post received
KUDOS
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
My answer is D
Let the diagonals be 15x,11x and 9x.
Area of a Rhombus is .5*d1*d2
 .5*11x*9x=> 11*9*x2/2. = (99x^2)/2
 Area of square with diagonal 15x is (225x^2)/2
Difference in areas is 63x^2.
Difference can be 63, for X = 1 ; 126 for x=root2 and 252 for x=2.
However when x= root2, the diagonals are not integers. Hence only 2 values are possible. 63 and 252
1 KUDOS received
Manager
Manager
avatar
Joined: 26 Feb 2013
Posts: 54
Concentration: Strategy, General Management
GMAT 1: 660 Q50 V30
WE: Consulting (Telecommunications)
Followers: 0

Kudos [?]: 3 [1] , given: 16

Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 23:06
1
This post received
KUDOS
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
My answer is D.
Total number of subsets that can be formed from {1,2,3,4,5} = 25 =32
1 KUDOS received
Manager
Manager
avatar
Joined: 26 Feb 2013
Posts: 54
Concentration: Strategy, General Management
GMAT 1: 660 Q50 V30
WE: Consulting (Telecommunications)
Followers: 0

Kudos [?]: 3 [1] , given: 16

Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 23:06
1
This post received
KUDOS
4. The functions f and g are defined for all the positive integers n by the following rule: f(n) is the number of 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
My answer C
Squares less than 36 : 1,4,9,16,25 = 5 primes less than 36 : 2,3,5,7,11,13,17,19,23,29,31. =11 and sum =16.
Hence the max value N has to be less than 37 as N =38 will increase the number of primes by 1 and squares by 1. And the sum will be 18
Minimum values of N has to be 32, as any value less than 32 will decrease the number of primes by 1.and the sum will be 15
1 KUDOS received
Manager
Manager
avatar
Joined: 26 Feb 2013
Posts: 54
Concentration: Strategy, General Management
GMAT 1: 660 Q50 V30
WE: Consulting (Telecommunications)
Followers: 0

Kudos [?]: 3 [1] , given: 16

Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 23:08
1
This post received
KUDOS
5. Which of the following is a factor of 18!+1?

A. 15
B. 17
C. 19
D. 33
E. 39
My answer is C.
15, 17,33 and 39 , perfectly divide into 18! Hence leave a reminder of 1, when they divide 18!+1. Hence can be eliminated , leaving 19 the answer.
1 KUDOS received
Manager
Manager
avatar
Joined: 26 Feb 2013
Posts: 54
Concentration: Strategy, General Management
GMAT 1: 660 Q50 V30
WE: Consulting (Telecommunications)
Followers: 0

Kudos [?]: 3 [1] , given: 16

Re: Fresh Meat!!! [#permalink] New post 19 Apr 2013, 23:08
1
This post received
KUDOS
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
My Answer C
66 = 26 *36 and 65 = 25 *35 . 4^3 = 26
Hence X should have 36 and It can have 20 till 26 that is 7 values from 20*36 till 26*36
Re: Fresh Meat!!!   [#permalink] 19 Apr 2013, 23:08
    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  [ 178 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®.