Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 39753

Fresh Meat!!! [#permalink]
Show Tags
17 Apr 2013, 06:11
12
This post received KUDOS
Expert's post
59
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. 252A. I only B. II only C. III only D. I and III only E. I, II and III Solution: freshmeat15104680.html#p12153182. 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: freshmeat151046100.html#p12153233. 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: freshmeat151046100.html#p12153294. 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: freshmeat151046100.html#p12153355. Which of the following is a factor of 18!+1?A. 15 B. 17 C. 19 D. 33 E. 39 Solution: freshmeat151046100.html#p12153386. 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: freshmeat151046100.html#p12153457. 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: freshmeat151046100.html#p12153498. 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: freshmeat151046100.html#p12153599. 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: freshmeat151046100.html#p121536710. 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=0A. I only B. II only C. III only D. I and III only E. None Solution: freshmeat151046100.html#p1215370Kudos points for each correct solution!!!
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Fresh Meat!!! [#permalink]
Show Tags
21 Apr 2013, 22:38
5
This post received KUDOS
Expert's post
11
This post was BOOKMARKED
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. Two consecutive integers are coprime, which means that they don't share ANY common factor but 1. For example 20 and 21 are consecutive integers, thus only common factor they share is 1. Now, since we can factor out each 15, 17, 33=3*11, and 39=3*13 out of 18!, then 15, 17, 33 and 39 ARE factors of 18! and are NOT factors of 18!+1. Therefore only 19 could be a factor of 18!+1. Answer: C.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Fresh Meat!!! [#permalink]
Show Tags
21 Apr 2013, 23:48
5
This post received KUDOS
Expert's post
7
This post was BOOKMARKED



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Fresh Meat!!! [#permalink]
Show Tags
21 Apr 2013, 21:53
4
This post received KUDOS
Expert's post
7
This post was BOOKMARKED
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. 252A. 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.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Fresh Meat!!! [#permalink]
Show Tags
21 Apr 2013, 22:07
4
This post received KUDOS
Expert's post
9
This post was BOOKMARKED
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.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Fresh Meat!!! [#permalink]
Show Tags
21 Apr 2013, 22:56
4
This post received KUDOS
Expert's post
13
This post was BOOKMARKED
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.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1122
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: Fresh Meat!!! [#permalink]
Show Tags
17 Apr 2013, 06:28
3
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
Side square = 15x \(AreaS = \frac{15^2}{2}x^2\) Diagonals= 9x, 11x\(AreaR = \frac{11*9*x^2}{2}\) Difference = \(\frac{15^2x^211*9x^2}{2}= \frac{126x^2}{2}= 63x^2\) \(63=3*3*7\) if x=1 diff = 63 possible and easy to see \(126=2*3*3*7\) x sould be \(\sqrt{2}\) => no integer \(252=2*2*3*3*7\) x=2 possible IMO D. I and III only
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Current Student
Joined: 04 Mar 2013
Posts: 69
Location: India
Concentration: Strategy, Operations
GPA: 3.66
WE: Operations (Manufacturing)

Re: Fresh Meat!!! [#permalink]
Show Tags
17 Apr 2013, 17:14
3
This post received KUDOS
Question 10 The answer would be none of these EI. X=1 ; x could be any no. if y=o II. Y=0; x could become 1 therefore negating this statement III. x=1 or y=0; well x could very well be 1; so not necessary
_________________
When you feel like giving up, remember why you held on for so long in the first place.



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Fresh Meat!!! [#permalink]
Show Tags
21 Apr 2013, 21:58
3
This post received KUDOS
Expert's post
2
This post was BOOKMARKED



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Fresh Meat!!! [#permalink]
Show Tags
21 Apr 2013, 22:29
3
This post received KUDOS
Expert's post
7
This post was BOOKMARKED
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 Perfect squares: 1, 4, 9, 16, 25, 36, .., Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ... If x = 31, then f(31) = 5 and g(31) = 10: f(x) + g(x) = 5 + 10 = 15. If x = 32, then f(32) = 5 and g(32) = 11: f(x) + g(x) = 5 + 11 = 16. ... If x = 36, then f(36) = 5 and g(36) = 11: f(x) + g(x) = 5 + 11 = 16. If x = 37, then f(37) = 6 and g(37) = 11: f(x) + g(x) = 6 + 11 = 17. Thus x could be 32, 33, 34, 35 or 36: 31<x<37. Answer: C.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1122
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: Fresh Meat!!! [#permalink]
Show Tags
17 Apr 2013, 06:34
2
This post received KUDOS
3. How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?It's like asking how many subsets has {1,2,3,4,5} \(2^5=32\) IMO D. 32
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 629

Re: Fresh Meat!!! [#permalink]
Show Tags
17 Apr 2013, 06:35
2
This post received KUDOS
1
This post was BOOKMARKED
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, thus coprime. All options apart from C are present in 18!. Thus 19 is the only factor present in 18!+1. C.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 629

Re: Fresh Meat!!! [#permalink]
Show Tags
17 Apr 2013, 06:55
2
This post received KUDOS
1
This post was BOOKMARKED
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 The two numbers can be represented as 25a and 25b, where a and b are coprime.Also, 25(a+b) = 350 > (a+b) = 14 Thus, a=1,b=13 or a=3,b=11 or a=9,b=5. C.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions
Last edited by mau5 on 18 Apr 2013, 02:11, edited 2 times in total.



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1122
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: Fresh Meat!!! [#permalink]
Show Tags
17 Apr 2013, 07:38
2
This post received KUDOS
2
This post was BOOKMARKED
9. What is the 101st digit after the decimal point in the decimal representation of 1/3 + 1/9 + 1/27 + 1/37?1/3=0.333 1/9=0.333/3=0.111 1/27=0.037 and then repeats 1/37=0.027 and then repeats We can work on the first 3 digits: 0.111+0.333+0.027+0.037=0.508 After the 0 we have at first place a 5, second a 0, third an 8; and so on 4th=5, 5th=0, 6th=8. Every 10th position we have a "change" 10th=5 20th=0 30th=8 and so on 100th=5 and finally 101st=0 IMO A.0 Thanks for the set Bunuel!
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]



Current Student
Joined: 02 Jan 2013
Posts: 57
GPA: 3.2
WE: Consulting (Consulting)

Re: Fresh Meat!!! [#permalink]
Show Tags
17 Apr 2013, 16:06
2
This post received KUDOS
Question 9:
The WONDERFUL thing is that 37*27 = 999, therefore, we can write the sum as: 1/3 + 1/9 + 1/27 + 1/37 = 333/999 + 111/999 + 37/999 + 27/999 = 508/999 = 0.508508508508508...
Note that the decimals repeat themselves in period of 3. Since 101 divided by 3 gives remainder 2, we're looking for the position #2 in the repeated set 508.
Therefore, the digit will be 0.
Answer A



Senior Manager
Joined: 16 Dec 2011
Posts: 430

Re: Fresh Meat!!! [#permalink]
Show Tags
19 Apr 2013, 10:20
2
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
Numbers are: x, 2^6, and (2^5)*(3^5) LCM of the numbers = (2^6)*(3^6) As 3^6 is not part of second and third numbers, it must be part of x. So, lowest and highest values of x can be 3^6 and 6^6 {=(3^6)*(2^6)}. So the values that x can take are: (3^6)*(2^0), (3^6)*(2^1), (3^6)*(2^2), (3^6)*(2^3), (3^6)*(2^4), (3^6)*(2^5), and (3^6)*(2^6).
Correct answer is C.



Senior Manager
Joined: 16 Dec 2011
Posts: 430

Re: Fresh Meat!!! [#permalink]
Show Tags
19 Apr 2013, 10:21
2
This post received KUDOS
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
1/3 = 0.333333……… (recurring 3) 1/9 = 0.111111……… (recurring 1) 1/27 = 0.037037…………. (recurring 037) 1/37 = 0.027027………….. (recurring 027)
1/3 + 1/9 + 1/27 + 1/37 =0.508508…………….. (recurring 508) > 8 will be in every 3rd position > 8 will be in 99th position > 0 will be in 101st position
Correct answer is A.



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Fresh Meat!!! [#permalink]
Show Tags
22 Apr 2013, 00:07



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: Fresh Meat!!! [#permalink]
Show Tags
31 Aug 2013, 10:55
2013gmat wrote: 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 I don;t understand what you mean... x can take the following 7 values: \(3^6\); \(2*3^6\); \(2^2*3^6\); \(2^3*3^6\); \(2^4*3^6\); \(2^5*3^6\); \(2^6*3^6\).
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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? Extrahard Quant Tests with Brilliant Analytics



VP
Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1122
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8

Re: Fresh Meat!!! [#permalink]
Show Tags
17 Apr 2013, 06:31
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?At most 3 letters = 0 letters or 1 letter or 2 letters or 3 letters 0=1 1=7C1=7 2=7C2=21 3=7C3=35 \(1+7+21+35=64\) IMO E. 64
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason Tips and tricks: Inequalities , Mixture  Review: MGMAT workshop Strategy: SmartGMAT v1.0  Questions: Verbal challenge SC III CR New SC set out !! , My QuantRules for Posting in the Verbal Forum  Rules for Posting in the Quant Forum[/size][/color][/b]







Go to page
1 2 3 4 5 6 7 8 9 10
Next
[ 191 posts ]




