Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: Fresh Meat!!!
[#permalink]
Show Tags
17 May 2014, 08:39
NGGMAT wrote: Bunuel wrote: NGGMAT wrote: Dear Bunnel
I didnt understand this.
y didnt we take the set {1,2,3,4,5} into consideration and solve like the above qs? where did we get 2^5 from? What do you mean by the red part? As for 2^5: the number of subsets of nelement set is 2^n, thus the number of subsets of 5element set {1, 2, 3, 4, 5} is 2^5 (note that this includes an empty set as well as the original set {1, 2, 3, 4, 5}). Now, all subsets of {1, 2, 3, 4, 5} are the subsets of {0, 1, 2, 3, 4, 5} and does not include 0. Does this make sense? By red part i meant that y we havent solved it like we did the below qs: 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
1 empty set; C^1_7=7 sets with one element; C^2_7=21 sets with two elements; C^3_7=35 sets with three element.
Total 1+7+21+35=64 setsy did 2^n come into qs 3 and not qs 2? We could use 2^n for the second question too: {The number of subsets with 0, 1, 2, or 3 terms} = {The total # of subsets}  {Subsets with 4, 5, 6, or 7 elements} = \(2^7  (C^4_7+C^5_7+C^6_7+C^7_7)=128(35+21+7+1)=64\). But as you can see this approach is longer than the one used in my solution for that question.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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



Intern
Joined: 10 Mar 2014
Posts: 14
Location: United States
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: Fresh Meat!!!
[#permalink]
Show Tags
25 May 2014, 11:41
Hi Bunuel, 1. I went about the combinatorial approach and got 31 and saw your response below that states that one subset is the null set (empty set) 2. Now I also came across M1623 in the GMAT club tests that states that "If the mean of the set S does not exceed mean of any subset of set S, which of the following must be true about set S?" And the right answer to that question is "all elements in set S are equal" and "the median of set S equals the mean of set S". Aren't 1 and 2 contradictory? The only way in question M1623 set S can have a mean more than mean of every subset including null set is if set S is null itself? I am sure I am overthinking this and just need my caffeine. Thanks, Meera 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.



Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: Fresh Meat!!!
[#permalink]
Show Tags
28 May 2014, 03:53
Miraarun12345 wrote: Hi Bunuel, 1. I went about the combinatorial approach and got 31 and saw your response below that states that one subset is the null set (empty set) 2. Now I also came across M1623 in the GMAT club tests that states that "If the mean of the set S does not exceed mean of any subset of set S, which of the following must be true about set S?" And the right answer to that question is "all elements in set S are equal" and "the median of set S equals the mean of set S". Aren't 1 and 2 contradictory? The only way in question M1623 set S can have a mean more than mean of every subset including null set is if set S is null itself? I am sure I am overthinking this and just need my caffeine. Thanks, Meera 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. The point is that an empty set has no mean or the median, so when considering the subsets of S, we can ignore an empty set. Anyway this is out of the scope of the GMAT, so I wouldn't worry about it at all.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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



Intern
Status: Learning
Joined: 07 Aug 2011
Posts: 36
Location: India
Schools: WBUT  Class of 2011
GMAT Date: 01062014
GPA: 2.6
WE: Research (Education)

Re: Fresh Meat!!!
[#permalink]
Show Tags
20 Aug 2014, 01:35
If x = 31, then f(31) = 5 and g(31) = 10: f(x) + g(x) = 5 + 10 = 15. Why g(31) = 10 is not a prime number. Bunuel wrote: 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.
_________________
If you like my post give me kudos.
Arindam Sur Researcher, Academian



Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: Fresh Meat!!!
[#permalink]
Show Tags
20 Aug 2014, 03:31
arindamsur wrote: If x = 31, then f(31) = 5 and g(31) = 10: f(x) + g(x) = 5 + 10 = 15. Why g(31) = 10 is not a prime number. Bunuel wrote: 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. Why should it be? g(n) is the number of primes numbers less than n: the number of prime numbers less than 31 is 10: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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



Intern
Joined: 03 Sep 2014
Posts: 6

Fresh Meat!!!
[#permalink]
Show Tags
Updated on: 09 Sep 2014, 07:46
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. I used a choose method and got 31. With the binary method you used, there is a set which contains no numbers. This increases the number to 32. But the question doesn't say there can be a subset with no numbers because 0 is also not included... but I like the binary method & may use it on these kinds of problems & just subtract 1 if that is necessary so THANK YOU. Thank you
Originally posted by logophobic on 09 Sep 2014, 07:35.
Last edited by logophobic on 09 Sep 2014, 07:46, edited 3 times in total.



Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: Fresh Meat!!!
[#permalink]
Show Tags
09 Sep 2014, 07:38
logophobic 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. I used a choose method and got 31. With the binary method you used, there is a set which contains no numbers. This increases the number to 32. But the question doesn't say there can be a subset with no numbers because 0 is also not included... Empty set is a subset of all nonempty sets.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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



Current Student
Joined: 10 Aug 2014
Posts: 49

Re: Fresh Meat!!!
[#permalink]
Show Tags
12 Dec 2014, 23:26
Bunuel wrote: 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. I believe the answer is wrong or please explain. My reasoning IF x=36, there are 6 perfect squares NOT 5 (1,2,3,4,5,,6), and the sum would be 17. Thus the answer A is correct.



Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: Fresh Meat!!!
[#permalink]
Show Tags
13 Dec 2014, 05:44
mika84 wrote: Bunuel wrote: 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. I believe the answer is wrong or please explain. My reasoning IF x=36, there are 6 perfect squares NOT 5 (1,2,3,4,5,,6), and the sum would be 17. Thus the answer A is correct. There are 5 positive perfect squares less than 36: 1 = 1^1, 4 = 2^2, 9 = 3^2, 16 = 4^4, and 25 = 5^2.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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: 49300

Re: Fresh Meat!!!
[#permalink]
Show Tags
13 Dec 2014, 06:56



Senior Manager
Joined: 18 Aug 2014
Posts: 325

Re: Fresh Meat!!!
[#permalink]
Show Tags
08 Jan 2016, 14:39
Bunuel wrote: 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
\(\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{37}=\frac{333}{999} + \frac{111}{999} + \frac{37}{999} + \frac{27}{999}=\frac{508}{999}=0.508508...\).
102nd digit will be 8, thus 101st digit will be 0.
Answer: A. Can we see that since 5 is the first digit it will be the 100th digit and count from there or is that pure luck on this problem?
_________________
Please help me find my lost Kudo's bird



Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: Fresh Meat!!!
[#permalink]
Show Tags
10 Jan 2016, 06:16
redfield wrote: Bunuel wrote: 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
\(\frac{1}{3} + \frac{1}{9} + \frac{1}{27} + \frac{1}{37}=\frac{333}{999} + \frac{111}{999} + \frac{37}{999} + \frac{27}{999}=\frac{508}{999}=0.508508...\).
102nd digit will be 8, thus 101st digit will be 0.
Answer: A. Can we see that since 5 is the first digit it will be the 100th digit and count from there or is that pure luck on this problem? Pattern starts with 5 and repeats in block of three: 508 508 508... Thus 5 will be 100th digit because 100 = {multiple of 3} + 1 and 101st digit will be next number in pattern  0.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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



Manager
Joined: 07 Jun 2017
Posts: 103

Re: Fresh Meat!!!
[#permalink]
Show Tags
18 Aug 2017, 02:21
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. Bunuel, please correct me if I am wrong, the 7 values included below? 1) 3 2) 2 3) 2^2 4) 2^3 5) 2^4 6) 2^5 7) 2^6 Thank you so much



Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: Fresh Meat!!!
[#permalink]
Show Tags
18 Aug 2017, 02:31
pclawong 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. Bunuel, please correct me if I am wrong, the 7 values included below? 1) 3 2) 2 3) 2^2 4) 2^3 5) 2^4 6) 2^5 7) 2^6 Thank you so much 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: Ultimate GMAT Quantitative Megathread  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: 49300

Re: Fresh Meat!!!
[#permalink]
Show Tags
18 Aug 2017, 02:38
pclawong wrote: Bunuel wrote: 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
We are told that the greatest common factor of two integers is 25. So, these integers are \(25x\) and \(25y\), for some positive integers \(x\) and \(y\). Notice that \(x\) and \(y\) must not share any common factor but 1, because if they do, then GCF of \(25x\) and \(25y\) will be more that 25.
Next, we know that \(25x+25y=350\) > \(x+y=14\) > since \(x\) and \(y\) don't share any common factor but 1 then (x, y) can be only (1, 13), (3, 11) or (5, 9) (all other pairs (2, 12), (4, 10), (6, 8) and (7, 7) do share common factor greater than 1).
So, there are only three pairs of such numbers possible: 25*1=25 and 25*13=325; 25*3=75 and 25*11=275; 25*5=125 and 25*9=225.
Answer: C. Bunuel, How do we know if x and y do not share any common factor? what is the hint? Thank you If x and y are NOT coprime, the GCD of \(25x\) and \(25y\) will be more than 25, not 25 as given.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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



Manager
Joined: 18 Mar 2015
Posts: 104
Location: India
GPA: 3.59

Re: Fresh Meat!!!
[#permalink]
Show Tags
30 Aug 2017, 05:14
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. Hu bunuel , I understood the logic but how the total came to 7 for 3power 6 and 2 power any value between 2 to 6?



Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: Fresh Meat!!!
[#permalink]
Show Tags
30 Aug 2017, 05:17
r19 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. Hu bunuel , I understood the logic but how the total came to 7 for 3power 6 and 2 power any value between 2 to 6? This is answered many times... 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: Ultimate GMAT Quantitative Megathread  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



Intern
Joined: 16 Jul 2016
Posts: 20

Fresh Meat!!!
[#permalink]
Show Tags
12 Sep 2017, 02:38
[quote="Bunuel"]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
Notice that if x=1 and y is any even number, then \((1)^{even}=1\), thus none of the options must be true.
Why is the option b incorrect? If x is equal to 1 and its raised to the power 0 then it will be 1 only.



Math Expert
Joined: 02 Sep 2009
Posts: 49300

Re: Fresh Meat!!!
[#permalink]
Show Tags
12 Sep 2017, 02:42



Intern
Joined: 09 Mar 2018
Posts: 7

Re: Fresh Meat!!!
[#permalink]
Show Tags
26 Apr 2018, 04:18
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 
Question can be rewritten in simpler forms as  (x*377910)/3300 And what we have to check here is  Can 3300 fully divide the numerator ?
Upon further simplification, it becomes  (x*12597)/110
Now prime factorize the denominator  2*5*11 None of these prime factors can further divide 12597. Therefore 12597 should be multiplied by 110 (i.e., x should be 110), in order for the expression to get fully reduced.
Hence D is the answer.




Re: Fresh Meat!!! &nbs
[#permalink]
26 Apr 2018, 04:18



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



