Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 06 Oct 2015
Posts: 86

Re: If n = x^5*y^7, where x and y are positive integers greater than 1 [#permalink]
Show Tags
08 Aug 2016, 07:38
MarkusKarl wrote: I'll give it a try.
A) X, Y = prime.
If X =/= Y then we would know the answer (6*8 factors). However, if X=Y then we would receive a lot of answers that would generate the same factors with the previous method. e.g. x=y=3 => 3^3*3^1=3^1*3^3.
Thus, A is insufficient.
As for B) (Which, in all honesty, was my first choice before I analyzed the question further). We now know that x and y consist of 2 prime numbers.
IF x and y are two different prime numbers we would be able to answer the question. However(and here was my mistake), that information is given in (A). (In that case it would indeed be 6*8 factors).
X and Y can still be different composite numbers without giving n more than 2 prime factors. e.g. x = 2*3 and y = 2*2*3. X and Y can also be composite numbers where x and y are two different prime numbers taken to any power.
Thus, (as written above) We needed the information about x and y being prime numbers from (A) and we needed the information that n only had two different prime factors from (B). Thus > C is the answer.
Great question, thanks! Can a single prime number work for both X and Y? If so then it should be written X and X, I think, not X and Y.



Manager
Joined: 15 Mar 2015
Posts: 113

Re: If n = x^5*y^7, where x and y are positive integers greater than 1 [#permalink]
Show Tags
08 Aug 2016, 08:21
NaeemHasan wrote: MarkusKarl wrote: I'll give it a try.
A) X, Y = prime.
If X =/= Y then we would know the answer (6*8 factors). However, if X=Y then we would receive a lot of answers that would generate the same factors with the previous method. e.g. x=y=3 => 3^3*3^1=3^1*3^3.
Thus, A is insufficient.
As for B) (Which, in all honesty, was my first choice before I analyzed the question further). We now know that x and y consist of 2 prime numbers.
IF x and y are two different prime numbers we would be able to answer the question. However(and here was my mistake), that information is given in (A). (In that case it would indeed be 6*8 factors).
X and Y can still be different composite numbers without giving n more than 2 prime factors. e.g. x = 2*3 and y = 2*2*3. X and Y can also be composite numbers where x and y are two different prime numbers taken to any power.
Thus, (as written above) We needed the information about x and y being prime numbers from (A) and we needed the information that n only had two different prime factors from (B). Thus > C is the answer.
Great question, thanks! Can a single prime number work for both X and Y? If so then it should be written X and X, I think, not X and Y. Hi, I am not sure that I understand your question, but i will try to respond. The question does not state that x and y are different numbers. As such, we are not able to answer the question with just a. We receive that information when a and b are combined. Please let me know if I misunderstood the question or if I can clarify further. Best wishes Posted from my mobile device
_________________
I love being wrong. An incorrect answer offers an extraordinary opportunity to improve.



Intern
Joined: 05 Aug 2016
Posts: 5

Re: If n = x^5*y^7, where x and y are positive integers greater than 1 [#permalink]
Show Tags
08 Aug 2016, 10:52
1
This post received KUDOS
If x and y are positive integers and n=x5∗y7n=x5∗y7, then how many positive divisors does n have? (1) x does not have a factor p such that 1 < p < x and y does not have a factor q such that 1 < q < y. (2) n has only two prime factors. Giving it a try (This was actually my second attempt): S1 states that X and Y are prime numbers with no current constraints Can we find the number of positive divisors of N from that? ( MGMAT says to work to prove the statement insuff) Scen 1: (X = 2, Y = 3) (2^5)(3^7) No of divisors (5+1)(7+1) = 48 Scen 2 (X = 2, Y = 2) (2^12) No. of Divisors =/= 48 S1 is insufficient due to multiple answers S2 states that N has two different prime numbers meaning that X and/or Y can be any numbers that share at most two prime factors (eg: [2,3],[2,6], [2,10], [5,15], [15,15]) Scen 1: (X = 2, Y = 3) (2^5)(3^7) No of divisors (5+1)(7+1) = 48 Scen 2 (X = 2, Y = 6) (PF = 2 & 3) Honestly, I don't even know what the number of divisors would be but I know it's not 48, and I'm not going to waste time trying to figure out what that number is. Knowing it's not 48 is enough for me to say it's insufficient. So A, D, & B are eliminatedNow to try S1 & S2 together: S1: X and Y are prime numbers & S2: X and Y must be different prime numbers Scen 1: (X = 2, Y = 3) (2^5)(3^7) No of divisors (5+1)(7+1) = 48 Scen 1: (X = 2, Y = 5) (2^5)(5^7) No of divisors (5+1)(7+1) = 48 So the answer is C. During my first try while I was scribbling on paper I read S2 as having the parameters of S1 & S2 combined. I essentially read it as X and Y have to be different prime numbers, which was the incorrect way to read it.



Manager
Joined: 06 Oct 2015
Posts: 86

Re: If n = x^5*y^7, where x and y are positive integers greater than 1 [#permalink]
Show Tags
09 Aug 2016, 03:35
MarkusKarl wrote: NaeemHasan wrote: MarkusKarl wrote: I'll give it a try.
A) X, Y = prime.
If X =/= Y then we would know the answer (6*8 factors). However, if X=Y then we would receive a lot of answers that would generate the same factors with the previous method. e.g. x=y=3 => 3^3*3^1=3^1*3^3.
Thus, A is insufficient.
As for B) (Which, in all honesty, was my first choice before I analyzed the question further). We now know that x and y consist of 2 prime numbers.
IF x and y are two different prime numbers we would be able to answer the question. However(and here was my mistake), that information is given in (A). (In that case it would indeed be 6*8 factors).
X and Y can still be different composite numbers without giving n more than 2 prime factors. e.g. x = 2*3 and y = 2*2*3. X and Y can also be composite numbers where x and y are two different prime numbers taken to any power.
Thus, (as written above) We needed the information about x and y being prime numbers from (A) and we needed the information that n only had two different prime factors from (B). Thus > C is the answer.
Great question, thanks! Can a single prime number work for both X and Y? If so then it should be written X and X, I think, not X and Y. Hi, I am not sure that I understand your question, but i will try to respond. The question does not state that x and y are different numbers. As such, we are not able to answer the question with just a. We receive that information when a and b are combined. Please let me know if I misunderstood the question or if I can clarify further. Best wishes Posted from my mobile device My point is that X and Y can not represent a sigle value. As X and Y are different letters they should reflect different values and hence A should be the answer. Hope, you got my point now.



Intern
Joined: 05 Aug 2016
Posts: 5

Re: If n = x^5*y^7, where x and y are positive integers greater than 1 [#permalink]
Show Tags
09 Aug 2016, 09:10
NaeemHasan wrote: My point is that X and Y can not represent a sigle value. As X and Y are different letters they should reflect different values and hence A should be the answer. Hope, you got my point now. X and Y are different variables that represent some integer value, and without specific constraints they each can represent any value on the number line: ∞ < X < ∞ & ∞ < Y < ∞. This also means that, unless otherwise stated, X = Y is a possibility.



Math Expert
Joined: 02 Sep 2009
Posts: 44657

Re: If n = x^5*y^7, where x and y are positive integers greater than 1 [#permalink]
Show Tags
09 Aug 2016, 09:52



Manager
Joined: 06 Oct 2015
Posts: 86

Re: If n = x^5*y^7, where x and y are positive integers greater than 1 [#permalink]
Show Tags
09 Aug 2016, 09:56
Bunuel wrote: NaeemHasan wrote: My point is that X and Y can not represent a sigle value. As X and Y are different letters they should reflect different values and hence A should be the answer. Hope, you got my point now.
Unless it is explicitly stated otherwise, different variables CAN represent the same number. Thank you for your explanation. I didn't know it.



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2582
GRE 1: 323 Q169 V154

Re: If n = x^5*y^7, where x and y are positive integers greater than 1 [#permalink]
Show Tags
21 Aug 2016, 04:47
NaeemHasan wrote: Statement 1 is sufficient alone. If we know that X and Y are primes then obviously we can determine the number of factors of n. Total factors are (5+1)*(7+1)=48. But unfortunately the OA is C. Where is my mistake? Can you, bunuel, help me to understand the fact, please. Hi there See if x=y => number of factors = 13 if not then the number of factors = 48 statement 2 is insufficient as x=2*3 and y=1 is different from x=3 and y=2 combining them we can say that x and y are both different primes hence the number of factors = 48 Smash that C
_________________
Getting into HOLLYWOOD with an MBA The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)Average GRE Scores At The Top Business Schools!



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2582
GRE 1: 323 Q169 V154

Re: If n = x^5*y^7, where x and y are positive integers greater than 1 [#permalink]
Show Tags
21 Nov 2016, 08:34
Hi Abhishek007 I am stuck on this one I seriously think the answer here should be A. Can you explain this to me. Why is A not correct here.? Here is my logic Here N= x^5*y^7 Statement 1=> x and y are prime So number of factors of N must be 6*8=> 48 Sufficient Statement 2 Here we can make test cases to see that its not sufficient e.g=> y=1 x=6 factors =36 x=7 y=5 factors = 48 Hence Insufficient Regards Stone Cold
_________________
Getting into HOLLYWOOD with an MBA The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)Average GRE Scores At The Top Business Schools!



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2582
GRE 1: 323 Q169 V154

Re: If n = x^5*y^7, where x and y are positive integers greater than 1 [#permalink]
Show Tags
21 Nov 2016, 08:36



Senior Manager
Joined: 03 Apr 2013
Posts: 290
Location: India
Concentration: Marketing, Finance
GPA: 3

Re: If n = x^5*y^7, where x and y are positive integers greater than 1 [#permalink]
Show Tags
26 Mar 2017, 04:37
Bunuel wrote: If x and y are positive integers and \(n = x^5*y^7\), then how many positive divisors does n have?
(1) x does not have a factor p such that 1 < p < x and y does not have a factor q such that 1 < q < y. (2) n has only two prime factors. BunuelHi..I got the correct answer..but I have a question. Consider statement (1) x does not have a factor p such that 1 < p < x and y does not have a factor q such that 1 < q < y. Does this statement stop any of x and y from being = 1 ?? If we translate it in mathematical terms..it will become 1<p<1. So x = 1 is possible because nothing satisfies the translated condition..maybe I'm just being silly but it still is intriguing to me
_________________
Spread some love..Like = +1 Kudos



Math Expert
Joined: 02 Sep 2009
Posts: 44657

Re: If n = x^5*y^7, where x and y are positive integers greater than 1 [#permalink]
Show Tags
26 Mar 2017, 04:51
ShashankDave wrote: Bunuel wrote: If x and y are positive integers and \(n = x^5*y^7\), then how many positive divisors does n have?
(1) x does not have a factor p such that 1 < p < x and y does not have a factor q such that 1 < q < y. (2) n has only two prime factors. BunuelHi..I got the correct answer..but I have a question. Consider statement (1) x does not have a factor p such that 1 < p < x and y does not have a factor q such that 1 < q < y. Does this statement stop any of x and y from being = 1 ?? If we translate it in mathematical terms..it will become 1<p<1. So x = 1 is possible because nothing satisfies the translated condition..maybe I'm just being silly but it still is intriguing to me 1 < p < x means that x is greater than 1. 1 < q < y means that y is greater than 1.
_________________
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: 44657

If n = x^5*y^7, where x and y are positive integers greater than 1 [#permalink]
Show Tags
17 Jul 2017, 10:28
Official Solution:If \(n = x^5*y^7\), where \(x\) and \(y\) are positive integers greater than 1, then how many positive divisors does \(n\) have? (1) \(x\) does not have a factor \(p\) such that \(1 < p < x\) and \(y\) does not have a factor \(q\) such that \(1 < q < y\). This statement implies that both \(x\) and \(y\) are primes (a prime number does not have a factor which is greater than 1 and less than itself, it has only two factors 1 and itself). Now, if \(x\) and \(y\) are different primes, then the number of factors of \(n\) will be \((5+1)(7+1)=48\) but if \(x=y\), then \(n = x^5*y^7=x^{12}\) and it will have 13 factors. Not sufficient. (2) \(n\) has only two prime factors. If those primes are \(x\) and \(y\), then the number of factors of \(n\) will be \((5+1)(7+1)=48\) but if, say \(x=2*3=6\) and \(y=2\), then \(n = x^5*y^7=2^{12}*3^5\) and it will have \((12+1)(5+1)=78\) factors. Not sufficient. (1)+(2) Since from (2) \(n\) has only two prime factors, then from (1) it follows that \(x\) and \(y\) are different primes so the number of factors of \(n\) will be \((5+1)(7+1)=48\). Sufficient. Answer: C
_________________
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



Senior Manager
Joined: 02 Apr 2014
Posts: 478

Re: If n = x^5*y^7, where x and y are positive integers greater than 1 [#permalink]
Show Tags
16 Nov 2017, 13:03
Trap for this question is x can be equal to y.
Answer (C)




Re: If n = x^5*y^7, where x and y are positive integers greater than 1
[#permalink]
16 Nov 2017, 13:03



Go to page
Previous
1 2
[ 34 posts ]



