Jul 26 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 27 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Jul 28 07:00 PM EDT  08:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Sunday, July 28th at 7 PM EDT
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 12 Aug 2015
Posts: 283
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37 GMAT 2: 650 Q43 V36 GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)

For nonnegative integers x , y , and m , what is the greatest value
[#permalink]
Show Tags
23 Jan 2016, 02:08
Question Stats:
47% (02:11) correct 53% (02:19) wrong based on 335 sessions
HideShow timer Statistics
For nonnegative integers x, y, and m, what is the greatest value of m for which x^m is a factor of y!? (1) y=x−1 (2) x is a prime number
Official Answer and Stats are available only to registered users. Register/ Login.
_________________




Math Expert
Joined: 02 Aug 2009
Posts: 7763

For nonnegative integers x , y , and m , what is the greatest value
[#permalink]
Show Tags
23 Jan 2016, 02:23
shasadou wrote: For nonnegative integers x, y, and m, what is the greatest value of m for which x^m is a factor of y!?
(1) y=x−1
(2) x is a prime number Hi, A Good Q.. the Q statement is "For nonnegative integers x, y, and m, what is the greatest value of m for which x^m is a factor of y!?"What doe sthis mean.. It means the largest power of x that is there in y!.. formula is y/x + y/x^2.. and so on till the fraction y/x^z becomes less than 1.. x is a prime number or the biggest prime in any integer.. lets see the sentences.. (1) y=x−1this means x^m in (x1)!.. y/x + y/x^2.. and so on means (x1)!/x.. if x is prime, answer is 0.. if not it will depend on x.. say x=6, so y=5.. check for 3s in 5! as 3 is the largest prime number in 6.. 5/3=1 so m=1.. different answers But we do not know if x is prime or what is the largest prime in the integer x.. insuff (2) x is a prime numbersince there is no corelation in y and x, we cannot answer .. say y is 50 and prime is 5, then it is 50/5+50/25=12.. and say 4 and prime is 3then 4/3=1.. insuff.. combined . we know that x is prime and y is x1..from this it becomes clear that y! or (x1)! will not have x..so power of x will be 0, or m=0.. suff C
_________________




CEO
Joined: 12 Sep 2015
Posts: 3857
Location: Canada

Re: For nonnegative integers x , y , and m , what is the greatest value
[#permalink]
Show Tags
23 Jan 2016, 14:21
Aside: Whenever you see the word "nonnegative," you should ask yourself "Why didn't they just say POSITIVE?" The answer to this question is a big hint. Nonnegative is not the same as positive, since ZERO is a nonnegative number and zero is not positive. So, when you see the word "nonnegative," be sure to consider the possibility that the number equals zero. Cheers, Brent
_________________
Test confidently with gmatprepnow.com



Current Student
Joined: 12 Aug 2015
Posts: 2609

Re: For nonnegative integers x , y , and m , what is the greatest value
[#permalink]
Show Tags
16 Mar 2016, 06:38
chetan2u wrote: shasadou wrote: For nonnegative integers x, y, and m, what is the greatest value of m for which x^m is a factor of y!?
(1) y=x−1
(2) x is a prime number Hi, A Good Q.. the Q statement is "For nonnegative integers x, y, and m, what is the greatest value of m for which x^m is a factor of y!?"What doe sthis mean.. It means the largest power of x that is there in y!.. formula is y/x + y/x^2.. and so on till the fraction y/x^z becomes less than 1.. x is a prime number or the biggest prime in any integer.. lets see the sentences.. (1) y=x−1this means x^m in (x1)!.. y/x + y/x^2.. and so on means (x1)!/x.. if x is prime, answer is 0.. if not it will depend on x.. say x=6, so y=5.. check for 3s in 5! as 3 is the largest prime number in 6.. 5/3=1 so m=1.. different answers But we do not know if x is prime or what is the largest prime in the integer x.. insuff (2) x is a prime numbersince there is no corelation in y and x, we cannot answer .. say y is 50 and prime is 5, then it is 50/5+50/25=12.. and say 4 and prime is 3then 4/3=1.. insuff.. combined . we know that x is prime and y is x1..from this it becomes clear that y! or (x1)! will not have x..so power of x will be 0, or m=0.. suff C This took me 4 minutes to solve Any other methods?
_________________



Current Student
Joined: 28 Nov 2014
Posts: 843
Concentration: Strategy
GPA: 3.71

For nonnegative integers x , y , and m , what is the greatest value
[#permalink]
Show Tags
28 Sep 2016, 00:13
Is there any alternate way to crack this problem. Bunuel please help. I tried solving it by making cases and took somewhere close to 3 minutes to figure it out.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9458
Location: Pune, India

Re: For nonnegative integers x , y , and m , what is the greatest value
[#permalink]
Show Tags
28 Sep 2016, 00:33
shasadou wrote: For nonnegative integers x, y, and m, what is the greatest value of m for which x^m is a factor of y!?
(1) y=x−1
(2) x is a prime number We need the greatest value of m for which x^m is a factor of y! We have no relative values of x, y and m given in the question stem. (1) y=x−1 Think what this means. Say x = 8. Then y = 7 We need greatest m such that 8^m is a factor of 7! 7! has a 2, a 4 and a 6 so it has four 2s. So it can make one 8. So m = 1. But what if x = 7? Then y = 6 We need greatest m such that 7^m is a factor of 6!. Can we make 7 out of first 6 numbers? No, because 7 is prime. So it means that you can never make 7 out of any other 2 factors. So m = 0 Not sufficient. (2) x is a prime number x could be 7 but y could be either 6 or 10 (or infinite other values). 6! will not have any 7s but 10! will. Not sufficient. Using both: This is our second case above. If x = prime, y is prime  1. All numbers till prime  1 will not be able to make a single prime. i.e. our second case above. If x = 7, then y = 6 and all positive integers till 6 will not be able to make a 7. So m will always be 0. Answer (C)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3625

Re: For nonnegative integers x , y , and m , what is the greatest value
[#permalink]
Show Tags
28 Sep 2016, 00:51
Keats wrote: Is there any alternate way to crack this problem. Bunuel please help. I tried solving it by making cases and took somewhere close to 3 minutes to figure it out. This took me only 1 min to solve. Here is how I approached. We are given x, y, and m and non negative integers. So, we need to have x,y and m >=0; We need to find the greatest value of m such that y!/x^m = Integer. Now Statement 1 : y=x−1. It means x and y are coprimes. Now, I checked the fraction for x=2, y=1, for this m has to be zero. Now I checked for a larger number say x=10; y = 9, for this m could be 0 and 1 but not greater than that.  INSUFFICIENT. Statement 2 : x is prime. Nothing about y. Insufficient Combining : So, for any value of prime, we will always have m = 0 because positive value of m will NEVER make the two co primes divisible.. HENCE I MARKED C.
_________________
My GMAT Story: From V21 to V40My MBA Journey: My 10 years long MBA DreamMy Secret Hacks: Best way to use GMATClub  Importance of an Error Log!Verbal Resources: All SC Resources at one place  All CR Resources at one placeBlog: Subscribe to Question of the Day BlogGMAT Club Inbuilt Error Log Functionality  View More. New Visa Forum  Ask all your Visa Related Questions  here. New! Best Reply Functionality on GMAT Club!Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for freeCheck our new About Us Page here.



Manager
Joined: 22 Feb 2016
Posts: 85
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47 GMAT 2: 710 Q47 V39
GPA: 3.57

Re: For nonnegative integers x , y , and m , what is the greatest value
[#permalink]
Show Tags
19 Dec 2016, 05:38
Just ensuring that my understanding of the concepts is correct. We have to find the maximum value of m for which x^m is is a factor of y!
Statement 1 y+1=x now if y=5 x=4 then m=1 but if y=10 and x=9 them m=2 NS
Statement 2 x is prime quite not sufficient in itself.
However combining 1 and 2 we have the following situation where x is prime and y is a coprime thus the only factor is 1 so C
I guess I am making a mistake here. Please correct me



Intern
Joined: 18 May 2016
Posts: 34

Re: For nonnegative integers x , y , and m , what is the greatest value
[#permalink]
Show Tags
20 Dec 2016, 08:39
Question asks: how many number x can be formed using elements in y!. Stat.1 gives x=y+1. So x is not in y!. Can x be constructed from elements of y!? Stat.2 gives that x is prime, thus x can't be built from other numbers. Answer: C.



Intern
Joined: 17 Jul 2017
Posts: 15

Re: For nonnegative integers x , y , and m , what is the greatest value
[#permalink]
Show Tags
31 Jul 2017, 13:19
Very tricky.
1) You should see X could be 1 and Y is 0!, 0! is 1 (for whatever reason) therefore M could be any number. Also if X=2, Y=1 therefore M =0 So not sufficient 2) If X =2, Y has no restriction. So Y! could also be 2! so M=1. But Y could also be 9! and M could equal 2 as 3^2 is a factor or 9! as 9! contains a 9 which is a factor of 3^2. So this number could be infinite.
In terms of CWe know Y! is always less than X and X is prime. So if Y! is less than X we know the prime is always above 6! A prime number such as 7^M doesn't go into 6! Because 7 is a prime and there are no prime factors of 7 in 6X5X4X3X2X1. Therefore, M always has to be zero because only 1 is a factor. This is now sufficient.



NonHuman User
Joined: 09 Sep 2013
Posts: 11757

Re: For nonnegative integers x , y , and m , what is the greatest value
[#permalink]
Show Tags
16 Aug 2018, 13:43
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: For nonnegative integers x , y , and m , what is the greatest value
[#permalink]
16 Aug 2018, 13:43






