Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 20 Aug 2013
Posts: 11
Location: United States
Concentration: Marketing, Strategy
WE: Project Management (Consulting)

If k is a positive integer, then 20k is divisible by how man [#permalink]
Show Tags
22 Aug 2013, 04:14
2
This post received KUDOS
9
This post was BOOKMARKED
Question Stats:
57% (01:35) correct
43% (00:29) wrong based on 482 sessions
HideShow timer Statistics
If k is a positive integer, then 20k is divisible by how many different positive integers? (1) k is prime (2) k = 7 Divisible by a positive integer > factor No of factors for a number in the form (a^x)(b^y)(c^z) is given by (x+1)(y+1)(z+1)
20k = (2^2)(5^1)(k)
Stmt 1 says k is prime. so 20k = (2^2)(5^1)(k^1). Total # of factors is (2+1)(1+1)(1+1). So sufficient.
Stmy 2 says k = 7 so again Total # of factors is (2+1)(1+1)(1+1). So sufficient.
Hence answer is D, but that is not the OA. What am I missing?
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 22 Aug 2013, 04:17, edited 1 time in total.
Edited the question.



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 629

Re: If k is a positive integer, then 20k is divisible by [#permalink]
Show Tags
22 Aug 2013, 04:21
4
This post received KUDOS
2
This post was BOOKMARKED
spjmanoli wrote: If k is a positive integer, then 20k is divisible by how many different positive integers? 1. k is prime 2. k is 7
Divisible by a positive integer > factor No of factors for a number in the form (a^x)(b^y)(c^z) is given by (x+1)(y+1)(z+1)
20k = (2^2)(5^1)(k)
Stmt 1 says k is prime. so 20k = (2^2)(5^1)(k^1). Total # of factors is (2+1)(1+1)(1+1). So sufficient.
Stmy 2 says k = 7 so again Total # of factors is (2+1)(1+1)(1+1). So sufficient.
Hence answer is D, but that is not the OA. What am I missing? What you are missing in F.S 1, is that we don't know the value of k. Scenario I: k=2, the total no of factors for 20k = \(2^2*5*2 = 2^3*5 = (3+1)*(1+1) = 8\) Scenario II: k=3, the total no of factors for 20k = \(2^2*5*3 = (2+1)*(1+1)*(1+1) = 12.\) Hence, 2 different answers, thus, Insufficient.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: If k is a positive integer, then 20k is divisible by how man [#permalink]
Show Tags
22 Aug 2013, 04:21
3
This post received KUDOS
Expert's post
12
This post was BOOKMARKED
spjmanoli wrote: If k is a positive integer, then 20k is divisible by how many different positive integers? (1) k is prime (2) k = 7 Divisible by a positive integer > factor No of factors for a number in the form (a^x)(b^y)(c^z) is given by (x+1)(y+1)(z+1)
20k = (2^2)(5^1)(k)
Stmt 1 says k is prime. so 20k = (2^2)(5^1)(k^1). Total # of factors is (2+1)(1+1)(1+1). So sufficient.
Stmy 2 says k = 7 so again Total # of factors is (2+1)(1+1)(1+1). So sufficient.
Hence answer is D, but that is not the OA. What am I missing? Finding the Number of Factors of an IntegerFirst make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers. The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself. Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\) Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors. Back to the original question:If k is a positive integer, then 20k is divisible by how many different positive integers? \(20k=2^2*5*k\). (1) k is prime. If \(k=2\), then \(20k=2^3*5\) > the # of factors = \((3+1)(1+1)=8\) but if \(k=5\), then \(20k=2^2*5^2\) > the # of factors = \((2+1)(2+1)=9\). Not sufficient. (2) k = 7 > \(20k=2^2*5*7\) > the # of factors = \((2+1)(1+1)(1+1)=12\). Sufficient. Answer: B. Hope it's clear.
_________________
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



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16024

Re: If k is a positive integer, then 20k is divisible by how man [#permalink]
Show Tags
27 Oct 2014, 08:18
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Intern
Joined: 18 Jan 2016
Posts: 25

Re: If k is a positive integer, then 20k is divisible by how man [#permalink]
Show Tags
24 Feb 2016, 11:43
Bunuel wrote: Back to the original question:
If k is a positive integer, then 20k is divisible by how many different positive integers?
\(20k=2^2*5*k\).
(1) k is prime. If \(k=2\), then \(20k=2^3*5\) > the # of factors = \((3+1)(1+1)=8\) but if \(k=5\), then \(20k=2^2*5^2\) > the # of factors = \((2+1)(2+1)=9\). Not sufficient.
(2) k = 7 > \(20k=2^2*5*7\) > the # of factors = \((2+1)(1+1)(1+1)=12\). Sufficient.
Answer: B.
Hope it's clear. Thanks, the outcome is clear but this method of picking random numbers to test with makes me very uneasy. If you get lucky and the 2 numbers you pick yield different results, then all is fine. But if they yield the same result, you don't know anything. Do you pick a 3rd candidate? A 4th?



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2185

Re: If k is a positive integer, then 20k is divisible by how man [#permalink]
Show Tags
14 Mar 2016, 00:09
Here Statement ! is not sufficient as the prime may be 2 or 5 or any other prime. But statement 2 is sufficient as we Number of divisors now = 2*3*2= 12 Hence B
_________________
Give me a hell yeah ...!!!!!



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16024

Re: If k is a positive integer, then 20k is divisible by how man [#permalink]
Show Tags
20 Apr 2017, 06:58
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: If k is a positive integer, then 20k is divisible by how man
[#permalink]
20 Apr 2017, 06:58








Similar topics 
Author 
Replies 
Last post 
Similar Topics:


1


If c and k are distinct positive integers, is c divisible by k? (1) 2

duahsolo 
2 
25 Aug 2016, 17:29 

7


If j and k are positive integers, is j divisible by 6?

Bunuel 
5 
17 Nov 2016, 12:03 

70


If k is a positive integer and n = k(k + 7k), is n divisible

Jem2905 
25 
29 Jan 2017, 16:34 



If c and k are distinct positive integers, is c divisible by

gmatpapa 
2 
24 Jan 2011, 03:38 

40


If n and k are positive integers, is n divisible by 6?

tarek99 
27 
15 Jun 2017, 09:01 



