|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
hellzangl
Joined: 20 Aug 2013
Last visit: 01 Feb 2015
Posts: 11
Location: United States
Concentration: Marketing, Strategy
Schools: Foster '16 (WA) Goizueta '16 (D) Duke '16 (WL) Anderson '16 (D) Kenan-Flagler '16 (D) Marshall '16 (A) Merage '16
GMAT 1: 720 Q38 V41
WE:Project Management (Consulting)
Schools: Foster '16 (WA) Goizueta '16 (D) Duke '16 (WL) Anderson '16 (D) Kenan-Flagler '16 (D) Marshall '16 (A) Merage '16
GMAT 1: 720 Q38 V41
Posts: 11
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
64% (01:09) correct
36%
(00:56)
wrong
based on 2378
sessions
History
Date
Time
Result
Not Attempted Yet
If k is a positive integer, then 20k is divisible by how many different positive integers?
(1) k is prime
(2) k = 7
(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?
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?
Every tricky question should trigger a follow up quiz.
Build that habit with
GMAT Club Forum Quiz →.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
spjmanoli
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.
_________________
spjmanoli
Finding the Number of Factors of an Integer
First 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 GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
Bunuel
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?
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
But statement 2 is sufficient as we Number of divisors now = 2*3*2= 12
Hence B
hellzangl
Very simple, no tricks here or anything. If we know the value of K then we obviously know the answer- though in the case of K being a prime number- what if K is 2? Then there is of course some overlap- do not forget 2 is a prime number.
K= 5 x 2 x 2 x (2 x 1)
Thus
B
hellzangl
20k = 2^2 * 5 * k
We already have 2 prime factors of 20k (2 and 5). The total number of factors depends on k.
(1) k is prime
k could be 2 or 5 or any other prime number. In each case, the number of factors would be different.
If k = 2, \(20k = 2^3 * 5\) has 4*2 = 8 factors
If k = 5, \(20k = 2^2 * 5^2\) has 3*3 = 9 factors
If k is any other prime number such as 11, \(20k = 2^2 * 5 * 11\) has 3*2*2 = 12 factors
Not sufficient
(2) k = 7
If k = 7,
20k = 2^2 * 5 * 7
Total number of factors = 3*2*2 = 12
Sufficient
Answer (B)
_________________
-
Start FREE with selected GMAT/EA Content upon registration at anaprep.com
YouTube Channel: karishma.anaprep
Start FREE with selected GMAT/EA Content upon registration at anaprep.com
YouTube Channel: karishma.anaprep
It’s easy to think that statement (1) is sufficient by thinking, “Well, I can figure out quickly that 20 has six factors (1, 2, 4, 5, 10, 20), and if k is a new prime number, then 20k will have six MORE factors than 20 has, because we can just take the new prime number and multiply it by each of the original six factors. For instance, if k were 3, then the factors of 20k would be each of the six factors of 20 PLUS six new ones - 3, 6, 12, 15, 30, 60. So statement (1) is sufficient.”
Statement (1) is a trap, however, because we aren’t told that k is a NEW prime number!!! It may be a prime that is ALREADY a factor of 20 – i.e., k could be 2 or 5. Suppose k were 2. If that were the case, then the factors of 20k would be 1, 2, 4, 5, 8, 10, 20 and 40 – i.e., we would be adding only two new factors, 8 and 40, to the original list of six. Statement (1) is therefore insufficient.
Statement (1) is a trap, however, because we aren’t told that k is a NEW prime number!!! It may be a prime that is ALREADY a factor of 20 – i.e., k could be 2 or 5. Suppose k were 2. If that were the case, then the factors of 20k would be 1, 2, 4, 5, 8, 10, 20 and 40 – i.e., we would be adding only two new factors, 8 and 40, to the original list of six. Statement (1) is therefore insufficient.
So everyone here agrees that the answer is "B." When I answered "B" on the OG online practice test the program said my answer was wrong and the answer is actually "D." Do we think the OG is wrong?
5e3
Was the question on the test slightly different? Can you put up a screenshot?
_________________
-
Start FREE with selected GMAT/EA Content upon registration at anaprep.com
YouTube Channel: karishma.anaprep
Start FREE with selected GMAT/EA Content upon registration at anaprep.com
YouTube Channel: karishma.anaprep
VeritasKarishma
As soon as I posted this I saw that I read the correct answer wrong...ha! Thank you for the response, though!
If k is a positive integer, then 20k is divisible by how many different positive integers?
(1) k is prime ns as K can be 5 or any other prime no ,ans will be diff for both
(2) k = 7 sufficient
(1) k is prime ns as K can be 5 or any other prime no ,ans will be diff for both
(2) k = 7 sufficient
Posts: 32
Bunuel
Dang it I missed 2! Arrgghh..
hopefulmba2021
Joined: 31 Aug 2020
Last visit: 24 Feb 2022
Posts: 56
Location: India
Concentration: Technology, General Management
GMAT 1: 710 Q48 V37
GMAT 1: 710 Q48 V37
Posts: 56
The question stem says that to find the no of DIFFERENT factors.
Statement 1 says k is a prime number.
So, 20k will always yield 4 factors (1,2,3 and k). The powers of each factor may be different for different values of k. But the question asks for the number of different positive factors. According to my reasoning, the question should have clearly asked for the total number of factors (NOT the number of different factors). And that's why I chose option D.
Need some expert opinions on this. cc: Bunuel VeritasKarishma
Statement 1 says k is a prime number.
So, 20k will always yield 4 factors (1,2,3 and k). The powers of each factor may be different for different values of k. But the question asks for the number of different positive factors. According to my reasoning, the question should have clearly asked for the total number of factors (NOT the number of different factors). And that's why I chose option D.
Need some expert opinions on this. cc: Bunuel VeritasKarishma
hopefulmba2021
hopefulmba2021
"No. of different factors" just means "no. of factors". The question says "different" to clarify that when you prime factorise and get
20 = 2^2 * 5, don't consider the two 2s as two factors. The word "different" is added to give extra clarity. Don't get confused. The question is not asking for "prime factors". You need total number of factors only. That depends on value of k.
If k = 2, 20k = 2^3 * 5 so total number of factors = (3+1)(1+1)
If k = 5, 20k = 2^2 * 5^2 so total number of factors = (2+1)(2+1)
If k = some other prime, 20k = 2^2*5*k so total number of factors = (2+1)(1+1)(1+1)
_________________
-
Start FREE with selected GMAT/EA Content upon registration at anaprep.com
YouTube Channel: karishma.anaprep
Start FREE with selected GMAT/EA Content upon registration at anaprep.com
YouTube Channel: karishma.anaprep
Posts: 7
This is a quite simple one:
What we need to do is to find out how many different factors does 20k have.
Here are my steps:
--We know that 20 has 6 different factors: 1, 2, 4, 5, 10, 20
Among the six factors, 2 and 5 are prime (hope you still remember what a prime number is)
(1)K is prime.
In this case, K only has 2 factors: 1 and itself.
Thus there are two possibilities:
--K = 2 or 5
--K ≠ 2 or 5
If k = 2 or 5, then K itself is one of the 6 factors of 20, thus K doesn't provide a new factor for 20K. (The question is to find how many 'distinct' factors 20K has! )
So it's clear that 20K has only 6 factors(namely the 6 factors of 20)
If K≠ 2 or 5, then K will provide one new factor to 20K (namely itself). So 20K has 6+1=7 factors.
See, (1) is not sufficient because 6 and 7 factors are both possible in this case.
(2) K is 7.
In this case, K is a prime AND K ≠ 2 or 5.
So according to the reasoning in (1), 20K will have 7 factors. SUFFICIENT
What we need to do is to find out how many different factors does 20k have.
Here are my steps:
--We know that 20 has 6 different factors: 1, 2, 4, 5, 10, 20
Among the six factors, 2 and 5 are prime (hope you still remember what a prime number is)
(1)K is prime.
In this case, K only has 2 factors: 1 and itself.
Thus there are two possibilities:
--K = 2 or 5
--K ≠ 2 or 5
If k = 2 or 5, then K itself is one of the 6 factors of 20, thus K doesn't provide a new factor for 20K. (The question is to find how many 'distinct' factors 20K has! )
So it's clear that 20K has only 6 factors(namely the 6 factors of 20)
If K≠ 2 or 5, then K will provide one new factor to 20K (namely itself). So 20K has 6+1=7 factors.
See, (1) is not sufficient because 6 and 7 factors are both possible in this case.
(2) K is 7.
In this case, K is a prime AND K ≠ 2 or 5.
So according to the reasoning in (1), 20K will have 7 factors. SUFFICIENT
Automated notice from GMAT Club BumpBot:
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
_________________
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
_________________
Moderator:
Announcements
How to Tell If Your GMAT Prep Resources Are Actually Helping You
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.