Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
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.
Jun 0810:30 AM PDT
-11:30 AM PDT
oin us for an insightful conversation with Selena Salazar, a seasoned product manager who has successfully navigated her career through industry giants like Meta and Apple.- Jun 11
05:40 AM PDT
-12:00 PM PDT
Register for the GMAT Club Virtual MBA Spotlight fair, the biggest MBA fair of the year. You will have a chance to hear Admissions directors from almost every Top 20 program speak, network with peers, and more. 
Jun 1111:00 AM PDT
-12:00 PM PDT
Magoosh students get into top business schools like MIT Sloan, HBS, Stanford GSB, Wharton and more! See why over 6 million students trust us for exam prep.
Jun 1310:00 AM EDT
-10:30 AM EDT
Level up your Chicago Booth MBA application! Sia Admissions will be LIVE on June 13th for expert guidance on crafting your application that resonates with admission committees. Learn core themes, personal branding tips, and strategies and more.
Jun 1311:00 AM EDT
-12:00 PM EDT
TTP has received over 700 reviews on GMAT Club! This incredible milestone is a testament to our dedication to helping students score high on the GMAT for over a decade.
Jun 1412:00 PM EDT
-01:00 PM EDT
Have you ever wondered how to score a PERFECT 805 on the GMAT Focus Edition? Meet Julia, a banking professional who used the Target Test Prep course to achieve this incredible feat. Julia's story is nothing short of an inspiration.
Jun 1511:00 AM IST
-01:00 PM IST
In this webinar, Rajat Sadana, GMAT Club’s #1 rated expert will help you create a personalized study plan so that each one of you can visualize your journey to a top GMAT Focus Score.
If a and b are positive integers, is b divisible by a?
[#permalink]
19 Sep 2022, 05:15
19 Sep 2022, 05:15
3
Bookmarks
Expert Reply
Show timer
00:00
A
B
C
D
E
Difficulty:
65%
(hard)
Question Stats:
51% (01:46) correct
49%
(01:25)
wrong
based on 59
sessions
If a and b are positive integers, is b divisible by a?
(1) 2b/a is an integer.
(2) b^2/a is an integer
(1) 2b/a is an integer.
(2) b^2/a is an integer
If a and b are positive integers, is b divisible by a?
[#permalink]
27 Sep 2022, 05:59
27 Sep 2022, 05:59
Bunuel wrote:
If a and b are positive integers, is b divisible by a?
so we need to know if b/a is an integer.
lets take a simple scenario where \(a = 2^Y\) and \(b=2^U\)
Rephrasing the Original Question(OQ): Is the power of 2 in \(b\) greater than or equal to power of 2 in \(a\)?
Quote:
(1) 2b/a is an integer.
Here, we can easily find values that will make 2b/a as well as b/a an integer. Lets see if it fails to be an integer only for b/a.
What if 2 is a factor of \(a\) but not of b? Take U=0 and Y=1. Here 2b/a is an integer but b/a is not, as b/a turns out to be 1/2, Hence not sufficient
Quote:
(2) b^2/a is an integer
Again, here we can easily find values that will make b^2/a as well as b/a an integer. Lets see if it fails to be an integer only for b/a.
What if the power of \(a\) is twice the power of \(b\)? Take U=1 and Y=2. Here b^2/a is an integer but b/a is not, as b/a turns out to be 2/4, Hence not sufficient
Quote:
combine (1) and (2)
Rephrase: b^2/a and 2b/a is an integer.
Again, here we can easily find values that will make the combined eqs. as well as b/a an integer. Lets see if it fails to be an integer only for b/a.
Lets try U=1 and Y=2 since we already know it does not hold for (2). Putting these values in (1), 2b/a is an integer but b/a is not, as b/a turns out to be 2/4. Hence not sufficient
Hence answer E.
GMATWhiz Representative
Joined: 23 May 2022
Posts: 640
Given Kudos: 6
Location: India
GMAT 1: 760 Q51 V40 
Re: If a and b are positive integers, is b divisible by a?
[#permalink]
01 Nov 2022, 08:10
01 Nov 2022, 08:10
Expert Reply
If a and b are positive integers, is b divisible by a?
(1) 2b/a is an integer.
(2) b^2/a is an integer
We need to find out if 'b' is divisible by 'a' or not. This is a yes-no-type DS question.
Statement 1: \(\frac{2b}{a}\) is an integer.
We suggest translating the statement into equations for easy inference.
Now, this is an integer when k is an even number. But we do not know that and hence this statement is not sufficient.
We can eliminate options A, and D.
Statement 2: \(\frac{b^2}{a}\) is an integer.
We again suggest translating the statement into equations for easy inference.
'b' will be divisible by 'a' only when the right side gives us an integer. Now that may or may not be the case.
If k = a, then it will be.
If k = 1, then it will not be.
Hence, this is not sufficient either. We eliminate B as well.
Combine:
When we combine we try to see if both yes and no are possible or not.
So if k = 4a (an even number), then we get YES
If k = 1, then we get NO.
Hence, even together they are not sufficient.
Answer: E
(1) 2b/a is an integer.
(2) b^2/a is an integer
We need to find out if 'b' is divisible by 'a' or not. This is a yes-no-type DS question.
Statement 1: \(\frac{2b}{a}\) is an integer.
We suggest translating the statement into equations for easy inference.
- We can say that \(\frac{2b}{a} = k\), where 'k' is an integer
- So,\(\frac{b}{a} =\frac{k}{2}\)
Now, this is an integer when k is an even number. But we do not know that and hence this statement is not sufficient.
We can eliminate options A, and D.
Statement 2: \(\frac{b^2}{a}\) is an integer.
We again suggest translating the statement into equations for easy inference.
- \(\frac{b^2}{a} = k\), where 'k' is an integer
- \(b^2\) =k × a
- \(b = \sqrt{a × k}\)
'b' will be divisible by 'a' only when the right side gives us an integer. Now that may or may not be the case.
If k = a, then it will be.
If k = 1, then it will not be.
Hence, this is not sufficient either. We eliminate B as well.
Combine:
When we combine we try to see if both yes and no are possible or not.
So if k = 4a (an even number), then we get YES
If k = 1, then we get NO.
Hence, even together they are not sufficient.
Answer: E
