Last visit was: 15 Jul 2024, 14:05 It is currently 15 Jul 2024, 14:05
Close
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

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94354
Own Kudos [?]: 641114 [2]
Given Kudos: 85011
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6020
Own Kudos [?]: 13785 [1]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Manager
Manager
Joined: 04 May 2020
Posts: 185
Own Kudos [?]: 551 [1]
Given Kudos: 68
Location: India
GMAT 1: 610 Q47 V27
WE:Programming (Computer Software)
Send PM
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4128
Own Kudos [?]: 9443 [1]
Given Kudos: 91
 Q51  V47
Send PM
Re: If a and b are integers, is ab/8 an integer? (1) 2a=b (2) ab/4 is an [#permalink]
1
Kudos
Expert Reply
Bunuel wrote:
If a and b are integers, is ab/8 an integer?

(1) 2a=b

(2) ab/4 is an integer.


Very nicely designed question, though I think it would be more realistic if it said a and b were positive integers, since almost all GMAT divisibility questions are restricted to positive integers.

The answer is quickly C or E. From Statement 1, we know a is divisible by one more '2' than b is. It's a bit like knowing "Azim has 1 more apple than Brenda". The total number of 2's in ab (or apples that Azim and Brenda have in total) then must be odd. Statement 2 tells us we can divide ab by 2^2, so ab contains at least two 2's, but if it also contains an odd number of 2's, it must contain at least three 2's, and must be divisible by 8.

Less abstractly, if b = 2a, substituting into Statement 2 we learn 2a^2/4 is an integer, so 2a^2 is divisible by 4, and a^2 is divisible by 2. If a^2 is divisible by 2, then a is divisible by 2, and if b = 2a, b must be divisible by 4. So ab must be divisible by 8, and the answer is C.
VP
VP
Joined: 14 Jul 2020
Posts: 1115
Own Kudos [?]: 1300 [1]
Given Kudos: 351
Location: India
Send PM
Re: If a and b are integers, is ab/8 an integer? (1) 2a=b (2) ab/4 is an [#permalink]
1
Kudos
If a and b are integers, is ab/8 an integer?

Stat1: 2a=b
Not sufficient, as a = 1, b = 2 and ab/8 won't be an integer in some cases. Not sufficient

Stat2:
ab/4 is an integer.
a = 1 and b=4, still ab/8 won't be an integer in some cases. Not sufficient

Combining both
, if a = 2, b =4, ab/8 will be an integer sufficient

So, I think C. :)
Senior Manager
Senior Manager
Joined: 24 Jun 2019
Posts: 428
Own Kudos [?]: 440 [1]
Given Kudos: 117
Location: India
Concentration: Marketing, Strategy
Send PM
Re: If a and b are integers, is ab/8 an integer? (1) 2a=b (2) ab/4 is an [#permalink]
1
Kudos
Bunuel wrote:
If a and b are integers, is ab/8 an integer?

(1) 2a=b

(2) ab/4 is an integer.


Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here


1)\(\frac{2a^2}{8 }= integer?\)
If a = 2, Yes!
If a = 3, No! - Insufficient!
2)ab/4 = integer!
if ab = 8, Yes!
If ab = 12, No! - Insufficient!
Combining (1) & (2):
\(\frac{2a^2}{4} = integer\)
For the above to be an integer, the minimum value of a has to be 2.
So, this will always be a divisible as 2a^ will be 8. Sufficient!
IMO, (C)!
UNC Kenan Flagler Moderator
Joined: 18 Jul 2015
Posts: 237
Own Kudos [?]: 252 [0]
Given Kudos: 120
GMAT 1: 530 Q43 V20
WE:Analyst (Consumer Products)
Send PM
Re: If a and b are integers, is ab/8 an integer? (1) 2a=b (2) ab/4 is an [#permalink]
Bunuel wrote:
If a and b are integers, is ab/8 an integer?

(1) 2a=b

(2) ab/4 is an integer.

Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here


Very tricky question. I got this wrong but realized my mistake. Sharing my learning here.

S1: 2a=b [Insufficient]

If we plug the value of \(b\) into \(\frac{ab}{8}\) then we get \(\frac{2a^2}{8}\) or \(\frac{a^2}{4}\). Now if \(a = 1\) then the entire expression is not an integer but if \(a = 4\) then it is

S1: ab/4 is an integer [Insufficient]

\(\frac{ab}{4} = k\) where \(k\) is an integer. We can multiply both sides with \(\frac{1}{2}\) to get \(\frac{ab}{8} = \frac{k}{2}\). Now if \(k = 1\) then the equation is not an integer but if \(k = 4\) then it is

S1 + S2 [Sufficient]

Plugging \(b = 2a\) in \(\frac{ab}{8} = \frac{k}{2}\) we get \(\frac{2a^2}{8} = \frac{k}{2}\) which upon further simplification gives \(a = \sqrt{2k}\)

Now since \(a\) is an integer \(\sqrt{2k}\) must be an integer so \(k =\) \(2\), \(8\) etc.

Taking the smallest value \(k = 2\) gives \(a = 2\) and \(b = 4\) (from \(b = 2a\))

Plugging these values into \(\frac{ab}{8}\) gives \(\frac{2 * 4}{8} = 1\) which is an integer

Ans. C
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33980
Own Kudos [?]: 851 [0]
Given Kudos: 0
Send PM
Re: If a and b are integers, is ab/8 an integer? (1) 2a=b (2) ab/4 is an [#permalink]
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 Club Bot
Re: If a and b are integers, is ab/8 an integer? (1) 2a=b (2) ab/4 is an [#permalink]
Moderator:
Math Expert
94354 posts