GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Aug 2019, 20:01

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

2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7741
GMAT 1: 760 Q51 V42
GPA: 3.82
2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?  [#permalink]

Show Tags

New post 08 Feb 2016, 00:23
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

67% (02:31) correct 33% (02:46) wrong based on 66 sessions

HideShow timer Statistics

2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?

1) 2a3 is divisible by 3.
2) 6b9 is divisible by 9.


* A solution will be posted in two days.

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7755
Re: 2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?  [#permalink]

Show Tags

New post 08 Feb 2016, 02:46
MathRevolution wrote:
2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?

1) 2a3 is divisible by 3.
2) 6b9 is divisible by 9.


* A solution will be posted in two days.


Hi,
first lets find the info being provided by the Q..
2a3+366=6b9...
this means a+6= 10+b.., as the hundred digits are 2+3=6, only when 1 is carried over from ten's place..

so a-b=4...

lets see the choices..
1) 2a3 is divisible by 3.
so 2+a+3 should be div by 3..
a can take values of 1,4, and 7..
now a-b=4,
if a=1, b=-3... not possible
if a=4, b=0..possible and a+b=4..
if a=7, b=3..possible and a+b=10..

so two values
insuff

2) 6b9 is divisible by 9.
again 6+b+9 should be div by 9..
so b can have value as 3 only..
only one value of b, a=7..
suff


B
_________________
Manager
Manager
User avatar
Joined: 06 Jan 2015
Posts: 59
Re: 2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?  [#permalink]

Show Tags

New post 08 Feb 2016, 07:26
If 2a3 + 366 = 6b9 means a + 6 >= 10 because the hundred digit clearly states that 2 + 3 = 6 therefore you must be carrying a 1 from the tens digit.

Therefore a could be 4 , 5 , 6 , 7 , 8 , 9

(1) 2 + a + 3 should be a multiple of 3. a could be 4 or 7 . NOT SUFFICIENT
(2) 2 + a ´3 should be a multiple of 9. a could be only 4 SUFFICIENT

ANSWER IS B

MathRevolution wrote:
2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?

1) 2a3 is divisible by 3.
2) 6b9 is divisible by 9.


* A solution will be posted in two days.

_________________
"No pain, no gain
Intern
Intern
avatar
Joined: 03 Dec 2013
Posts: 10
Location: Uzbekistan
Concentration: Finance, Entrepreneurship
GMAT 1: 620 Q42 V33
GRE 1: Q790 V400
GPA: 3.4
WE: Analyst (Commercial Banking)
GMAT ToolKit User Reviews Badge
Re: 2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?  [#permalink]

Show Tags

New post 08 Feb 2016, 11:11
(1) a = 1, 4, or 7
*a must be a number that if you add it to 6, the sum must be 10 or greater.
We have two options: 4 and 7 that satisfy the given* condition. So, (1) is insufficient.
(2) is sufficient because there is only one 7 that satisfies (2) condition.
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7741
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: 2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?  [#permalink]

Show Tags

New post 09 Feb 2016, 18:13
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?

1) 2a3 is divisible by 3.
2) 6b9 is divisible by 9.


In the original condition, there are 2 variables(a,b) and 1 equation(2a3+366=6b9), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), it becomes 2a3=3t는 2+a+3=3t and there are many values for a like a=1,4.., which is not unique and not sufficient.
For 2), 6b9=9k -> 6+b+9=9k -> b=3, a=7, which is unique and sufficient.
Therefore, the answer is B.


 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 12054
Re: 2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?  [#permalink]

Show Tags

New post 06 Aug 2019, 07:37
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: 2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?   [#permalink] 06 Aug 2019, 07:37
Display posts from previous: Sort by

2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne