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

 It is currently 20 Aug 2019, 20:01 ### 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. ### Request Expert Reply # 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

Math Revolution GMAT Instructor 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 00:00

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.

_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 7755
Re: 2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?  [#permalink]

### Show Tags

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

### Show Tags

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  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)
Re: 2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?  [#permalink]

### Show Tags

(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 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

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.
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 12054
Re: 2a3 is a 3-digit positive integer. If 2a3+366=6b9, a+b=?  [#permalink]

### Show Tags

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.
_________________ 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

#### MBA Resources  