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

 It is currently 06 Dec 2019, 08:52

### 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

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

# If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42
GPA: 3.82
If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

### Show Tags

03 Aug 2017, 01:26
1
1
00:00

Difficulty:

45% (medium)

Question Stats:

55% (00:58) correct 45% (01:19) wrong based on 105 sessions

### HideShow timer Statistics

If a, b, and c are positive integers, is (a+b)c divisible by 3?

1) 2-digit integer ab is divisible by 3.
2) When c is divided by 3, the remainder is 0.

_________________
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"
Intern
Joined: 31 Jan 2017
Posts: 47
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

### Show Tags

03 Aug 2017, 02:44
Statement 1: let a=3 and b=2 then ab=6 which is divisble by 3 then putting the value in the eq we get 5c which is not divisible by 3 so no
put a=3 and b=3 then ab is divisible by 3 and also 6c which is divisible by 3 so yes
Insufficient

Statement 2: since c is divisible by 3 therefore (a+b)c is also divisible by 3
Sufficient

Ans: B

Sent from my SM-J210F using GMAT Club Forum mobile app
Intern
Joined: 03 Apr 2016
Posts: 1
Location: United States (TX)
GMAT 1: 740 Q49 V42
GPA: 3.58
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

### Show Tags

03 Aug 2017, 09:09
Is "two digit integer ab" supposed to reflect a number where a is the tens digit, and b the ones digit? Or does it mean the product of a and b?
Intern
Joined: 21 Jun 2017
Posts: 10
GMAT 1: 750 Q50 V41
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

### Show Tags

03 Aug 2017, 10:49
1
Statement 1: ab = 10a+b = (a+b)+9a is divisible by 3 so a+b is divisible by 3
Statement 2: Obvious yes
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

### Show Tags

06 Aug 2017, 18:13
==> If you modify the original condition and the question, in order to have (a+b)c to be divided by 3, a+b or c has to be divided by 3. However, if you look at con 2), c is divisible by 3, hence it is yes and sufficient. For con 1), ab is also divisible by 3, and thus a+b is also divisible by 3, hence it is yes and sufficient.
Therefore, the answer is D. This type of question is a 5051-level question which applies CMT 4 (B: if you get A or B too easily, consider D).

_________________
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"
Intern
Joined: 18 Apr 2019
Posts: 10
Location: United Kingdom
Schools: LBS '22 (A)
GMAT 1: 730 Q49 V40
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

### Show Tags

07 May 2019, 22:41
1
MathRevolution wrote:
==> If you modify the original condition and the question, in order to have (a+b)c to be divided by 3, a+b or c has to be divided by 3. However, if you look at con 2), c is divisible by 3, hence it is yes and sufficient. For con 1), ab is also divisible by 3, and thus a+b is also divisible by 3, hence it is yes and sufficient.
Therefore, the answer is D. This type of question is a 5051-level question which applies CMT 4 (B: if you get A or B too easily, consider D).

I am not following your logic for con 1).
If a=1 and b=3, then ab=3 divisible by 3, however a+b=4 so it would not be true.
I am still not convinced that B is the right answer. Could you please elaborate ?
Manager
Joined: 07 May 2016
Posts: 56
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

### Show Tags

15 May 2019, 11:30
krasha wrote:
MathRevolution wrote:
==> If you modify the original condition and the question, in order to have (a+b)c to be divided by 3, a+b or c has to be divided by 3. However, if you look at con 2), c is divisible by 3, hence it is yes and sufficient. For con 1), ab is also divisible by 3, and thus a+b is also divisible by 3, hence it is yes and sufficient.
Therefore, the answer is D. This type of question is a 5051-level question which applies CMT 4 (B: if you get A or B too easily, consider D).

I am not following your logic for con 1).
If a=1 and b=3, then ab=3 divisible by 3, however a+b=4 so it would not be true.
I am still not convinced that B is the right answer. Could you please elaborate ?

ISB School Moderator
Joined: 08 Dec 2013
Posts: 615
Location: India
Concentration: Nonprofit, Sustainability
Schools: ISB '21
GMAT 1: 630 Q47 V30
WE: Operations (Non-Profit and Government)
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

### Show Tags

15 May 2019, 17:08
MathRevolution wrote:
If a, b, and c are positive integers, is (a+b)c divisible by 3?

1) 2-digit integer ab is divisible by 3.
2) When c is divided by 3, the remainder is 0.

c= 3K, so (a+b)c is definitely divisible by 3.

Now, statement 1,

TU
ab
21
48

All two digit numbers (Any numbers) that are divisible by three their sum is also divisible by 3. This is divisibility rule of three.

So, (a+b) must be divisible by three.

Either statement independently sufficient.
Manager
Joined: 07 May 2016
Posts: 56
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

### Show Tags

15 May 2019, 22:49
LeoN88 wrote:
MathRevolution wrote:
If a, b, and c are positive integers, is (a+b)c divisible by 3?

1) 2-digit integer ab is divisible by 3.
2) When c is divided by 3, the remainder is 0.

c= 3K, so (a+b)c is definitely divisible by 3.

Now, statement 1,

TU
ab
21
48

All two digit numbers (Any numbers) that are divisible by three their sum is also divisible by 3. This is divisibility rule of three.

So, (a+b) must be divisible by three.

Either statement independently sufficient.

I think I know where the confusion comes from. ab doesn’t have a multiplication sign between them. It is not a.b, it is ab without the multiplication.

However, I still think the positioning of the question is a bit confusing

Posted from my mobile device
Intern
Joined: 06 Jan 2019
Posts: 4
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

### Show Tags

16 May 2019, 08:23
Sorry, I also don’t get, how ab divisible by 3 get us a+b divisible by 3
3*4 div by 3, but 3+4 is not...
Pls explain and give us several examples.

Posted from my mobile device
Intern
Joined: 06 Jan 2019
Posts: 4
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-  [#permalink]

### Show Tags

16 May 2019, 08:26
nyashka wrote:
Sorry, I also don’t get, how ab divisible by 3 get us a+b divisible by 3
3*4 div by 3, but 3+4 is not...
Pls explain and give us several examples.

Posted from my mobile device

Oh, sorry, I got it...
E.g. 12 is a two-digit number, it is divisible by 3, and the sum of the DIGITS is also divisible
Hence the answer is really D.
Re: If a, b, and c are positive integers, is (a+b)c divisible by 3? 1) 2-   [#permalink] 16 May 2019, 08:26
Display posts from previous: Sort by