November 18, 2018 November 18, 2018 07:00 AM PST 09:00 AM PST Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST November 20, 2018 November 20, 2018 09:00 AM PST 10:00 AM PST The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 22 Mar 2011
Posts: 52

If a and b are both singledigit positive integers, is a + b
[#permalink]
Show Tags
28 May 2011, 18:34
Question Stats:
65% (02:07) correct 35% (02:00) wrong based on 280 sessions
HideShow timer Statistics
If a and b are both singledigit positive integers, is a + b a multiple of 3? (1) The twodigit number "ab" (where a is in the tens place and b is in the ones place) is a multiple of 3. (2) a – 2b is a multiple of 3. If we take a scenario for part 1 A = 9 B = 3 A x B = 27 A + B = 9 (Divisible by 3) A = 4 B = 3 A x B = 12 A + B = 7 (Not Divisible by 3) So it should be insufficient. Please help.
Official Answer and Stats are available only to registered users. Register/ Login.



Senior Manager
Joined: 24 Mar 2011
Posts: 370
Location: Texas

Re: Multiples of 3
[#permalink]
Show Tags
28 May 2011, 19:33
i think you misunderstood it.
what it is saying you is The twodigit number "ab" (where a is in the tens place and b is in the ones place) is a multiple of 3.
meaning integer like 10 where a = 1 and b=0; 11 where a =1, b=1 ; 12 where a = 1 and b =2 (note that it reads 2 digit number 'ab' and is not a * b)
so basically all the numbers that satisfy condition 1 will be 12, 15, 18, 21, 24, 27, 30, 33, 36, 39....and so on notice that are multiple of 3.
now a+b for all these numbers = 3, 6, 9, 3, 6, 9, 3, 6 follow the patter of 3, 6 , 9 and are multiple of 3.



Current Student
Joined: 26 May 2005
Posts: 508

Re: Multiples of 3
[#permalink]
Show Tags
28 May 2011, 20:59
melguy wrote: If a and b are both singledigit positive integers, is a + b a multiple of 3?
(1) The twodigit number "ab" (where a is in the tens place and b is in the ones place) is a multiple of 3.
(2) a – 2b is a multiple of 3.
If we take a scenario for part 1
A = 9 B = 3 A x B = 27 A + B = 9 (Divisible by 3)
A = 4 B = 3 A x B = 12 A + B = 7 (Not Divisible by 3)
So it should be insufficient. Please help. Question asks if a+b is divisible by 3 1. pick up the numbers 12, 15,18, 21 24, 30 all are multiple of 3 and a+b ( 1+2,1+5,1+9....) is a multiple of 3  hence sufficient 2. if a is a multiple of 3 and b is a multiple of 3 then ab is also a multiple of 3 pick up numbers for a2b, remember this should be a multiple of 3., thus a is multiple of 3 and 2b is a multiple of 3 a = 9 b = 3 then a2b is 3 ..multiple of 3 a= 24 b= 6 a2b = 12 multiple of 3..........sufficient hence D



Current Student
Joined: 08 Jan 2009
Posts: 304

Re: Multiples of 3
[#permalink]
Show Tags
29 May 2011, 01:12
1) is also the check for 'division by 3'.
I.e. a number is a multiple of 3 if its digits added together are divisible by 3. Therefore, if ab is divisible by 3, then a+b must be divisible by 3.



Retired Moderator
Joined: 16 Nov 2010
Posts: 1428
Location: United States (IN)
Concentration: Strategy, Technology

Re: Multiples of 3
[#permalink]
Show Tags
29 May 2011, 01:16
(1) Clearly Sufficient as "ab" is a multiple of 3 when a+b is so You should consider AB as 93, instead of A * B = 27 (2) a  2b = 3k, where k is an integer => a = 3k + 2b => ab is in a format "3k+2bb" So a + b = 3k + 2b + b = 3(k+b), a multiple of 3 => ab is a multiple of 3 Sufficient Answer  D
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Math Expert
Joined: 02 Sep 2009
Posts: 50622

If a and b are both singledigit positive integers, is a + b a multipl
[#permalink]
Show Tags
24 Oct 2014, 08:21



Intern
Joined: 27 Jul 2012
Posts: 25

Re: If a and b are both singledigit positive integers, is a + b a multipl
[#permalink]
Show Tags
24 Oct 2014, 15:44
Answer is D, both are sufficient.
1) for any number to be a multiple of 3, the sum of its digits needs to be a multiple of 3. So therefore, if given ab is a multiple of 3, then a + b is also a multiple of 3.
2) a 2b is a multiple of 3. If we add to this a multiple of 3, the resultant sum should also be a multiple of 3. a2b + 3b(multiple of 3) = a+b which by virtue of being a sum of 2 multiple of 3, is also a multiple.
Thus each statement alone is sufficient



Manager
Joined: 22 Jan 2014
Posts: 176
WE: Project Management (Computer Hardware)

Re: If a and b are both singledigit positive integers, is a + b a multipl
[#permalink]
Show Tags
25 Oct 2014, 04:14
Bunuel wrote: Tough and Tricky questions: Multiples. If a and b are both singledigit positive integers, is a + b a multiple of 3? (1) The twodigit number "ab" (where a is in the tens place and b is in the ones place) is a multiple of 3. (2) a – 2b is a multiple of 3. D. 1) ab is a multiple of 3. By basic rule of division, a number is div by 3 if the sum of its digits is div by 3. Reason: 10a+b mod 3 = 0 => (a+b) mod 3 = 0 [since 10 mod 3 = 1] so sufficient. 2) a2b = 3k a = 3k+2b => a+b = 3k+2b+b = 3(k+b) which is div by 3 so sufficient.
_________________
Illegitimi non carborundum.



Intern
Joined: 27 Dec 2015
Posts: 29

Re: If a and b are both singledigit positive integers, is a + b a multipl
[#permalink]
Show Tags
13 Jun 2016, 10:51
I know this is an older post, but can someone clarify how it is we go from => a = 3k + 2b to a + b = 3k + 2b + b = 3(k+b) for statement 2? thanks



Math Expert
Joined: 02 Sep 2009
Posts: 50622

Re: If a and b are both singledigit positive integers, is a + b a multipl
[#permalink]
Show Tags
13 Jun 2016, 10:58



Intern
Joined: 27 Dec 2015
Posts: 29

Re: If a and b are both singledigit positive integers, is a + b a multipl
[#permalink]
Show Tags
13 Jun 2016, 11:09
makes perfect sense now, thank you!!



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6517
GPA: 3.82

Re: If a and b are both singledigit positive integers, is a + b a multipl
[#permalink]
Show Tags
14 Jun 2016, 08:26
Before solving the question, you need some knowledge. “The remainder of a certain positive integer divided by 3 and 9 is same as the sum of every digit place of n divided by 3 and 9. There are 2 variables in the original condition. In order to match the number of variables to the number of equations, we need 2 equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that C is the correct answer. Using the condition 1) and the condition 2) at the same time: Condition 1) – a multiple of ab=3 is a multiple of a+b=3. Hence, the answer is yes and the condition is sufficient. Condition 2) – If a+b is a multiple of a2b=3, then, it becomes a multiple of a2b+3b=3 plus 3b and a multiple of a+b=3 plus 3b=3(multiple+b)=3. Hence, the answer is yes and the condition is sufficient. Thus, the correct answer is D. This is 5051 level question. Please remember the common mistake type 4(B). If the answer is too easily A or B, please consider D.  For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
Attachments
variable approach's answer probability.jpg [ 219.74 KiB  Viewed 3523 times ]
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Intern
Joined: 03 Sep 2017
Posts: 3

Re: If a and b are both singledigit positive integers, is a + b a multipl
[#permalink]
Show Tags
20 Nov 2017, 11:13
1) two digit integer ab is a multiple of 3 <=> (a+b) = 3k => clearly sufficient 2) a2b =3k => a2b+3b is also a multiple of 3 => a+b = 3k => sufficient => D




Re: If a and b are both singledigit positive integers, is a + b a multipl &nbs
[#permalink]
20 Nov 2017, 11:13






