December 10, 2018 December 10, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills. December 11, 2018 December 11, 2018 09:00 PM EST 10:00 PM EST Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51072

If a and b are positive, what is the value of a + b?
[#permalink]
Show Tags
31 Aug 2018, 22:01
Question Stats:
23% (01:00) correct 77% (01:08) wrong based on 133 sessions
HideShow timer Statistics



Manager
Joined: 11 May 2018
Posts: 92
Location: India

Re: If a and b are positive, what is the value of a + b?
[#permalink]
Show Tags
31 Aug 2018, 22:44
Statement 13^a * 3^b =81 3^(a+b)=3^4 Therefore a+b=4: SUFFICIENT Statement 23^a * 5^b =225 3^a * 5^b =15^2 3^a * 5^b =(3*5)^2 3^a * 5^b =3^2 * 5^2 therefore a=2 b =2 a+b =4 SUFFICIENT; Dis the answer
_________________
If you want to Thank me Give me a KUDOS "I’ve spent months preparing for the day I’d face you. I’ve come a long way, GMAT" SonGoku



Math Expert
Joined: 02 Aug 2009
Posts: 7098

Re: If a and b are positive, what is the value of a + b?
[#permalink]
Show Tags
31 Aug 2018, 23:01
If a and b are positive, what is the value of a + b? (1) (3^a)(3^b) = 81 \((3^a)(3^b) = 81........3^{a+b}=3^4=(3)^4\) a+b=4 sufficient (2) (3^a)(5^b) = 225 \((3^a)(5^b) = 225=3^2*5^2\) Easy to fall trap of choosing a=b=2. But it is nowhere given that a and b are integersFor each value of a, there will be a value of b to fit in the equation, it may be in decimals or fractions.. Insuff A
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Director
Joined: 06 Jan 2015
Posts: 525
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)

Re: If a and b are positive, what is the value of a + b?
[#permalink]
Show Tags
31 Aug 2018, 23:20
chetan2u wrote: If a and b are positive, what is the value of a + b?
(1) (3^a)(3^b) = 81 \((3^a)(3^b) = 81........3^{a+b}=3^4=(3)^4\) a+b=4 sufficient
(2) (3^a)(5^b) = 225 \((3^a)(5^b) = 225=3^2*5^2\) Easy to fall trap of choosing a=b=2. But it is nowhere given that a and b are integers For each value of a, there will be a value of b to fit in the equation, it may be in decimals or fractions.. Insuff
A HI chetan2uCan you please explain this part? Examples pls Quote: For each value of a, there will be a value of b to fit in the equation, it may be in decimals or fractions
_________________
आत्मनॊ मोक्षार्थम् जगद्धिताय च
Resource: GMATPrep RCs With Solution



ISB, NUS, NTU Moderator
Joined: 11 Aug 2016
Posts: 343

If a and b are positive, what is the value of a + b?
[#permalink]
Show Tags
31 Aug 2018, 23:23
Might sound stupid but chetan2u Can you please explain the part in red with examples ? We have to compare the indices of similar bases: 3 with 3 and 5 with 5. IMO a=2 and b=2 is the only solution. chetan2u wrote: If a and b are positive, what is the value of a + b?
(1) (3^a)(3^b) = 81 \((3^a)(3^b) = 81........3^{a+b}=3^4=(3)^4\) a+b=4 sufficient
(2) (3^a)(5^b) = 225 \((3^a)(5^b) = 225=3^2*5^2\) Easy to fall trap of choosing a=b=2. But it is nowhere given that a and b are integers For each value of a, there will be a value of b to fit in the equation, it may be in decimals or fractions.. Insuff
A
_________________
~R. If my post was of any help to you, You can thank me in the form of Kudos!! Applying to ISB ? Check out the ISB Application Kit.



Math Expert
Joined: 02 Aug 2009
Posts: 7098

Re: If a and b are positive, what is the value of a + b?
[#permalink]
Show Tags
31 Aug 2018, 23:39
GmatDaddy wrote: Might sound stupid but chetan2u Can you please explain the part in red with examples ? We have to compare the indices of similar bases: 3 with 3 and 5 with 5. IMO a=2 and b=2 is the only solution. chetan2u wrote: If a and b are positive, what is the value of a + b?
(1) (3^a)(3^b) = 81 \((3^a)(3^b) = 81........3^{a+b}=3^4=(3)^4\) a+b=4 sufficient
(2) (3^a)(5^b) = 225 \((3^a)(5^b) = 225=3^2*5^2\) Easy to fall trap of choosing a=b=2. But it is nowhere given that a and b are integers For each value of a, there will be a value of b to fit in the equation, it may be in decimals or fractions.. Insuff
A \(3^a5^b=225\).. ofcourse integer values are a=b=2 but say a = 1....\(3^15^b=225.....5^b=75\) so b will be close to 2.68267.... but there will be a specific value where it will be equal to 75
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



ISB, NUS, NTU Moderator
Joined: 11 Aug 2016
Posts: 343

Re: If a and b are positive, what is the value of a + b?
[#permalink]
Show Tags
01 Sep 2018, 10:05
Hi chetan2u, This is the first time I am coming across question that uses such a concept in equating powers. Thanks to you. Just as a measure of caution, how frequent is such a trick(or this particular concept) on the official questions that you have seen so far. I was really surprised by the fact that I have never come across such an application of the concept on any question. chetan2u wrote: GmatDaddy wrote: Might sound stupid but chetan2u Can you please explain the part in red with examples ? We have to compare the indices of similar bases: 3 with 3 and 5 with 5. IMO a=2 and b=2 is the only solution. chetan2u wrote: If a and b are positive, what is the value of a + b?
(1) (3^a)(3^b) = 81 \((3^a)(3^b) = 81........3^{a+b}=3^4=(3)^4\) a+b=4 sufficient
(2) (3^a)(5^b) = 225 \((3^a)(5^b) = 225=3^2*5^2\) Easy to fall trap of choosing a=b=2. But it is nowhere given that a and b are integers For each value of a, there will be a value of b to fit in the equation, it may be in decimals or fractions.. Insuff
A \(3^a5^b=225\).. ofcourse integer values are a=b=2 but say a = 1....\(3^15^b=225.....5^b=75\) so b will be close to 2.68267.... but there will be a specific value where it will be equal to 75
_________________
~R. If my post was of any help to you, You can thank me in the form of Kudos!! Applying to ISB ? Check out the ISB Application Kit.



Intern
Joined: 15 Aug 2018
Posts: 4

Re: If a and b are positive, what is the value of a + b?
[#permalink]
Show Tags
01 Sep 2018, 10:45
Hi then why doesn’t this apply to the first statement
Posted from my mobile device



Manager
Joined: 11 May 2018
Posts: 92
Location: India

Re: If a and b are positive, what is the value of a + b?
[#permalink]
Show Tags
01 Sep 2018, 10:57
Abhinav93 wrote: Hi then why doesn’t this apply to the first statement
Posted from my mobile device We don’t have individual values to add in statement 1 : a and b can be of any value but we need a+b as a whole. IN statement 2 : We have individual values so if the values are different then the a+b value will be changed based on the individual values Hope it helps.
_________________
If you want to Thank me Give me a KUDOS "I’ve spent months preparing for the day I’d face you. I’ve come a long way, GMAT" SonGoku



Manager
Joined: 10 Jan 2013
Posts: 156
Location: India
Concentration: General Management, Strategy
GPA: 3.95

Re: If a and b are positive, what is the value of a + b?
[#permalink]
Show Tags
01 Sep 2018, 21:40
Bunuel wrote: If a and b are positive, what is the value of a + b?
(1) (3^a)(3^b) = 81 (2) (3^a)(5^b) = 225 Ok so I fell into the trap and picked D but I haven't seen such kind of questions! Bunuel.. can you please post your solution?



Manager
Joined: 10 May 2018
Posts: 126
Concentration: Finance, Sustainability

Re: If a and b are positive, what is the value of a + b?
[#permalink]
Show Tags
01 Sep 2018, 21:56
I believe it is because in one we get the sum directly from the equations but in the other we ought to put in values in a and b to find the sum. Consider this In option (B) If we put a=2; b=2, we get a+b=4 [that is just one of the many cases possible.] Since statement 2 is an equation of an ellipse, a shape which would have many more points that satisfy its equation, hence B is insufficient. Abhinav93 wrote: Hi then why doesn’t this apply to the first statement
Posted from my mobile device
_________________



Intern
Joined: 11 Oct 2018
Posts: 2

Re: If a and b are positive, what is the value of a + b?
[#permalink]
Show Tags
21 Nov 2018, 11:58
Given: a and b are positive
To Find: value of a+b
Statement 1: (3^a)(3^b) = 81
=> (3^a)(3^b) = 3^4
=> a+b = 4
Sufficient.
Statement 2: (3^a)(5^b) = 225
=> Since it is not mentioned a and b are integers [if they were integers, then a=2 and b=2; as 225 = (3^2)(5^2)] a and b can take any values. For example, a can be 1.752 and b can 2.225 and thus (3^a)(5^b) will give you 225. Or, a can be 1.575 and b can 2.457 and thus (3^a)(5^b) will be equal to 225.
=> Therefore, a+b can result in multiple values.
Insufficient.
Answer: Only statement 1 is sufficient.



Manager
Joined: 31 Mar 2018
Posts: 54

Re: If a and b are positive, what is the value of a + b?
[#permalink]
Show Tags
21 Nov 2018, 18:24
Pakshalljain wrote: Given: a and b are positive
To Find: value of a+b
Statement 1: (3^a)(3^b) = 81
=> (3^a)(3^b) = 3^4
=> a+b = 4
Sufficient.
Statement 2: (3^a)(5^b) = 225
=> Since it is not mentioned a and b are integers [if they were integers, then a=2 and b=2; as 225 = (3^2)(5^2)] a and b can take any values. For example, a can be 1.752 and b can 2.225 and thus (3^a)(5^b) will give you 225. Or, a can be 1.575 and b can 2.457 and thus (3^a)(5^b) will be equal to 225.
=> Therefore, a+b can result in multiple values.
Insufficient.
Answer: Only statement 1 is sufficient. Thanks a lot for the clear explanation Posted from my mobile device



Intern
Joined: 19 Oct 2017
Posts: 5
Location: India
Concentration: General Management, Strategy
GPA: 3.22
WE: Operations (Manufacturing)

Re: If a and b are positive, what is the value of a + b?
[#permalink]
Show Tags
25 Nov 2018, 07:24
Abhinav93 wrote: Hi then why doesn’t this apply to the first statement
Posted from my mobile device Because the decrease in power of one term requires increase in power of other term, making the net sum of power always equal to 4




Re: If a and b are positive, what is the value of a + b? &nbs
[#permalink]
25 Nov 2018, 07:24






