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

It is currently 10 Dec 2018, 11:55

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free lesson on number properties

     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.
  • Free GMAT Prep Hour

     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.

If a and b are positive, what is the value of a + b?

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51072
If a and b are positive, what is the value of a + b?  [#permalink]

Show Tags

New post 31 Aug 2018, 22:01
1
4
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

23% (01:00) correct 77% (01:08) wrong based on 133 sessions

HideShow timer Statistics

Manager
Manager
User avatar
B
Joined: 11 May 2018
Posts: 92
Location: India
GMAT 1: 460 Q42 V14
GMAT ToolKit User
Re: If a and b are positive, what is the value of a + b?  [#permalink]

Show Tags

New post 31 Aug 2018, 22:44
Statement 1
3^a * 3^b =81
3^(a+b)=3^4
Therefore a+b=4:
SUFFICIENT
Statement 2
3^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
User avatar
V
Joined: 02 Aug 2009
Posts: 7098
Re: If a and b are positive, what is the value of a + b?  [#permalink]

Show Tags

New post 31 Aug 2018, 23:01
2
1
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Director
Director
User avatar
V
Joined: 06 Jan 2015
Posts: 525
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE: Information Technology (Computer Software)
Premium Member
Re: If a and b are positive, what is the value of a + b?  [#permalink]

Show Tags

New post 31 Aug 2018, 23:20
1
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 chetan2u

Can 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
User avatar
G
Joined: 11 Aug 2016
Posts: 343
Reviews Badge CAT Tests
If a and b are positive, what is the value of a + b?  [#permalink]

Show Tags

New post 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
User avatar
V
Joined: 02 Aug 2009
Posts: 7098
Re: If a and b are positive, what is the value of a + b?  [#permalink]

Show Tags

New post 31 Aug 2018, 23:39
1
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/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

ISB, NUS, NTU Moderator
User avatar
G
Joined: 11 Aug 2016
Posts: 343
Reviews Badge CAT Tests
Re: If a and b are positive, what is the value of a + b?  [#permalink]

Show Tags

New post 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
Intern
avatar
B
Joined: 15 Aug 2018
Posts: 4
Re: If a and b are positive, what is the value of a + b?  [#permalink]

Show Tags

New post 01 Sep 2018, 10:45
Hi then why doesn’t this apply to the first statement

Posted from my mobile device
Manager
Manager
User avatar
B
Joined: 11 May 2018
Posts: 92
Location: India
GMAT 1: 460 Q42 V14
GMAT ToolKit User
Re: If a and b are positive, what is the value of a + b?  [#permalink]

Show Tags

New post 01 Sep 2018, 10:57
1
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
Manager
avatar
S
Joined: 10 Jan 2013
Posts: 156
Location: India
Concentration: General Management, Strategy
GMAT 1: 600 Q43 V30
GPA: 3.95
GMAT ToolKit User Reviews Badge
Re: If a and b are positive, what is the value of a + b?  [#permalink]

Show Tags

New post 01 Sep 2018, 21:40
1
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
Manager
User avatar
G
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

New post 01 Sep 2018, 21:56
2
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

_________________

Stuck in the 600-700 score bracket? I welcome you to read my four-step course of action to a modest score.
I also invite you to critique and help me find flaws in my modus operandi. Thanks!

Intern
Intern
avatar
B
Joined: 11 Oct 2018
Posts: 2
Re: If a and b are positive, what is the value of a + b?  [#permalink]

Show Tags

New post 21 Nov 2018, 11:58
1
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
Manager
avatar
B
Joined: 31 Mar 2018
Posts: 54
Re: If a and b are positive, what is the value of a + b?  [#permalink]

Show Tags

New post 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
Intern
User avatar
B
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

New post 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
GMAT Club Bot
Re: If a and b are positive, what is the value of a + b? &nbs [#permalink] 25 Nov 2018, 07:24
Display posts from previous: Sort by

If a and b are positive, what is the value of a + b?

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.