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Math Expert V
Joined: 02 Sep 2009
Posts: 56372
If a and b are positive, what is the value of a + b?  [#permalink]

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5 00:00

Difficulty:   95% (hard)

Question Stats: 22% (01:32) correct 78% (01:26) wrong based on 168 sessions

### HideShow timer Statistics If a and b are positive, what is the value of a + b?

(1) $$(3^a)(3^b) = 81$$

(2) $$(3^a)(5^b) = 225$$

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Manager  B
Joined: 11 May 2018
Posts: 91
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GMAT 1: 460 Q42 V14 Re: If a and b are positive, what is the value of a + b?  [#permalink]

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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;
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Math Expert V
Joined: 02 Aug 2009
Posts: 7763
Re: If a and b are positive, what is the value of a + b?  [#permalink]

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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
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Re: If a and b are positive, what is the value of a + b?  [#permalink]

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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

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Retired Moderator G
Joined: 11 Aug 2016
Posts: 375
Re: If a and b are positive, what is the value of a + b?  [#permalink]

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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

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Math Expert V
Joined: 02 Aug 2009
Posts: 7763
Re: If a and b are positive, what is the value of a + b?  [#permalink]

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1
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
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Retired Moderator G
Joined: 11 Aug 2016
Posts: 375
Re: If a and b are positive, what is the value of a + b?  [#permalink]

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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:
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

_________________
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If my post was of any help to you, You can thank me in the form of Kudos!!
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Intern  B
Joined: 15 Aug 2018
Posts: 4
Re: If a and b are positive, what is the value of a + b?  [#permalink]

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Hi then why doesn’t this apply to the first statement

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Manager  B
Joined: 11 May 2018
Posts: 91
Location: India
GMAT 1: 460 Q42 V14 Re: If a and b are positive, what is the value of a + b?  [#permalink]

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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.
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Manager  G
Joined: 10 Jan 2013
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Location: India
Concentration: General Management, Strategy
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Re: If a and b are positive, what is the value of a + b?  [#permalink]

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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!

Manager  G
Joined: 10 May 2018
Posts: 123
Concentration: Finance, Sustainability
Re: If a and b are positive, what is the value of a + b?  [#permalink]

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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

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

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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  G
Joined: 31 Mar 2018
Posts: 88
Re: If a and b are positive, what is the value of a + b?  [#permalink]

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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
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Re: If a and b are positive, what is the value of a + b?  [#permalink]

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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?   [#permalink] 25 Nov 2018, 08:24
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