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

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

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31 Aug 2018, 22:01
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95% (hard)

Question Stats:

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

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

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

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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
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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

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

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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

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

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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

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Math Expert
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Posts: 7098
Re: If a and b are positive, what is the value of a + b?  [#permalink]

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31 Aug 2018, 23:39
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
_________________

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
Joined: 11 Aug 2016
Posts: 343
Re: If a and b are positive, what is the value of a + b?  [#permalink]

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

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

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

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

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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!

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

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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

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

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

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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

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

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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
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