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

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Math Expert
Joined: 02 Sep 2009
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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, 23:01
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Question Stats:

14% (01:19) correct 86% (01:13) wrong based on 65 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, 23:44
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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Re: If a and b are positive, what is the value of a + b?  [#permalink]

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01 Sep 2018, 00:01
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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01 Sep 2018, 00:20
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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Joined: 11 Aug 2016
Posts: 189
If a and b are positive, what is the value of a + b?  [#permalink]

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01 Sep 2018, 00:23
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: 6786
Re: If a and b are positive, what is the value of a + b?  [#permalink]

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01 Sep 2018, 00:39
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

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Joined: 11 Aug 2016
Posts: 189
Re: If a and b are positive, what is the value of a + b?  [#permalink]

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01 Sep 2018, 11:05
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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Joined: 15 Aug 2018
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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, 11:45
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, 11:57
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.
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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, 22:40
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, 22:56
1
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? &nbs [#permalink] 01 Sep 2018, 22:56
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