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# If a = 3^(b – 1), what is the value of a + b ?

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Math Expert
Joined: 02 Sep 2009
Posts: 54371
If a = 3^(b – 1), what is the value of a + b ?  [#permalink]

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04 Nov 2014, 10:26
1
00:00

Difficulty:

25% (medium)

Question Stats:

79% (01:31) correct 21% (01:30) wrong based on 159 sessions

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Tough and Tricky questions: Exponents.

If a = 3^(b – 1), what is the value of a + b ?

(1) 3^(b + 2) = 243
(2) a = 3^(2b – 4)

Kudos for a correct solution.

_________________
Manager
Joined: 05 Jun 2014
Posts: 61
GMAT 1: 630 Q42 V35
Re: If a = 3^(b – 1), what is the value of a + b ?  [#permalink]

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04 Nov 2014, 10:42
1
Statement 1 tells that 3^b+2 = 3^5 so b=3, and a = 9. Sufficient.

Statement 2 tells that a = 3^2b-4. From the stem we know that a=3^b-1, so
3^2b-4 = 3^b-1 --------> (3^2b-4)/ (3^b-1) = 1 (b/c they are equal to each other and no expression can equal zero) -------> 3^2b-b-4+1 = 1 ------> 3^b-3=1 so b=3 and a=9. Sufficient.
Manager
Joined: 21 Jan 2014
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Re: If a = 3^(b – 1), what is the value of a + b ?  [#permalink]

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04 Nov 2014, 21:05
1
Given a=3^(b-1) .......(1)

1) 3^(b+2)=243=3^5
so , b +2=5 & b=3

Inserting the value of b in equation (1) one can get the value for 'a', which will further give the complete value for a+b. SUFFICIENT.

2) a=3^(2b-4)
From equation (1) we can say :
3^(2b-4)=3^(b-1)
so, 2b-4=b-1
b=3
Again value for 'a' can be found from any of the equations above and one can can easily obtain the complete value for a+b. SUFFICIENT.

hence, correct option is D
Manager
Joined: 22 Sep 2012
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Re: If a = 3^(b – 1), what is the value of a + b ?  [#permalink]

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04 Nov 2014, 21:46
1
Statement 1 : 3^b+2 = 243 = 3 ^ 5

b=3, a = 3^b-1 = 3^2 = 9

therefore, a+b =12, Sufficient

Statement 2: a =3^(2b-4)

Therefore, 3^b-1 = 3^(2b-4)

b-1 = 2b - 4

Therefore, b = 3 , a=9, Sufficient.

Hence D)
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Re: If a = 3^(b – 1), what is the value of a + b ?  [#permalink]

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08 Sep 2017, 22:39
Bunuel wrote:

Tough and Tricky questions: Exponents.

If a = 3^(b – 1), what is the value of a + b ?

(1) 3^(b + 2) = 243
(2) a = 3^(2b – 4)

Kudos for a correct solution.

Nice question Bunuel

St 1

3^(b+3) = 3^5 - just gotta quickly imagine the numbers

Suff

St 2

Set equal
2b-4 =b-1

suff

D
Re: If a = 3^(b – 1), what is the value of a + b ?   [#permalink] 08 Sep 2017, 22:39
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