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04 Nov 2014, 10:26
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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77% (01:37) correct
23%
(01:36)
wrong
based on 305
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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.
04 Nov 2014, 10:42
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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.
Answer is D.
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.
Answer is D.
04 Nov 2014, 21:05
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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
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
