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31 Aug 2018, 23:01
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
25% (01:24) correct
75%
(01:28)
wrong
based on 340
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If a and b are positive, what is the value of a + b?
(1) \((3^a)(3^b) = 81\)
(2) \((3^a)(5^b) = 225\)
(1) \((3^a)(3^b) = 81\)
(2) \((3^a)(5^b) = 225\)
01 Sep 2018, 00:01
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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
(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
General Discussion
31 Aug 2018, 23:44
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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;
Dis the answer
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;
Dis the answer
