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If a and b are positive, what is the value of a + b?
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31 Aug 2018, 23:01
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14% (01:19) correct 86% (01:13) wrong based on 65 sessions
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Re: If a and b are positive, what is the value of a + b?
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31 Aug 2018, 23:44
Statement 13^a * 3^b =81 3^(a+b)=3^4 Therefore a+b=4: SUFFICIENT Statement 23^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
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Re: If a and b are positive, what is the value of a + b?
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01 Sep 2018, 00:01
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 integersFor 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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Re: If a and b are positive, what is the value of a + b?
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01 Sep 2018, 00:20
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 chetan2uCan 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?
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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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Re: If a and b are positive, what is the value of a + b?
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01 Sep 2018, 00:39
GmatDaddy 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?
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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: GmatDaddy 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?
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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?
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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?
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01 Sep 2018, 22:40
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! Bunuel.. can you please post your solution?



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Re: If a and b are positive, what is the value of a + b?
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01 Sep 2018, 22:56
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
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