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If 8^a+8^b=3^(b-2)*8^(a-1), a and b are positive integers, then what

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If 8^a+8^b=3^(b-2)*8^(a-1), a and b are positive integers, then what  [#permalink]

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New post Updated on: 16 Aug 2018, 00:46
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If \(8^a+8^b=3^{b-2}*8^{a-1}\), a and b are positive integers, then what is the product of a and b ?

A. 10
B. 12
C. 15
D. 18
E. 20

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PKN

Rise above the storm, you will find the sunshine


Originally posted by PKN on 15 Aug 2018, 21:37.
Last edited by Bunuel on 16 Aug 2018, 00:46, edited 1 time in total.
Renamed the topic.
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Re: If 8^a+8^b=3^(b-2)*8^(a-1), a and b are positive integers, then what  [#permalink]

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New post 15 Aug 2018, 21:58
PKN wrote:
If \(8^a+8^b=3^{b-2}*8^{a-1}\), a and b are positive integers, then what is the product of a and b ?

A. 10
B. 12
C. 15
D. 18
E. 20



\(8^a+8^b=3^{b-2}*8^{a-1}.................8^b=3^{b-2}*8^{a-1}-8^a...............8^b=8^{a-1}(3^{b-2}-8)\)
so \(3^{b-2}-8\) should be multiple of 8 or should be equal to 1
multiple of 8 with b as positive integer is not possible
so \(3^{b-2}-8=1.........3^{b-2}=8+1=9........3^{b-2}=3^2.....b=4\)
a -1 = b.....a= 4+1=5
ab=4*5=20

E
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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 8^a+8^b=3^(b-2)*8^(a-1), a and b are positive integers, then what &nbs [#permalink] 15 Aug 2018, 21:58
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