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codensnap
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If a and b are nonzero integers and a^(3b) = a^(b-6), what is the valu Updated on: 17 Nov 2014, 01:58
Originally posted by codensnap on 16 Nov 2014, 23:36.
Last edited by Bunuel on 17 Nov 2014, 01:58, edited 1 time in total.
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35% (medium)

Question Stats:

70% (01:25) correct 30% (01:31) wrong based on 80 sessions

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If a and b are nonzero integers and \(a^{3b} = a^{b-6}\), what is the value of \(b^{a}\)?

(A) a^3 = 8

(B) a^2 = 4

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I understand that (A) is sufficient. But if I simplify the given equation algebraically -
a^3b = a^b–6
a^3b/ a^b–6 = 1
a^(3b-b+6) = 1
a^(2b+6) = 1
(a^2)^b * a^6 = 1
(a^2)^b * (a^2)^3 = 1

This would make (B) sufficient, wouldn't it? Am I missing something in my simplification? Appreciate any pointers. Thanks.

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A
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manpreetsingh86
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If a and b are nonzero integers and a^(3b) = a^(b-6), what is the valu 17 Nov 2014, 01:35
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codensnap
If a and b are nonzero integers and \(a^{3b}\) = \(a^{b-6}\), what is the value of \(b^{a}\)?

(A) \(a^{3}\) = 8

(B) \(a^{2}\) = 4

Show Spoiler
I understand that (A) is sufficient. But if I simplify the given equation algebraically -
a^3b = a^b–6
a^3b/ a^b–6 = 1
a^(3b-b+6) = 1
a^(2b+6) = 1
(a^2)^b * a^6 = 1
(a^2)^b * (a^2)^3 = 1

This would make (B) sufficient, wouldn't it? Am I missing something in my simplification? Appreciate any pointers. Thanks.
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\(a^{3b}\) = \(a^{b-6}\)
as bases are same on both side, thus 3b=b-6
or 2b=-6, b=-3
now to find the value of \(b^{a}\), we need to find the value of a.

st.1 \(a^{3}\)=8
\(a^{3}\)=\(2^{3}\). thus a must be 2. hence sufficient

st.2 \(a^{2}\)=4
both a=2, and a=-2 can satisfy the above equation. hence st.2 alone is not sufficient.
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akumar5
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If a and b are nonzero integers and a^(3b) = a^(b-6), what is the valu 17 Nov 2014, 02:58
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Given that a^3b=a^(b-6)
a^(3b-b+6)=1
2b+6=0
b=-3

we need value for a so as to solve the riddle

1) a^3=8
a=2 Sufficent

2) a^2=4
a=+-2 Two distinct values for a hence its Insufficient.

Answer A
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codensnap
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If a and b are nonzero integers and a^(3b) = a^(b-6), what is the valu 17 Nov 2014, 07:35
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Please refer to my original question stem regarding my simplification steps, which makes is possible to arrive at b^a, given a^2. My question is not what the solution to the problem is, but if I'm going wrong in my exponential simplification. Thanks.
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If a and b are nonzero integers and a^(3b) = a^(b-6), what is the valu 17 Nov 2014, 08:02
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Please refer to my original question stem regarding my simplification steps, which makes is possible to arrive at b^a, given a^2. My question is not what the solution to the problem is, but if I'm going wrong in my exponential simplification. Thanks.
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As per the question we have to find the value for b^a

for your information your exponential simplification is correct but this will only give you value for b =-3
Remember you have to find value for b^a and you need to have the value "a" as well to solve this riddle...right?

hence as you will see through second statement it is a^2=4
so, here you will get two different values for a=-2 ,+2 which further results in two different values for b^a which is your main question .
Clearly, this will not give a definite result for the expression b^a.

Statement B is of no use .

Hope it helps .
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If a and b are nonzero integers and a^(3b) = a^(b-6), what is the valu 17 Nov 2014, 14:06
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Thanks, I see the point. I was so engrossed in simplifying the equation that I missed going back to the original question.

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