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What is the product of integers a, b, and c if 2^{a} * 3^{b} * 5^{c} = [#permalink]
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09 Jul 2017, 06:43
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What is the product of integers a, b, and c if \(2^{a} * 3^{b} * 5^{c} = 270,000,000\) A. 141 B. 147 C. 162 D. 235 E. 270
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Re: What is the product of integers a, b, and c if 2^{a} * 3^{b} * 5^{c} = [#permalink]
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09 Jul 2017, 07:08
ydmuley wrote: What is the product of integers a, b, and c if \(2^{a} * 3^{b} * 5^{c} = 270,000,000\)
A. 141
B. 147
C. 162
D. 235
E. 270 270000000=\(3^3*10^7\) So a=c=7 and b=3.. abc=7*7*3=147 B
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What is the product of integers a, b, and c if 2^{a} * 3^{b} * 5^{c} = [#permalink]
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09 Jul 2017, 07:30
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ydmuley wrote: What is the product of integers a, b, and c if \(2^{a} * 3^{b} * 5^{c} = 270,000,000\)
A. 141
B. 147
C. 162
D. 235
E. 270 \(2^{a} * 3^{b} * 5^{c} = 270,000,000\), simplify RHS \(2^{a} * 3^{b} * 5^{c} = 27 * 10^{7}\), factor \(10^7\) \(2^{a} * 3^{b} * 5^{c} = 3^{3}*2^{7}*5^{7}\) Bases are now the same, so a = 7, b = 3, and c = 7. Product = 7*3*7 = 147. Answer B.
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Re: What is the product of integers a, b, and c if 2^{a} * 3^{b} * 5^{c} = [#permalink]
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10 Nov 2017, 03:46
ydmuley wrote: What is the product of integers a, b, and c if \(2^{a} * 3^{b} * 5^{c} = 270,000,000\)
A. 141
B. 147
C. 162
D. 235
E. 270 Responding to a pm: Note that cyclicity has no role to play in this. For it to work in a question, we need to know the power of the term. Here there are too many variables. It is a simple question of prime factorisation. This is the reason GMAT is tricky  it's not the concept per say which is hard to understand, it's more about WHICH concept will help solve the problem.
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Re: What is the product of integers a, b, and c if 2^{a} * 3^{b} * 5^{c} = [#permalink]
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14 Nov 2017, 06:06
ydmuley wrote: What is the product of integers a, b, and c if \(2^{a} * 3^{b} * 5^{c} = 270,000,000\)
A. 141
B. 147
C. 162
D. 235
E. 270 Let’s break 270,000,000 into its prime factors. 270,000,000 = 27 x 10,000,000 = 3^3 x 10^7 = 2^7 x 3^3 x 5^7, so a x b x c = 7 x 3 x 7 = 147. Answer: B
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