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What is the product of integers a, b, and c if 2^{a} * 3^{b} * 5^{c} =

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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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New post 09 Jul 2017, 07:43
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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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New post 09 Jul 2017, 08:08
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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



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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New post 09 Jul 2017, 08:30
2
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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New post 10 Nov 2017, 04:46
2
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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New post 14 Nov 2017, 07:06
1
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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Re: What is the product of integers a, b, and c if 2^{a} * 3^{b} * 5^{c} = &nbs [#permalink] 14 Nov 2017, 07:06
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