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What is the product of integers a, b, and c if...

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What is the product of integers a, b, and c if...

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What is the product of integers a, b, and c if
$$2^a\ \cdot\ 3^b\ \cdot\ 5^c\ =\ 270,000,000$$

A. 141
B. 147
C. 162
D. 235
E. 270

The OA is B.

Please, can any expert assist me with this PS question? I need help to solve it. Thanks.

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GMAT/MBA Expert

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Hi LUANDATO,

You should notice that all of the 'bases' are PRIME numbers, so this question is all about 'prime factorization.' To start, we have to prime factor 270,000,000 down into its 'pieces'...

(270)(1,000)(1,000) =

270 = (3)(3)(3)(2)(5)
1,000 = (2)(2)(2)(5)(5)(5)

Thus 270,000,000 = (2^7)(3^3)(5^7)

The product of those three exponents is (7)(3)(7) = 147

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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GMAT/MBA Expert

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Quote:
What is the product of integers a, b, and c if
$$2^a\ \cdot\ 3^b\ \cdot\ 5^c\ =\ 270,000,000$$

A. 141
B. 147
C. 162
D. 235
E. 270

The OA is B.

Please, can any expert assist me with this PS question? I need help to solve it. Thanks.
Hi LUANDATO,
Lets take a look at your question.

$$2^a\ \cdot\ 3^b\ \cdot\ 5^c\ =\ 270,000,000$$
$$2^a.3^b.5^c=27\times10,000,000$$ $$2^a.3^b.5^c=\left(3\times3\times3\right)\times\left(2\times5\right)\times\left(2\times5\right)\times\left(2\times5\right)\times\left(2\times5\right)\times\left(2\times5\right)\times\left(2\times5\right)\times\left(2\times5\right)$$
$$2^a.3^b.5^c=3^3\times2^7\times5^7$$
$$a=3,\ b=7,\ c=7$$
$$abc=3\times7\times7$$
$$abc=147$$

Therefore, option B is correct.

I am available if you'd like any follow up.

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GMAT Prep From The Economist
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GMAT/MBA Expert

Post
LUANDATO wrote:
What is the product of integers a, b, and c if
$$2^a\ \cdot\ 3^b\ \cdot\ 5^c\ =\ 270,000,000$$

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

_________________

Jeffrey Miller
Head of GMAT Instruction
jeff@targettestprep.com



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