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

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BTGmoderatorLU: Moderator; Posts: 2544; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Sat Nov 04, 2017 6:58 am

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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Source: Beat The GMAT — Problem Solving | Sat Nov 04, 2017 6:58 am

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by [email protected] » Sat Nov 04, 2017 11:33 am

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

Contact Rich at [email protected]

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EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

by EconomistGMATTutor » Sat Nov 04, 2017 2:17 pm

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.

GMAT Prep From The Economist
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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue Nov 14, 2017 6:06 am

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
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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