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# QOTD#19 Evaluate the fraction

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4756
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1668 [0], given: 396

QOTD#19 Evaluate the fraction [#permalink]  16 Dec 2016, 18:53
Expert's post
00:00

Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 1 sessions
$$210^2 \times 21^3 \times 49^0^.^5 \div 30^4 \times 3 = 7^x . x$$

Enter the value of x.

Drill 4
Question: 13
Page: 295

[Reveal] Spoiler: OA
6

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4756
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1668 [0], given: 396

Re: QOTD#19 Evaluate the fraction [#permalink]  16 Dec 2016, 19:06
Expert's post
Explanation

Break down the left side of the equation into prime factors to make it easier to simplify. You should get:

$$\frac{(3^2 \times 7^2 \times 2^2 \times 5^2) \times (3^3 \times 7^3) \times 7}{(2^4 \times 5^4 \times 3^4)\times(3)}=7^x$$

Then group all the like terms:

$$\frac{2^4 \times 3^5 \times 5^4 \times 7^6}{2^4 \times 3^5 \times 5^4}=7^x$$

Everything cancels out on the left side except for $$7^6$$, which makes 6 your answer.
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Intern
Joined: 15 Dec 2016
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Re: QOTD#19 Evaluate the fraction [#permalink]  18 Dec 2016, 16:00
Can you please explain the significance of the .x and also shouldn't 210 simplify to 7*3*5*2 so where did you get 5^4 and 2^4 from in the numerator? I can only simplify it to 7^6/2^2 x 5^2, i.e. 7^6/100.
Re: QOTD#19 Evaluate the fraction   [#permalink] 18 Dec 2016, 16:00
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# QOTD#19 Evaluate the fraction

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