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Which of the following is equivalent to 5^5(6^4 - 3^4)/5 ?

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Which of the following is equivalent to 5^5(6^4 - 3^4)/5 ?  [#permalink]

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New post 10 Aug 2018, 03:52
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

71% (01:25) correct 29% (01:37) wrong based on 112 sessions

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Re: Which of the following is equivalent to 5^5(6^4 - 3^4)/5 ?  [#permalink]

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New post 10 Aug 2018, 04:06
1
Bunuel wrote:
Which of the following is equivalent to \(\frac{5^5(6^4 - 3^4)}{5}\) ?


A. 15^5
B. 15^4
C. 10^5
D. 10^4
E. 10^4−1


\(\frac{5^5(6^4 - 3^4)}{5}\)
Or, \(5^{5-1}((6^2)^2 - (3^2)^2)\)
=\(5^4(6^2+3^2)(6^2-3^2)\)
=\(5^4*45*27\)
=\(5^4*5*3^2*3^3\)
=\(5^5*3^5\)
=\((5*3)^5\)
=\(15^5\)

Ans. (A)
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Re: Which of the following is equivalent to 5^5(6^4 - 3^4)/5 ?  [#permalink]

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New post 10 Aug 2018, 04:06
1
1
Bunuel wrote:
Which of the following is equivalent to \(\frac{5^5(6^4 - 3^4)}{5}\) ?


A. 15^5
B. 15^4
C. 10^5
D. 10^4
E. 10^4−1



Given

\(\frac{5^5(6^4 - 3^4)}{5}\)

= \((5)^4 (6)^4 - (5)^4 (3)^4\)

=\((30)^4 - (15)^4\)

= \(15^4 2^4 - 15^4\)

= \(15^4 ( 2^4 - 1)\)

= \(15^5\)

The best answer is A.
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Re: Which of the following is equivalent to 5^5(6^4 - 3^4)/5 ?  [#permalink]

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New post 10 Aug 2018, 04:30
1
Bunuel wrote:
Which of the following is equivalent to \(\frac{5^5(6^4 - 3^4)}{5}\) ?

5^5 * ( 6^4 - 3^4 ) / 5
5^4 * ( ( 2^4*3^4 ) - 3^4 )
5^4 * 3^4 ( 2^4 - 1 )
5^4 * 3^4 * 15
5^4 * 3^4 * 5 * 3
5^5 * 3^5
15^5

Hence, A.
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Re: Which of the following is equivalent to 5^5(6^4 - 3^4)/5 ?  [#permalink]

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New post 10 Aug 2018, 08:38
Bunuel wrote:
Which of the following is equivalent to \(\frac{5^5(6^4 - 3^4)}{5}\) ?


A. 15^5
B. 15^4
C. 10^5
D. 10^4
E. 10^4−1

\(\frac{5^5(6^4 - 3^4)}{5}\)

= \(5^4(6^4 - 3^4)\)

= \(5^4(2^43^4 - 3^4)\)

= \(5^43^4(2^4 - 1)\)

= \(15^4*15\)

= \(15^5\), Answer must be (A)
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Re: Which of the following is equivalent to 5^5(6^4 - 3^4)/5 ?  [#permalink]

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New post 11 Feb 2019, 18:05
selim wrote:
Bunuel wrote:
Which of the following is equivalent to \(\frac{5^5(6^4 - 3^4)}{5}\) ?


A. 15^5
B. 15^4
C. 10^5
D. 10^4
E. 10^4−1



Given

\(\frac{5^5(6^4 - 3^4)}{5}\)

= \((5)^4 (6)^4 - (5)^4 (3)^4\)

=\((30)^4 - (15)^4\)

= \(15^4 2^4 - 15^4\)

= \(15^4 ( 2^4 - 1)\)

= \(15^5\)

The best answer is A.


Hello selim !

This was also my approach but I thought I was wrong and lost time trying to get the answer from a different method.

Is it okay if I reach just half of the answer like this example?

Kind regards!
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Re: Which of the following is equivalent to 5^5(6^4 - 3^4)/5 ?  [#permalink]

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New post 02 Mar 2019, 23:20
jfranciscocuencag wrote:
selim wrote:
Bunuel wrote:
Which of the following is equivalent to \(\frac{5^5(6^4 - 3^4)}{5}\) ?


A. 15^5
B. 15^4
C. 10^5
D. 10^4
E. 10^4−1



Given

\(\frac{5^5(6^4 - 3^4)}{5}\)

= \((5)^4 (6)^4 - (5)^4 (3)^4\)

=\((30)^4 - (15)^4\)

= \(15^4 2^4 - 15^4\)

= \(15^4 ( 2^4 - 1)\)

= \(15^5\)

The best answer is A.


Hello selim !

This was also my approach but I thought I was wrong and lost time trying to get the answer from a different method.

Is it okay if I reach just half of the answer like this example?

Kind regards!



Half is not allowed . U know that GMAT sometimes rearrange the answer options. Thus, practice hard to get the exact answer. try to scan answer choices first .

Happy preparing.
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Re: Which of the following is equivalent to 5^5(6^4 - 3^4)/5 ?   [#permalink] 02 Mar 2019, 23:20
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