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

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Math Expert
Joined: 02 Sep 2009
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Which of the following is equivalent to 5^5(6^4 - 3^4)/5 ?  [#permalink]

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10 Aug 2018, 03:52
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Difficulty:

25% (medium)

Question Stats:

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

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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

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

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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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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

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

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

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

= $$15^4 2^4 - 15^4$$

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

= $$15^5$$

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

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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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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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Posts: 246
Re: Which of the following is equivalent to 5^5(6^4 - 3^4)/5 ?  [#permalink]

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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

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

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

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

= $$15^4 2^4 - 15^4$$

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

= $$15^5$$

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!
VP
Joined: 31 Oct 2013
Posts: 1354
Concentration: Accounting, Finance
GPA: 3.68
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Re: Which of the following is equivalent to 5^5(6^4 - 3^4)/5 ?  [#permalink]

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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

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

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

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

= $$15^4 2^4 - 15^4$$

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

= $$15^5$$

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.
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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