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30^10 / 150^5=? A. 6^5 B. 5^6 C. 3^6 D. 6^3 E. 15^3 *

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by Max@Math Revolution » Thu Feb 25, 2016 5:13 pm
30^10 / 150^5=?

A. 6^5
B. 5^6
C. 3^6
D. 6^3
E. 15^3


* A solution will be posted in two days.
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by Brent@GMATPrepNow » Thu Feb 25, 2016 7:11 pm
Max@Math Revolution wrote:30¹�/150� = ?

A. 6^5
B. 5^6
C. 3^6
D. 6^3
E. 15^3
One approach:

30¹�/150� = (30�)(30�)/150�
= (30�) x [30�/150�]
= (30�) x (30/150)�
= (30�) x (1/5)�
= 30�/5�
= (30/5)�
= 6�
= A

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Brent
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by Brent@GMATPrepNow » Thu Feb 25, 2016 7:12 pm
Max@Math Revolution wrote:30¹�/150� = ?

A. 6^5
B. 5^6
C. 3^6
D. 6^3
E. 15^3
Another approach:

Notice that 30 = (2)(3)(5)
And 150 = (2)(3)(5²)

So, 30¹�/150� = [(2)(3)(5)]¹�/[(2)(3)(5²)]�
Simplify to get: [(2¹�)(3¹�)(5¹�)]/[(2�)(3�)(5¹�)]
Simplify in parts to get: (2�)(3�)
Rewrite to get: 6�

Answer: A

Cheers,
Brent
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by Max@Math Revolution » Sun Feb 28, 2016 4:48 pm
30^10 / 150^5=?

A. 6^5
B. 5^6
C. 3^6
D. 6^3
E. 15^3


-> 30^10 / 150^5=(30^10)/(5^5)(30^5)=(30^5)/(5^5)=(6^5)(5^5)/(5^5)=6^5.
Thus, A is the answer.
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