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2^20/3^15
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21 Feb 2021, 10:25
21 Feb 2021, 10:25
Expert Reply
00:00
Question Stats:
97% (00:35) correct
2% (01:37) wrong based on 34 sessions
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Quantity A |
Quantity B |
\(\frac{2^{20}}{3^{15}}\) |
\(\frac{16^5}{27^5 }\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
2^20/3^15
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21 Feb 2021, 10:37
21 Feb 2021, 10:37
Solution:
Qty A: \(\frac{2^2^0}{3^1^5}\)
Qty B: \(\frac{16^5}{27^5}\)
We know 16=\(2^4\) & 27=\(3^3\)
Thus, \(\frac{16^5}{27^5}\)=\(\frac{2^4^*^5}{3^3^*^5}\)=\(\frac{2^2^0}{3^1^5}\)
Hence, QTY A=QTY B
IMO C
Hope this helps!
Qty A: \(\frac{2^2^0}{3^1^5}\)
Qty B: \(\frac{16^5}{27^5}\)
We know 16=\(2^4\) & 27=\(3^3\)
Thus, \(\frac{16^5}{27^5}\)=\(\frac{2^4^*^5}{3^3^*^5}\)=\(\frac{2^2^0}{3^1^5}\)
Hence, QTY A=QTY B
IMO C
Hope this helps!
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2^20/3^15
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21 Feb 2021, 12:13
21 Feb 2021, 12:13
1
Carcass wrote:
Quantity A |
Quantity B |
\(\frac{2^{20}}{3^{15}}\) |
\(\frac{16^5}{27^5 }\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Power of a Power law: \((b^x)^y=b^{xy}\)
Given:
Quantity A: \(\frac{2^{20}}{3^{15}}\)
Quantity B: \(\frac{16^5}{27^5 }\)
Rewrite \(16\) as \(2^4\) and rewrite \(27\) as \(3^3\) to get:
Quantity A: \(\frac{2^{20}}{3^{15}}\)
Quantity B: \(\frac{(2^4)^5}{(3^3)^5 }\)
Apply the Power of a Power law to get:
Quantity A: \(\frac{2^{20}}{3^{15}}\)
Quantity B: \(\frac{2^{20}}{3^{15}}\)
Answer: C
