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10^4 or 5^6
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16 Jul 2021, 04:35
16 Jul 2021, 04:35
Expert Reply
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Question Stats:
72% (00:36) correct
27% (00:31) wrong based on 11 sessions
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Quantity A |
Quantity B |
\(10^4\) |
\(5^6\) |
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
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Posts: 6218
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10^4 or 5^6
[#permalink]
16 Jul 2021, 05:15
16 Jul 2021, 05:15
1
Carcass wrote:
Quantity A |
Quantity B |
\(10^4\) |
\(5^6\) |
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
For Quantity B, let's rewrite \(10\) as \(5 \times 2\), and then simplify to get:
QUANTITY A: \(10^4=(5 \times 2)^4=5^5 \times 2^4=(5^4)(2^4)\)
QUANTITY B: \(5^6\)
From here, let's divide both quantities by \(5^4\) to get:
QUANTITY A: \(2^4\)
QUANTITY B: \(5^2\)
Finally, we can evaluate the two quantities as follows:
QUANTITY A: \(2^4=16\)
QUANTITY B: \(5^2=25\)
Answer: B
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10^4 or 5^6
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16 Jul 2021, 09:44
16 Jul 2021, 09:44
Quantity A: \(10^4\)
\(10^4\) = \((5*2)^4\) = \(5^4\) * \(2*4\) = \(5^4\) * 16 = 16*\(5^4\)
Quantity B: \(5^6\)
\(5^6\) = \(5^{4+2}\) = \(5^4 * 5^2\) = \(5^4\) * 25 = 25*\(5^4\)
Clearly Quantity B (25*\(5^4\)) > Quantity A (16*\(5^4\)) [ as 25 > 16 ]
So, answer will be B
Hope it helps!
\(10^4\) = \((5*2)^4\) = \(5^4\) * \(2*4\) = \(5^4\) * 16 = 16*\(5^4\)
Quantity B: \(5^6\)
\(5^6\) = \(5^{4+2}\) = \(5^4 * 5^2\) = \(5^4\) * 25 = 25*\(5^4\)
Clearly Quantity B (25*\(5^4\)) > Quantity A (16*\(5^4\)) [ as 25 > 16 ]
So, answer will be B
Hope it helps!
