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81% (01:10) correct
18% (01:07) wrong based on 204 sessions
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Quantity A
Quantity B
\(79^{43}\)
\(80^{31}\)
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.
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.
APPROACH #1: Number sense
First recognize that \(79^{43}\) = \(79^{31} \times 79^{12}\)
While \(79^{31}\) might be a little bit smaller than 80^{31}, once we multiply \(79^{31}\) by \(79^{12}\) (a very large number), the resulting \(79^{43}\) will definitely be greater than \(80^{31}\)
Answer: A
APPROACH #2: Exponent laws and inequality laws Let's first start with some matching operations (see video below on this technique)
Re: 79^43 or 80^31
[#permalink]
24 Jul 2020, 05:05
1
I approximated, since 79 is close to 80 and we can match powers like 79 has the power 43 and 80 has power 31, which is a big difference and digit difference is only one i.e. 79 and 80 (80-79=1) 79 has 43 power so it should be greater than 80 which has power 31 only.
Re: 79^43 or 80^31
[#permalink]
10 Aug 2020, 20:43
1
Carcass wrote:
Quantity A
Quantity B
\(79^{43}\)
\(80^{31}\)
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.
You can start off by setting up an equality with a question mark(we can change the question mark to >, <, or = afterwards, consider it a placeholder until simplyfing is done).
\(79^{43}\) ? \(80^{31}\)
\(\frac{(79^{31})}{80^{31}}\) * \(79^{12}\) ? 1
\((\frac{79}{80})^{31}\) * \(79^{12}\) ? 1
Now \(\frac{79}{80}\) is pretty close to 0.99. This means that increasing the exponent of \(\frac{79}{80}\) will bring the fraction closer to 0, but very slowly.
So the question is: would ~\(0.99^{31}\) multiplied by \(79^{12}\) be greater than or less than 1? (doesn't look like it's equaling it). Since \(79^{12}\) is such an enormous number, and \(0.99^{31}\) is small but not so small that it dwarfs the enormity of \(79^{12}\), I guessed it would be greater than 1.
Though that's just an estimation. Brent has a more rigorous way of explaining it above which is much cleaner.
Re: 79^43 or 80^31
[#permalink]
28 Oct 2020, 04:27
1
Carcass wrote:
Quantity A
Quantity B
\(79^{43}\)
\(80^{31}\)
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.
we can write, 80^{31}= 80^{43-12} = 80^{43}/80^{13} Column A Column B 79^{43} 80^{43}/80^{13} exchanging...... 80^{13} 80^{43}/79^{43} next... 80^{13} (80/79)^{43} next... 80^{13} 1.0126^{43} SO, Ans is "A"
Re: 79^43 or 80^31
[#permalink]
03 Oct 2024, 08:10
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