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Re: 79^43 or 80^31 [#permalink]
Is there a shortcut to solving such kind of question?
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Re: 79^43 or 80^31 [#permalink]
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Yes , of course.

Do you have a roughly idea Sir ?? how to solve it ?? or blank ??
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Re: 79^43 or 80^31 [#permalink]
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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.

However I would like to see the break up of 79
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Re: 79^43 or 80^31 [#permalink]
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Fast approach

80^43 > 80^31 and -1^43 is just one.

The first quantity minus 1^43 must be bigger than B

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Re: 79^43 or 80^31 [#permalink]
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Carcass wrote:
Fast approach

80^43 > 80^31 and -1^43 is just one.

The first quantity minus 1^43 must be bigger than B

Ciao


Where does -1^43 enter the picture?
We can't say that 79^43 - 80^43 = (-1)^43
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Re: 79^43 or 80^31 [#permalink]
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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.
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Re: 79^43 or 80^31 [#permalink]
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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"
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79^43 or 80^31 [#permalink]
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Aaka wrote:
Is there a shortcut to solving such kind of question?



79^43 v/s 80^31

Divide both sides by 79^31;

79^12 v/s (80/79)^31

Now, 80/79 is just above 1
We can clearly see, A would be greater than B

Hence, option A
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Re: 79^43 or 80^31 [#permalink]
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79^43 => (80-1)^43 => 80^43 - 1^43 => 80^43 - 1 Thus A is greater than B.
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Re: 79^43 or 80^31 [#permalink]
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Re: 79^43 or 80^31 [#permalink]
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