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Re: 4^50/5^50 or 8^25/10^25 [#permalink]
Carcass wrote:
Not so a difficult question if we follow the right approach

The best thing to do is to dissect Qa and QB in primes and then take the ratio of both and see if it is <1, >1, or equal

QA

\(\frac{(2^2)^{50}}{5^{50}}=\frac{2^{100}}{5^{50}}\)

QB

\(\frac{8^{25}}{10^{25}}=\frac{(2^3)^{25}}{2^{25} \times 5^{25}}=\frac{2^{75}}{2^{25} \times 5^{25}}=\frac{2^{50}}{5^{25}}\)

Taking the ratio

QA/QB= \(\dfrac{\frac{2^{100}}{5^{50}}}{\frac{2^{50}}{5^{25}}}=\frac{2^{100}}{5^{50}} \times \frac{5^{25}}{2^{50}}=\frac{2^{50}}{5^{25}}=\frac{4^{25}}{5^{25}}=(\frac{4}{5})^{25}\)

The ratio is less than 1

So A<B



why would you calculate the ratio of QA/QB ??
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Re: 4^50/5^50 or 8^25/10^25 [#permalink]
Expert Reply
Because it is one of the different ways to compare fractions

See more our chapter about fractions https://gre.myprepclub.com/forum/gre-ma ... tml#p97122 and ratio/proportions https://gre.myprepclub.com/forum/gre-ma ... tml#p82702
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Re: 4^50/5^50 or 8^25/10^25 [#permalink]
2
A B

4^50/5^50 8^25/10^25

2^100/5^50 2^75/2^25X 5^25

Divide both sides by 2^75

2^25/5^50 1/2^25x 5^25


Multiply both sides by 5^25

(2/5)^25 (1/2)^25


Multiply both powers by 1/25



2/5 1/2

Answer B

Adewale Fasipe, quant instructor from Lagos Nigeria.
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Re: 4^50/5^50 or 8^25/10^25 [#permalink]
Expert Reply
adewale223 wrote:
A B

4^50/5^50 8^25/10^25

2^100/5^50 2^75/2^25X 5^25

Divide both sides by 2^75

2^25/5^50 1/2^25x 5^25


Multiply both sides by 5^25

(2/5)^25 (1/2)^25


Multiply both powers by 1/25



2/5 1/2

Answer B

Adewale Fasipe, quant instructor from Lagos Nigeria.


:thumbsup: :thumbsup:
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