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4^50/5^50 or 8^25/10^25
[#permalink]
12 Jun 2024, 00:15
12 Jun 2024, 00:15
Expert Reply
00:00
Question Stats:
61% (01:20) correct
38% (00:30) wrong based on 13 sessions
Hide Show timer Statistics
Quantity A |
Quantity B |
\( \frac{4^{50}}{5^{50}} \) |
\(\frac{8^{25}}{10^{25}} \) |
Part of the project: GRE Quant & Verbal ADVANCED Daily Challenge 2024 Edition - Gain 20 Kudos & Get FREE Access to GRE Prep Club TESTS
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Free Materials for the GRE General Exam - Where to get it!!
Shorter GRE - Preparing for the Quantitative Reasoning Measure
Shorter GRE - Preparing for the Verbal Reasoning Measure
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Free Materials for the GRE General Exam - Where to get it!!
Shorter GRE - Preparing for the Quantitative Reasoning Measure
Shorter GRE - Preparing for the Verbal Reasoning Measure
4^50/5^50 or 8^25/10^25
[#permalink]
13 Jun 2024, 22:10
13 Jun 2024, 22:10
Expert Reply
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
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
