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21 Apr 2022, 07:15
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A
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Difficulty:
95%
(hard)
Question Stats:
45% (02:01) correct
55%
(02:10)
wrong
based on 198
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\(\{17^{88}, \ 31^{69}, \ 63^{55}\}\)
Which of the following is the correct ordering of the numbers in the list above?
A. \(17^{88} > 31^{69} > 63^{55}\)
B. \(17^{88} > 63^{55} > 31^{69} \)
C. \(31^{69} > 17^{88} > 63^{55}\)
D. \(31^{69} > 63^{55} > 17^{88} \)
E. \(63^{55} > 17^{88} > 31^{69} \)
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
Which of the following is the correct ordering of the numbers in the list above?
A. \(17^{88} > 31^{69} > 63^{55}\)
B. \(17^{88} > 63^{55} > 31^{69} \)
C. \(31^{69} > 17^{88} > 63^{55}\)
D. \(31^{69} > 63^{55} > 17^{88} \)
E. \(63^{55} > 17^{88} > 31^{69} \)
Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
06 May 2022, 00:30
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it can be done by approximation
\({17^{88}, 31^{69}, 63^{55}}\)
first lets compare \(17^{88}\) and \(~31^{69}\)
\(17^{88}\) can be written as ~\(16^{88}\)
and
\(31^{69}\) can be written as ~\(32^{69}\)
these two can now be compared and \(17^{88}\) is greater than \(31^{69}\)
similarly \(63^{55}\) can be written as ~\(64^{55}\) and compared with \(32^{69}\) to find that \(63^{55}\) is smaller than \(31^{69}\).
\({17^{88}, 31^{69}, 63^{55}}\)
first lets compare \(17^{88}\) and \(~31^{69}\)
\(17^{88}\) can be written as ~\(16^{88}\)
and
\(31^{69}\) can be written as ~\(32^{69}\)
these two can now be compared and \(17^{88}\) is greater than \(31^{69}\)
similarly \(63^{55}\) can be written as ~\(64^{55}\) and compared with \(32^{69}\) to find that \(63^{55}\) is smaller than \(31^{69}\).
16 Apr 2024, 14:39
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It's hard to assess those numbers in their original forms. But all of them are very close to the power of 2.
For example:
17 is close to 16 which can be expressed as 2^4
31 is close to 32 which can be expressed as 2^5
63 is close to 64 which can be expressed as 2^6
So therefore:
17^88 can be expressed as (2^4)^88 = 2^352
31^69 can be expressed as (2^5)^69 = 2^345
63^55 can be expressed as (2^6)^55 = 2^330
Hence, 17^88 > 31^69 > 63^55
Answer: A
For example:
17 is close to 16 which can be expressed as 2^4
31 is close to 32 which can be expressed as 2^5
63 is close to 64 which can be expressed as 2^6
So therefore:
17^88 can be expressed as (2^4)^88 = 2^352
31^69 can be expressed as (2^5)^69 = 2^345
63^55 can be expressed as (2^6)^55 = 2^330
Hence, 17^88 > 31^69 > 63^55
Answer: A
