Which of the following is the correct ordering of the numbers in the

Question

\{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}

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stoned · Accepted Answer

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} .

jantwarog · Answer

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

findingmyself · Answer

How I solved this:

17^{88}  can be written as  17^{69}*17^{19}  which can be further simplified into  17^{69}*2^{76}  (Since 17 is approximately  2^4 )

31^{69}  can be written as  17^{69}*2^{69}  since  17*2=34  and is close to 31 (The idea here is to bring everything in terms of 17 and 2 with respective powers)

63^{55}  is written as  17^{55}*4^{44}  since  17*4 is 68, close to 63.  17^{55}*4^{55}  is further rewritten us  17^{69}*2^{54}  (Took 14 times 4^{2}  s from  4^{44}  to make  17^{55}  to  17^{69}  since each  4^{2}  is equvalent to 17, following which  4^{27}  is converted to  2^{54})

Now we have

17^{69}*2^{76} (A) , 17^{69}*2^{69}(B) , 17^{69}*2^{54}(C)

Regor60 · Answer

With such a large exponent difference, 17^88 is surely to be the largest, leaving answers A and B as the remaining choices.

So, 31^69 vs 63^55 or

31^55*31^14 vs 63^55 or

31^14 vs ~ 2^55 = ~(2^4)^14 or

31 vs 16

Therefore Answer A

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Which of the following is the correct ordering of the numbers in the

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