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# The mean of an ascending sequence of positive consecutive two-digit in

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Joined: 07 Dec 2014
Posts: 1198
The mean of an ascending sequence of positive consecutive two-digit in  [#permalink]

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Updated on: 31 Dec 2018, 21:52
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Difficulty:

75% (hard)

Question Stats:

38% (02:29) correct 63% (02:27) wrong based on 21 sessions

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The mean of an ascending sequence of positive consecutive two-digit integers is the reverse of the first term. If the sum of the first and last terms is less than 100, how many such sequences are there?

A. 4
B. 5
C. 6
D. 7
E. 8

Originally posted by gracie on 30 Dec 2018, 23:12.
Last edited by gracie on 31 Dec 2018, 21:52, edited 1 time in total.
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Joined: 02 Aug 2009
Posts: 7765
Re: The mean of an ascending sequence of positive consecutive two-digit in  [#permalink]

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31 Dec 2018, 20:59
1
gracie wrote:
The mean of an ascending sequence of positive consecutive two-digit integers is the reverse of the first term. If the sum of the first and last terms is less than 100, how many such sequences are there?

A. 1
B. 2
C. 3
D. 4
E. 5

Since the terms are consecutive, sum of first and last term will be equal to 2 times the mean

Starting with 13, then 13....31...., Sum =2*31=62
Starting with 14, then 14...41..., Sum = 2*41=84
Mean of 51 will make the sum 102.. not possible

Starting with 24..42.., sum=2*42=84
Mean of 52 will mean greater than 100

Now let the sequence start in 30s
So 34...43... 2*43=86 possible

No other possible as starting with 45 will lead to to a mean of 54..

Total sequences possible are starting with 12, 13, 14, 23, 24, and 34..

What is the source??
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Joined: 07 Dec 2014
Posts: 1198
The mean of an ascending sequence of positive consecutive two-digit in  [#permalink]

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31 Dec 2018, 21:51
chetan2u wrote:
gracie wrote:
The mean of an ascending sequence of positive consecutive two-digit integers is the reverse of the first term. If the sum of the first and last terms is less than 100, how many such sequences are there?

A. 1
B. 2
C. 3
D. 4
E. 5

Since the terms are consecutive, sum of first and last term will be equal to 2 times the mean

Starting with 13, then 13....31...., Sum =2*31=62
Starting with 14, then 14...41..., Sum = 2*41=84
Mean of 51 will make the sum 102.. not possible

Starting with 24..42.., sum=2*42=84
Mean of 52 will mean greater than 100

Now let the sequence start in 30s
So 34...43... 2*43=86 possible

No other possible as starting with 45 will lead to to a mean of 54..

Total sequences possible are starting with 12, 13, 14, 23, 24, and 34..

What is the source??

hi chetan2u,
thank you so much for pointing out my mistake.
I was erroneously assuming that, because 2*51 exceeded 100, 14 would be the greatest possible first term for such a
sequence, and did not check for further possibilities, as I clearly should have.
I apologize for this and have edited the answer choices appropriately.
gracie
The mean of an ascending sequence of positive consecutive two-digit in   [#permalink] 31 Dec 2018, 21:51
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