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n is an integer greater than or equal to 0. The sequence Tn for n>0..

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n is an integer greater than or equal to 0. The sequence Tn for n>0..  [#permalink]

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New post 23 Jul 2017, 19:35
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Q. n is an integer greater than or equal to 0. The sequence Tn for n>0 is defined by Tn = Tn-1 + n. If T0 = 3, is nth Term, i.e. Tn even ?

1) n+1 is divisible by 3
2) n-1 is divisible by 4

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Re: n is an integer greater than or equal to 0. The sequence Tn for n>0..  [#permalink]

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New post 23 Jul 2017, 19:40
Both conditions are together sufficient

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Re: n is an integer greater than or equal to 0. The sequence Tn for n>0..  [#permalink]

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New post 23 Jul 2017, 19:56
amsey1382 wrote:
Q. n is an integer greater than or equal to 0. The sequence Tn for n>0 is defined by Tn = Tn-1 + n. If T0 = 3, is nth Term, i.e. Tn even ?

1) n+1 is divisible by 3
2) n-1 is divisible by 4


I tried to solve this.

Testing 1st premise:

If your prepare the list , it will come something like : 3,4,6,9,13,18,24,31,39,48,58,69,81,94,108,123,139,156..
if you notice the sequence become..OEEOOEEOOEEOOEEOO... IF n+1 is divisible by 3 ..n has to be 2,5,8,11,14..term...clearly ,this gives that Tn can be even or odd..so Insufficient.

Testing 2nd premise:

if n-1 is divisible by 4 , term has to be 5,9,13,17,21..and so on...if you notice, this will always give an even number , because sequence OEEO repeats at every 4th term, giving O in every 4th

SO B is sufficient . didn't have OA , that's why posted ?
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n is an integer greater than or equal to 0. The sequence Tn for n>0..  [#permalink]

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New post 23 Jul 2017, 19:59
Since Tn = Tn-1 + n and T0 = 3
T1 = 3 + 1 = 4, T2 = 4 + 2 = 6,
T3 = 6 + 3 = 9, T4 = 9 + 4 =13,
T5 = 13 + 5 = 18, T6 = 18 + 6 = 24,
T7 = 24 + 7 = 31, T8 = 31+8 = 39,
T9 = 39 + 9 = 48, T10 = 48 + 10 = 58,
T11 = 58 + 11 = 69, T12 = 69 + 12 = 81,
T13 = 81 + 13 = 94

The pattern formed is as follows : E,E,O,O,E,E,O,O,E,E,O,O,E.....

1. If n+1 is divisble by 3, n could be 2,5,8.. and so on.
From the question stem T2 and T5 are even but, T8 is odd
Hence, insufficient
2. n-1 is divisible by 4
If n-1 is divisible by 4, n could be 5,9,13... and so on.
From the question stem, T5,T9,T13 are all even. Sufficient(Option B)
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Re: n is an integer greater than or equal to 0. The sequence Tn for n>0..  [#permalink]

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New post 24 Jul 2017, 05:51
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amsey1382 wrote:
Q. n is an integer greater than or equal to 0. The sequence Tn for n>0 is defined by Tn = Tn-1 + n. If T0 = 3, is nth Term, i.e. Tn even ?

1) n+1 is divisible by 3
2) n-1 is divisible by 4


This question is discussed here: n-is-an-integer-greater-than-or-equal-to-0-the-sequence-tn-110969.html

Hope it helps.

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This discussion does not meet community quality standards. It has been retired.


If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: n is an integer greater than or equal to 0. The sequence Tn for n>0..   [#permalink] 24 Jul 2017, 05:51
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