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The infinite sequence a{1}, a{2}, …, a{n}, … is such that a{ [#permalink]
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Updated on: 26 Jul 2013, 12:35
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The infinite sequence \(a_{1}\), \(a_{2}\), …, \(a_{n}\), … is such that \(a_{1} = 7\), \(a_{2} = 8\), \(a_{3} = 10\), and \(a_n=a_{n3} + 7\) for values of n > 3. What is the remainder when \(a_{n}\) is divided by 7? (1) n is a multiple of 3. (2) n is an even number. Disclaimer: I have used the Search Box Before Posting. I used the first sentence of the question or a string of words exactly as they show up in the question below for my search. I did not receive an exact match for my question. Source: Veritas Prep; Book 04 Chapter: Homework Topic: Algebra Question: 94 Question: Page 227 Edition: Third My Question: Please provide an explanation on how to arrive at the answer.
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Originally posted by hb on 26 Jul 2013, 12:09.
Last edited by Bunuel on 26 Jul 2013, 12:35, edited 2 times in total.
Edited the question and moved to DS forum.





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Re: The infinite sequence a{1}, a{2}, …, a{n}, … is such that a{ [#permalink]
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26 Jul 2013, 12:40
The infinite sequence \(a_{1}\), \(a_{2}\), …, \(a_{n}\), … is such that \(a_{1} = 7\), \(a_{2} = 8\), \(a_{3} = 10\), and \(a_n=a_{n3} + 7\) for values of n > 3. What is the remainder when \(a_{n}\) is divided by 7?\(a_{1} = 7\) \(a_{2} = 8\) \(a_{3} = 10\) \(a_{4} = a_1+7=7+7=14\) \(a_{5} = a_2+7=8+7=15\) \(a_{6} = a_3+7=10+7=17\) ... Notice that the remainder upon division the above terms by 7 repeats in blocks of 3: {0, 1, 3} {0, 1, 3}... (1) n is a multiple of 3 > every third term has the remainder of 3 (\(a_{3}\), \(a_{6}\), \(a_{9}\), ...). Sufficient. (2) n is an even number. Not sufficient: consider \(a_2\) and \(a_4\). Answer: A.
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Re: The infinite sequence a{1}, a{2}, …, a{n}, … is such that a{ [#permalink]
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26 Jul 2013, 12:42
hb wrote: The infinite sequence \(a_{1}\), \(a_{2}\), …, \(a_{n}\), … is such that \(a_{1} = 7\), \(a_{2} = 8\), \(a_{3} = 10\), and \(a_n=a_{n3} + 7\) for values of n > 3. What is the remainder when \(a_{n}\) is divided by 7? (1) n is a multiple of 3. (2) n is an even number. Disclaimer: I have used the Search Box Before Posting. I used the first sentence of the question or a string of words exactly as they show up in the question below for my search. I did not receive an exact match for my question. Source: Veritas Prep; Book 04 Chapter: Homework Topic: Algebra Question: 94 Question: Page 227 Edition: Third My Question: Please provide an explanation on how to arrive at the answer. Similar question to practice: asequencea164a266a367an8an3whichofthe43871.html
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Re: The infinite sequence a{1}, a{2}, …, a{n}, … is such that a{ [#permalink]
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03 Jan 2014, 16:25
Hey,
I don't get how the OA can be A. Can anyone please explain?
As per my understanding the OA should be E:
Statement 1 says "n is a multiple of 3."
By applying the formula given in the question stem, we can find that a5=15 and that a7=21. Yet, 15 divided by 7 gives a remainder of 1, while 21 divided by 7 gives a remainder of 0. Hence, IMO statement 1 is insufficient.
Statement 2 says "n is an even number".
Also insufficient: a2=8 gives a remainder of 1, while a4=14 gives a remainder of 0.
Statements 1 and 2 combined say "n is a multiple of 3 and n is an even number".
IMO insufficient. For instance, a9=24 and a14=36. Both are multiples of 3 and are even. However, the former result gives a remainder of 3 whereas the latter one gives a remainder of 1.
Is there something that I'm misunderstanding? Please advise.



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Re: The infinite sequence a{1}, a{2}, …, a{n}, … is such that a{ [#permalink]
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04 Jan 2014, 06:26
Aurele wrote: Hey,
I don't get how the OA can be A. Can anyone please explain?
As per my understanding the OA should be E:
Statement 1 says "n is a multiple of 3."
By applying the formula given in the question stem, we can find that a5=15 and that a7=21. Yet, 15 divided by 7 gives a remainder of 1, while 21 divided by 7 gives a remainder of 0. Hence, IMO statement 1 is insufficient.
Statement 2 says "n is an even number".
Also insufficient: a2=8 gives a remainder of 1, while a4=14 gives a remainder of 0.
Statements 1 and 2 combined say "n is a multiple of 3 and n is an even number".
IMO insufficient. For instance, a9=24 and a14=36. Both are multiples of 3 and are even. However, the former result gives a remainder of 3 whereas the latter one gives a remainder of 1.
Is there something that I'm misunderstanding? Please advise. Please read here: theinfinitesequencea1a2anissuchthata156741.html#p1250455We need to find the remainder when when \(a_{n}\) is divided by 7. (1) says n is a multiple of 3. Why are you checking the remainder when \(a_5\) or \(a_7\) is divided by 7. Is 5 or 7 a multiple of 3? Hope it helps.
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Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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Re: The infinite sequence a{1}, a{2}, …, a{n}, … is such that a{ [#permalink]
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08 Jan 2014, 01:45
Thanks a lot for the explanation. Don't know why I confused both.



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Re: The infinite sequence a{1}, a{2}, …, a{n}, … is such that a{ [#permalink]
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