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The terms of the sequence {An}, where n is a positive intege [#permalink]
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07 Mar 2018, 03:41
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[GMAT math practice question] The terms of the sequence {A n}, where n is a positive integer, satisfy A 1=81, A 2=82, A 3=83, and A n+3=A n+4. Which of the following cannot be a value of A n? A. 801 B. 802 C. 803 D. 804 E. 805
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The terms of the sequence {An}, where n is a positive intege [#permalink]
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Updated on: 18 Mar 2018, 11:39
Sequence = 81,82,83, 85,86,87, 89,90,91, 93,94,95, 97,98,99, 101,102,102,.. Every 4th number is missing :After every 3 numbers, the number jumpy by 2 : so we don't have 84,92,96,100,..... : This is in AP with an increment of 4. So we know numbers divisible by 4 cannot be there in the given series Test the numbers : 1. 801  This is not divisible by 4 2. 802  This is not divisible by 4 3. 803  This is not divisible by 4 4. 804  This is divisible by 45. 805  This is not divisible by 4
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Originally posted by Leo8 on 07 Mar 2018, 05:02.
Last edited by Leo8 on 18 Mar 2018, 11:39, edited 1 time in total.



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Re: The terms of the sequence {An}, where n is a positive intege [#permalink]
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09 Mar 2018, 00:22
=> The terms of the sequence can be divided into three groups: A 1 = 81, A 4 = 85, A 7 = 89, … : These have a remainder of 1 when they are divided by 4. A 2 = 82, A 5 = 86, A 8 = 90, … : These have a remainder of 2 when they are divided by 4. A 3 = 83, A 6 = 87, A 9 = 91, … : These have a remainder of 3 when they are divided by 4. No term of the sequence is a multiple of 4. Since 804 is a multiple of 4, it cannot be a term of the sequence. Therefore, the answer is D. Answer: D
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Re: The terms of the sequence {An}, where n is a positive intege [#permalink]
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18 Mar 2018, 08:16
Leo8 wrote: Sequence = 81,82,83, 84,85,86, 89,90,91, 93,94,95, 97,98,99, 101,102,102,..
Every 4th number is missing :After every 3 numbers, the number jumpy by 2 :
so we don't have 84,92,96,100,..... : This is in AP with an increment of 4.
So we know numbers divisible by 4 cannot be there in the given series
Test the numbers :
1. 801  This is not divisible by 4 2. 802  This is not divisible by 4 3. 803  This is not divisible by 4 4. 804  This is divisible by 4 5. 805  This is not divisible by 4 hi very new to sequence can you please tell me how you have arrived at the sequential order (81,82,83, 84,85,86, 89,90,91, 93,94,95, 97,98,99, 101,102,102..) ? thanks in advance



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Re: The terms of the sequence {An}, where n is a positive intege [#permalink]
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18 Mar 2018, 11:41
gmatcracker2018 wrote: Leo8 wrote: Sequence = 81,82,83, 84,85,86, 89,90,91, 93,94,95, 97,98,99, 101,102,102,..
Every 4th number is missing :After every 3 numbers, the number jumpy by 2 :
so we don't have 84,92,96,100,..... : This is in AP with an increment of 4.
So we know numbers divisible by 4 cannot be there in the given series
Test the numbers :
1. 801  This is not divisible by 4 2. 802  This is not divisible by 4 3. 803  This is not divisible by 4 4. 804  This is divisible by 4 5. 805  This is not divisible by 4 hi very new to sequence can you please tell me how you have arrived at the sequential order (81,82,83, 8485,86,87, 89,90,91, 93,94,95, 97,98,99, 101,102,102..) ? thanks in advance Hi  Sorry there is a correction in the my post  we will not have term 84 in the series The terms of the sequence {An}, where n is a positive integer, satisfy A1=81, A2=82, A3=83, and An+3=An+4. Which of the following cannot be a value of An? A1 = 81, A2 = 82, A3 = 83 to derive A4  we will use the formula given : A(1+3) = A1 + 4 : so A4 = 81 + 4 = 85, likewise A5 = A2 + 4 = 82 + 4 = 86 A6 = A3 + 4 = 83 + 4 = 87 as you can see there is a jump of 2 unit after every 3rd number.. hence the sequence is : 81, 82, 83, 85, 86, 87, 89, 90, 91,
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The terms of the sequence {An}, where n is a positive intege [#permalink]
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18 Mar 2018, 12:42
Leo8 wrote: gmatcracker2018 wrote: Leo8 wrote: Sequence = 81,82,83, 84,85,86, 89,90,91, 93,94,95, 97,98,99, 101,102,102,..
Every 4th number is missing :After every 3 numbers, the number jumpy by 2 :
so we don't have 84,92,96,100,..... : This is in AP with an increment of 4.
So we know numbers divisible by 4 cannot be there in the given series
Test the numbers :
1. 801  This is not divisible by 4 2. 802  This is not divisible by 4 3. 803  This is not divisible by 4 4. 804  This is divisible by 4 5. 805  This is not divisible by 4 hi very new to sequence can you please tell me how you have arrived at the sequential order (81,82,83, 8485,86,87, 89,90,91, 93,94,95, 97,98,99, 101,102,102..) ? thanks in advance Hi  Sorry there is a correction in the my post  we will not have term 84 in the series The terms of the sequence {An}, where n is a positive integer, satisfy A1=81, A2=82, A3=83, and An+3=An+4. Which of the following cannot be a value of An? A1 = 81, A2 = 82, A3 = 83 to derive A4  we will use the formula given : A(1+3) = A1 + 4 : so A4 = 81 + 4 = 85, likewise A5 = A2 + 4 = 82 + 4 = 86 A6 = A3 + 4 = 83 + 4 = 87 as you can see there is a jump of 2 unit after every 3rd number.. hence the sequence is : 81, 82, 83, 85, 86, 87, 89, 90, 91, hi thank you, + 1 please let me first understand what the formula given "An+3 = An + 4" really means ? how can "An + 4" and "An + 3" be the same number, and how did you get A (1 + 3) = An + 4 thanks



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Re: The terms of the sequence {An}, where n is a positive intege [#permalink]
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18 Mar 2018, 13:07
gmatcracker2018 The formula is given in the question as a representation of nth number by A(1 + 3)  I meant A(n +3)th term can be expressed in terms of Anth term + 4 or every (n + 3)th term is addition of nth term and the number 4
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The terms of the sequence {An}, where n is a positive intege [#permalink]
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18 Mar 2018, 14:23
Leo8 wrote: gmatcracker2018 The formula is given in the question as a representation of nth number by A(1 + 3)  I meant A(n +3)th term can be expressed in terms of Anth term + 4 or every (n + 3)th term is addition of nth term and the number 4 thanks a lot, again +1 please know that I am very new to sequence problem, so please guide through my explanation we are given A1 =81, A2 = 82 and A3 = 83 and also there is formula, "An+3 = An + 4" to find A4 or any subsequent number in the sequence now since we are to find out A4, we can let n = 1 thus A( 1 + 3 ) = A1 + 4 A4 = 81 + 4 = 85 and when to find A5 we can set n to equal to 2 A( 2 + 3 ) = A2 + 4 =) a5 = 82 + 4 = 86 In the same way, to find A6, we have to let, n = 3 A (3 + 3) = A3 + 4 =) a6 = 83 + 4 + 87 and a7 = A (4 + 3) = a4 + 4 =) 85 + 4 = 89 so we have a4 = 85 a5 = 86 a6 = 87 a7 = 89 and so on ... thus it is evident that multiples of 4 are missing so, the number, 804 cannot be a value of An I think this is what you wanted to mean ? is that okay? thanks in advance, man




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