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the sequence x1,x2 ... xn is such that x1=5, x2=-5, x3=0, x4=-2

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the sequence x1,x2 ... xn is such that x1=5, x2=-5, x3=0, x4=-2 [#permalink]

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New post 07 Apr 2018, 04:12
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Question Stats:

47% (01:46) correct 53% (01:48) wrong based on 76 sessions

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The sequence \(x_1\),\(x_2\) ... \(x_n\) is such that \(x_1\) = 5, \(x_2\) = -5, \(x_3\) = 0, \(x_4\) = -2, \(x_5\) = 4 and \(x_n\)= \(x_{n-5}\). If the sum of the first P terms as well as the sum of the first P-3 terms is 18, P= ?

A. 39
B. 42
C. 45
D. 48
E. 51

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Posts: 6210
Re: the sequence x1,x2 ... xn is such that x1=5, x2=-5, x3=0, x4=-2 [#permalink]

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New post 07 Apr 2018, 18:51
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benejo wrote:
The sequence \(x_1\),\(x_2\) ... \(x_n\) is such that \(x_1\) = 5, \(x_2\) = -5, \(x_3\) = 0, \(x_4\) = -2, \(x_5\) = 4 and \(x_n\)= \(x_{n-5}\). If the sum of the first P terms as well as the sum of the first P-3 terms is 18, P= ?

A. 39
B. 42
C. 45
D. 48
E. 51

Source: ExpertsGlobal



The first 5 terms are being repeated, so let's see their SUM..
5+(-5)+0+(-2)+4=2...
So 18 will be 2*9, that is it will be sum of 9 such sets, each containing 5 numbers..
So number =5*9=45..
But we are given both P and P-3 have same sum..
If we go down by 3 terms, it will change the sum by 4+(-2)+0=2, so sum will be 18-2=16..

Therefore add the next three terms = 5+(-5)+0=0..
So these will not effect the SUM and sum will remain 18..
So P-3=45....P=45+3=48

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: the sequence x1,x2 ... xn is such that x1=5, x2=-5, x3=0, x4=-2 [#permalink]

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New post 05 Jun 2018, 22:15
chetan2u wrote:
benejo wrote:
The sequence \(x_1\),\(x_2\) ... \(x_n\) is such that \(x_1\) = 5, \(x_2\) = -5, \(x_3\) = 0, \(x_4\) = -2, \(x_5\) = 4 and \(x_n\)= \(x_{n-5}\). If the sum of the first P terms as well as the sum of the first P-3 terms is 18, P= ?

A. 39
B. 42
C. 45
D. 48
E. 51

Source: ExpertsGlobal



The first 5 terms are being repeated, so let's see their SUM..
5+(-5)+0+(-2)+4=2...
So 18 will be 2*9, that is it will be sum of 9 such sets, each containing 5 numbers..
So number =5*9=45..
But we are given both P and P-3 have same sum..
If we go down by 3 terms, it will change the sum by 4+(-2)+0=2, so sum will be 18-2=16..

Therefore add the next three terms = 5+(-5)+0=0..
So these will not effect the SUM and sum will remain 18..
So P-3=45....P=45+3=48

D




Hi chetan2u,

Could you please help me understand the highlighted bit? Based on the calculations, we deduced that the no. of terms for which the sum would be 18 is 45 which is what the question asks, right?
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Posts: 6210
Re: the sequence x1,x2 ... xn is such that x1=5, x2=-5, x3=0, x4=-2 [#permalink]

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New post 06 Jun 2018, 05:11
Shruti0805 wrote:
chetan2u wrote:
benejo wrote:
The sequence \(x_1\),\(x_2\) ... \(x_n\) is such that \(x_1\) = 5, \(x_2\) = -5, \(x_3\) = 0, \(x_4\) = -2, \(x_5\) = 4 and \(x_n\)= \(x_{n-5}\). If the sum of the first P terms as well as the sum of the first P-3 terms is 18, P= ?

A. 39
B. 42
C. 45
D. 48
E. 51

Source: ExpertsGlobal



The first 5 terms are being repeated, so let's see their SUM..
5+(-5)+0+(-2)+4=2...
So 18 will be 2*9, that is it will be sum of 9 such sets, each containing 5 numbers..
So number =5*9=45..
But we are given both P and P-3 have same sum..
If we go down by 3 terms, it will change the sum by 4+(-2)+0=2, so sum will be 18-2=16..

Therefore add the next three terms = 5+(-5)+0=0..
So these will not effect the SUM and sum will remain 18..
So P-3=45....P=45+3=48

D




Hi chetan2u,

Could you please help me understand the highlighted bit? Based on the calculations, we deduced that the no. of terms for which the sum would be 18 is 45 which is what the question asks, right?



Hi..
The question further adds that the sum is 18 for both P and P-3 terms..
If you subtract 3 from 45, the sum does not remain 18..
But by adding next 3 terms to first 45 terms, the sum remains 18..

Now same is P and P-3, so we take larger as P..
Had it been P and P+3, ans would be 45
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: the sequence x1,x2 ... xn is such that x1=5, x2=-5, x3=0, x4=-2   [#permalink] 06 Jun 2018, 05:11
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