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# If sequence X1, X2, X3, ...Xn is such that X(n+1) is 5 more

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If sequence X1, X2, X3, ...Xn is such that X(n+1) is 5 more [#permalink]  30 Jul 2008, 17:32
If sequence X1, X2, X3, ...Xn is such that X(n+1) is 5 more than Xn for n>=2, does X99 have a units' digit of 9?
(1) The 100 term plus 1 is a multiple of 5.
(2) The first term is 4.
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient
Current Student
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Re: SERIES... [#permalink]  30 Jul 2008, 17:52
but from stat 2, how does one come to know the 2nd term. it gives only the 1st term, and says for n>=2. what is the relation betn term 2 and term 1?
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Re: SERIES... [#permalink]  30 Jul 2008, 17:55
good catch. that's a tricky one.

in that case the answer is E.
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Re: SERIES... [#permalink]  30 Jul 2008, 19:18
1
KUDOS
If sequence X1, X2, X3, ...Xn is such that X(n+1) is 5 more than Xn for n>=2, does X99 have a units' digit of 9?
(1) The 100 term plus 1 is a multiple of 5.
(2) The first term is 4.

S1. x [100]+1 = x[99]+5+1
if the multiple of x [100]+1 ends in 0 then the units digit for X99 will be 4
if the multiple of x [100]+1 ends in 5 then the units digit for X99 will be 9
Hence MAYBE CASE and AD out

S2. Does not tell you anything since it gives the value of X1 only and X(n+1) is 5 more than Xn for n>=2 Hence B is out

Combining S2 does not add anything hence C is out

IMO E
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Re: SERIES... [#permalink]  30 Jul 2008, 19:45
A very very good ans.

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Re: SERIES... [#permalink]  03 Aug 2008, 06:42
arjtryarjtry wrote:
If sequence X1, X2, X3, ...Xn is such that X(n+1) is 5 more than Xn for n>=2, does X99 have a units' digit of 9?
(1) The 100 term plus 1 is a multiple of 5.
(2) The first term is 4.
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient

obtained the eqns from given condns :
x99=97(5)+x2
x100=98(5)+x2

(1) states that x100+1 is div by 5 = x2+1 is div by 5 => x2 can be 4,9,14,19 etc hence units digit will vary accordingly for x99

=> insufficient

(2) first term does not play any role hence infoi is redundant => insufficient

(1) and (2) combined also dont help hence insuffi

IMO E
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Re: SERIES...   [#permalink] 03 Aug 2008, 06:42
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