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If sequence X1, X2, X3, ...Xn is such that X(n+1) is 5 more [#permalink]
 30 Jul 2008, 18:32
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
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Current Student
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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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Manager
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good catch. that's a tricky one. in that case the answer is E.
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Senior Manager
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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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Manager
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A very very good ans.
Answer is E.
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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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