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# If S is a series of numbers of the form X, XX, XXX, XXXX,

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If S is a series of numbers of the form X, XX, XXX, XXXX, [#permalink]  13 Feb 2008, 15:46
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If S is a series of numbers of the form X, XX, XXX, XXXX, XXXXX, ..., where X is a non-zero digit, is every number in this series a multiple of the same prime number P?

(1) P is an odd number such that P < X

(2) X is a multiple of P
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Re: DS - Primes [#permalink]  13 Feb 2008, 17:48
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JCLEONES wrote:
If S is a series of numbers of the form X, XX, XXX, XXXX, XXXXX, ..., where X is a non-zero digit, is every number in this series a multiple of the same prime number P?

(1) P is an odd number such that P < X

(2) X is a multiple of P

(1) P is an odd single-digit prime number. It can be either 3, 5 or 7. If every number of series S were to be a multiple of P, then X is divisible by P. Also, X > P. So if P = 3, X can be either 6 or 9. If P = 5 or P = 7, no value of X suffices. Hence the series can be {6, 66, 666...} or {9, 99, 999...} and each term is divisible by 3. Sufficient.

(2) Sufficient. Try plugging in X=2, P=2 or X=6, P=3.
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Re: DS - Primes [#permalink]  14 Feb 2008, 01:58
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Expert's post
B

If S is a series of numbers of the form X, XX, XXX, XXXX, XXXXX, ..., where X is a non-zero digit, is every number in this series a multiple of the same prime number P?

(1) P is an odd number such that P < X
P can be 3,5,7
for example, P=3:
in series 6,66,666,6666... every number is divisible by 3
in series 7,77,777,7777... not every number is divisible by 3
insuff.

(2) X is a multiple of P: X=k*P
XXXX...XXX=X*(111...111)=P*(k*111...111) is divisible by P
suff.
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Re: DS - Primes [#permalink]  14 Feb 2008, 09:21
walker wrote:
B

If S is a series of numbers of the form X, XX, XXX, XXXX, XXXXX, ..., where X is a non-zero digit, is every number in this series a multiple of the same prime number P?

(1) P is an odd number such that P < X
P can be 3,5,7
for example, P=3:
in series 6,66,666,6666... every number is divisible by 3
in series 7,77,777,7777... not every number is divisible by 3
insuff.

(2) X is a multiple of P: X=k*P
XXXX...XXX=X*(111...111)=P*(k*111...111) is divisible by P
suff.

+1. Made an assumption I shouldn't have!
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Re: DS - Primes   [#permalink] 14 Feb 2008, 09:21
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