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p and q are integers. If p is divisible by 10^q and cannot

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p and q are integers. If p is divisible by 10^q and cannot [#permalink] New post 10 Feb 2011, 16:05
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p and q are integers. If p is divisible by 10^q and cannot be divisible by 10^(q + 1), what is the value of q?
(1) p is divisible by 2^5, but is not divisible by 2^6.
(2) p is divisible by 5^6, but is not divisible by 5^7
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Re: p and q are integers. If p is divisible by 10q and canno [#permalink] New post 10 Feb 2011, 16:43
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banksy wrote:
p and q are integers. If p is divisible by 10^q and cannot be divisible by 10^(q + 1), what is the value of q?
(1) p is divisible by 2^5, but is not divisible by 2^6.
(2) p is divisible by 5^6, but is not divisible by 5^7


p is divisible by 10^q and cannot be divisible by 10^(q + 1) means that # of trailing zeros of p is q (p ends with q zeros).

(1) p is divisible by 2^5, but is not divisible by 2^6 --> # of trailing zeros, q, is less than or equal to 5: q\leq{5} (as for each trailing zero we need one 2 and one 5 in prime factorization of p then this statement says that there are enough 2-s for 5 zeros but we don't know how many 5-s are there). Not sufficient.

(2) p is divisible by 5^6, but is not divisible by 5^7 --> # of trailing zeros, q, is less than or equal to 6: q\leq{6} (there are enough 5-s for 6 zeros but we don't know how many 2-s are there). Not sufficient.

(1)+(2) 2-s and 5-s are enough for 5 trailing zeros: q=5 (# of 2-s are limiting factor). Sufficient.

Answer: C.
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Manager
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Re: p and q are integers. If p is divisible by 10q and canno [#permalink] New post 15 Nov 2012, 12:28
Bunuel wrote:
banksy wrote:
p and q are integers. If p is divisible by 10^q and cannot be divisible by 10^(q + 1), what is the value of q?
(1) p is divisible by 2^5, but is not divisible by 2^6.
(2) p is divisible by 5^6, but is not divisible by 5^7


p is divisible by 10^q and cannot be divisible by 10^(q + 1) means that # of trailing zeros of p is q (p ends with q zeros).

(1) p is divisible by 2^5, but is not divisible by 2^6 --> # of trailing zeros, q, is less than or equal to 5: q\leq{5} (as for each trailing zero we need one 2 and one 5 in prime factorization of p then this statement says that there are enough 2-s for 5 zeros but we don't know how many 5-s are there). Not sufficient.

(2) p is divisible by 5^6, but is not divisible by 5^7 --> # of trailing zeros, q, is less than or equal to 6: q\leq{6} (there are enough 5-s for 6 zeros but we don't know how many 2-s are there). Not sufficient.

(1)+(2) 2-s and 5-s are enough for 5 trailing zeros: q=5 (# of 2-s are limiting factor). Sufficient.

Answer: C.

From condition 1 and condition 2 it we got q\leq{5} and q\leq{6} so possible cases can be q\leq{5} so q can be anything 5,4,3,2,...... So both together aren't sufficient right?
Re: p and q are integers. If p is divisible by 10q and canno   [#permalink] 15 Nov 2012, 12:28
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