chloe2m wrote:
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 by5^7
(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 by5^7
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:
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Statistics : Posted by Bunuel • on 10 Feb 2011, 15:05 • Replies 10 • Views 24205
