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Re: p and q are integers. If p is divisible by 10q and canno [#permalink]
10 Feb 2011, 15:43

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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.

Re: p and q are integers. If p is divisible by 10q and canno [#permalink]
15 Nov 2012, 11:28

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]
14 Jan 2014, 21:08

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.

How do we know the question is asking us to use the concept of trailing zeroes. I understand the concept but how do we know that we have to apply trailing zeroes concept.

Re: p and q are integers. If p is divisible by 10q and canno [#permalink]
14 Jan 2014, 21:34

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Vidhi1 wrote:

How do we know the question is asking us to use the concept of trailing zeroes. I understand the concept but how do we know that we have to apply trailing zeroes concept.

Isn't that the core challenge of GMAT? The concepts tested are quite basic. Why then, does everyone not get Q50? Because you really need to understand them very well to be able to see which particular concept is used in a particular question. Here, when you see

"If p is divisible by 10^q and cannot be divisible by 10^(q + 1)" you should understand that p has q trailing 0s (that's how it is will be divisible by 10^q) but it does not have q+1 trailing 0s. This means it has exactly q trailing 0s.

If p has q trailing 0s, it must have at least q 2s and at least q 5s (but both 2s and 5s cannot be more than q) Statement 1 tells you about the 2s but not about the 5s. Statement 2 tells you about the 5s but not about the 2s. Both statements together tell you that you can make five 0s. and hence q must be 5.
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