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If p and q are positive integers, can the fraction p/q be expressed as 29 Aug 2019, 06:44
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55% (hard)

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58% (01:17) correct 42% (01:06) wrong based on 143 sessions

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If p and q are positive integers, can the fraction p/q be expressed as a decimal with only a finite number of nonzero digits?

(1) q is a factor of 12.

(2) p is a factor of 12.
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E
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If p and q are positive integers, can the fraction p/q be expressed as 29 Aug 2019, 08:12
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Using both Statements, we might have p = 4 and q = 12, and then p/q = 4/12 = 1/3 = 0.333.... which has an infinite number of digits when written as a decimal, or we might have p = 6 and q = 12, and then p/q = 6/12 = 1/2 = 0.5, which has a finite number of digits when written as a decimal. So the answer is E.
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If p and q are positive integers, can the fraction p/q be expressed as 30 Aug 2019, 09:52
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Bunuel
If p and q are positive integers, can the fraction p/q be expressed as a decimal with only a finite number of nonzero digits?

(1) q is a factor of 12.

(2) p is a factor of 12.
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#1
q=12,24,60 we get yes for 60 as it has factor of 2&5 but no for others
#2
p =12 insufficient as q value is not know
from 1&2
again value of both p & q will result in yes and no
IMO E
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If p and q are positive integers, can the fraction p/q be expressed as 18 Oct 2024, 02:40
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I don't understand why it couldn't be p=12 and q= 6, where the ratio would be 2 and so the anwer would be C because it CAN be an integer number
IanStewart
Using both Statements, we might have p = 4 and q = 12, and then p/q = 4/12 = 1/3 = 0.333.... which has an infinite number of digits when written as a decimal, or we might have p = 6 and q = 12, and then p/q = 6/12 = 1/2 = 0.5, which has a finite number of digits when written as a decimal. So the answer is E.
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If p and q are positive integers, can the fraction p/q be expressed as 18 Oct 2024, 08:52
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GioPiste
I don't understand why it couldn't be p=12 and q= 6, where the ratio would be 2 and so the anwer would be C because it CAN be an integer number
IanStewart
If p and q are positive integers, can the fraction p/q be expressed as a decimal with only a finite number of nonzero digits?

(1) q is a factor of 12.

(2) p is a factor of 12.

Using both Statements, we might have p = 4 and q = 12, and then p/q = 4/12 = 1/3 = 0.333.... which has an infinite number of digits when written as a decimal, or we might have p = 6 and q = 12, and then p/q = 6/12 = 1/2 = 0.5, which has a finite number of digits when written as a decimal. So the answer is E.
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Yes, p could be 12 and q could be 6, making p/q equal 2, and thus giving a YES answer to the question. However, we could also have p = 4 and q = 12, making p/q = 1/3 = 0.333..., and thus giving a NO answer to the question. Since we cannot get a definite YES or a definite NO answer to the question (we get sometimes YES and sometimes NO), the statements taken together are not sufficient to answer the question.
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