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If a, b are positive integers, is a/b a terminating decimal?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 9006
GMAT 1: 760 Q51 V42
GPA: 3.82
If a, b are positive integers, is a/b a terminating decimal?  [#permalink]

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12 Oct 2017, 00:47
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25% (medium)

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69% (00:38) correct 31% (00:55) wrong based on 86 sessions

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If a, b are positive integers, is a/b a terminating decimal?

1) a is a multiple of 2
2) b is a factor of 10

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Joined: 05 Dec 2016
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Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: If a, b are positive integers, is a/b a terminating decimal?  [#permalink]

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12 Oct 2017, 01:30
For a/b to be a terminating decimal, b should have either 2 or 5 or both as its prime factors
(2) If b is a factor of 10, and 10 has 2 and 5 as its prime factors, then b can be 2;5;10 which means that a/b is a terminating decimal
Sufficient

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 9006
GMAT 1: 760 Q51 V42
GPA: 3.82
If a, b are positive integers, is a/b a terminating decimal?  [#permalink]

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16 Oct 2017, 06:13
Forget conventional ways of solving math questions. In DS, VA (Variable Approach) method is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution.

The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.

The property that an irreducible fraction a/b is a terminating decimal depends on the denumerator only. When the denumerator of an irreducible only has 2 and 5 as prime factors, it is a terminating decimal.
Thus, only condition 2) is sufficient.
Therefore, B is the answer unlike our expectation.

Normally for cases where we need 2 more equations, such as original conditions with 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, we have 1 equation each in both con 1) and con 2). Therefore, C has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) together. Here, there is 70% chance that C is the answer, while E has 25% chance. These two are the key questions. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer according to DS definition, we solve the question assuming C would be our answer hence using con 1) and con 2) together. (It saves us time). Obviously, there may be cases where the answer is A, B, D or E.

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Re: If a, b are positive integers, is a/b a terminating decimal?  [#permalink]

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05 Aug 2019, 08:59
MathRevolution - It is not mentioned that a and b are distinct Integers. therefore, it is possible that a=b, in that case, a/b is not a decimal, it is an Integer. Hence the answer should be E
Re: If a, b are positive integers, is a/b a terminating decimal?   [#permalink] 05 Aug 2019, 08:59