MathRevolution wrote:
[GMAT math practice question]
If \(x\) is a positive integer, is \(\frac{x}{30}\) a terminating decimal?
1) \(x\) is divisible by \(3\)
2) \(x\) is divisible by \(4\)
Target question: Is x/30 a terminating decimal?This is a good candidate for
rephrasing the target question.
-------------ASIDE------------------
Let's say that
x = a/b where the fraction a/b is written in
simplest terms.
There's a nice rule that says something like,
If a/b results in a terminating decimal, then the denominator, b, MUST be the product of 2's and 5's only!So, for example, if b = 20, the fraction a/b will result in a terminating decimal. The same holds true for other values of b such as 4, 5, 25, 40, 2, 8, and so on.
-------BACK TO THE QUESTION--------------------
Given the above information, we can REPHRASE the target question....
REPHRASED target question: Can the denominator of the SIMPLIFIED version of x/30 be written as the product of 2's and 5's only?Aside: for tips on rephrasing the target question, see the video below Statement 1: x is divisible by 3 This means that
x = 3k, for some integer k
So, we can say: x/30 =
3k/30 = k/10
The denominator (10) can be written as follows: 10 = (2)(5)
So, the answer to the REPHRASED target question is
YES, the denominator of the simplified version of x/30 CAN be written as the product of 2's and 5's onlySince we can answer the
REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: x is divisible by 4 There are several values of x that satisfy statement 2. Here are two:
Case a: x = 12. In this case, x/30 = 12/30 = 2/5. Here,
the denominator (5) CAN be written as the product of 2's and 5's onlyCase b: x = 4. In this case, x/30 = 4/30. Here,
the denominator (30) CANNOT be written as the product of 2's and 5's onlySince we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
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