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30 Jan 2018, 07:19
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
47% (01:58) correct
53%
(01:50)
wrong
based on 356
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If x and y are positive integers, is x/y a terminating decimal?
(1) y/x is even
(2) The greatest common factor of x and y is 1
M36-72
(1) y/x is even
(2) The greatest common factor of x and y is 1
M36-72
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30 Jan 2018, 09:24
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Bunuel
For \(x/y\) to be a terminating decimal, y should be multiple of 2 or 5 only..
Let's see the statements..
1) y/x is even...
Just confirms that y is MULTIPLE of 2 and also of y..
But y can be 2, x/y will be terminating decimal
If y is 18 and X is 3, x/y will be 1/6, a non terminating decimal.
Insufficient
2) GCF of x and y is 1.
x as 3 and y as 2 will give x/y is terminating decimal.
x as 3 and y as 7 will give x/y as non-terminating decimal.
Insufficient
Combined
X and y are co-prime and y/x as even means x is 1 and y is MULTIPLE of 2..
If x is 1 and y is 10, x/y is terminating..
If x is 1 and y is 30, x/y is not terminating..
Insufficient
E
09 Nov 2021, 08:55
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Bunuel
Official Solution:
If \(x\) and \(y\) are positive integers, is \(\frac{x}{y}\) a terminating decimal?
We get a terminating decimal when a fraction, reduced to its lowest term, has no primes other than 2 and/or 5 in the denominator. If a fraction, reduced to its lowest term, has primes other than 2 and/or 5 in the denominator, the fraction will NOT terminate.
(1) \(\frac{y}{x}\) is even
\(y=x*even=even\).
\(\frac{x}{y}=\frac{x}{x*even}=\frac{1}{even}\). If that even number has no primes other than 2 and/or 5 in the denominator (for example, if that even number is 2, 4, 8, 10, 16, 20, 32, 40, ...), then the fraction will terminate but if that even number has primes other than 2 and/or 5 in the denominator (for example, if that even number is 6, 12, 14, 18, ...), then the fraction will NOT terminate. Not sufficient.
(2) The greatest common factor of \(x\) and \(y\) is 1
This one is clearly insufficient. Consider \(x=1\) and \(y=2\) for an YES answer and \(x=1\) and \(y=3\) for a NO answer.
(1)+(2) From (1) we know that \(x\) is a factor of \(y\) and from (2) we know that only common factor they share is 1, so \(x=1\). So, now we know that \(x=1\) and \(y=even\) but we still don't know whether \(y\) has primes other than 2 and/or 5. For example, if \(x=1\) and \(y=2\), then the answer is YES but if \(x=1\) and \(y=6\), then the answer is NO. Not sufficient.
Answer: E
