x/y will be a terminating decimal only if y is 1 or a multiple of 2 and/or 5. y cannot be a multiple of any other number other than 2 and/or 5.
With this principle in mind, let's look at the statements
Statement 1: y/x is even. So, this means either x=1 and y=even number or x is a factor of y such that the resulting fraction y/x is even
Let's take examples to understand this.
If x=3 and y=6, then y/x=6/3=2(=even number). But since y=6, x/y can't be terminating decimal
If x=5 and y=10, then y/x=10/5=2(=even number). Since y=10, x/y is a terminating decimal
Thus,
this statement is insufficientStatement 2: If the greatest common factor between two numbers is 1, this proves that any of the following cases can be true: 1) the two numbers are odd and even or 2) the two numbers are prime number or 3) that at least one of the two numbers is 1.
In any of the above cases, we cannot distinguish which one will y be, hence we cannot be sure if x/y will be terminating or not.
Thus,
this statement is insufficientCombining statements 1 & 2: we get that contrary to what we had deduced in statement 1, x cannot be a factor of y. Thus, x=1 and y is an even number.
Checking on the three cases:
1) x=1 and y= even doesn't prove whether x/y will necessarily be terminating. Eg: x=1 and y=10: results in x/y terminating vs x=1 and y=14, results in x/y non-terminating
Although this is enough to prove that statement 2 is insufficient, let's check the other two cases as well for our understanding.
2) This cannot hold true since x=1 which is neither prime nor composite
3) This is a repeat of case 1.
Thus,
the statements when combined are also insufficientAnswer is E
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