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20 July, 14:08

What is the greatest common divisor of x and y

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  1. 20 July, 14:52
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    What is the greatest common factor of x and y?

    (1) x and y are both divisible by 4 - -> clearly insufficient: of course 4 itself could be the GCD but it's also possible that x and y share some other common factor more than 4, for example 5 (in this case both will be divisible by 20), or 8, or 4,000,000 ... so GCD could be more than 4 as well. Though from this statement we know that GCD cannot possibly be less than 4.

    (2) x - y = 4 - -> according to the property #2: GCD (x, y) ≤4

    GCD (x, y) ≤4, but still insufficient.

    (1) + (2) From (1) GCD≥4

    GCD≥4 and from (2) GCD≤4

    GCD≤4 - -> GCD=4

    GCD=4 Sufficient.

    Answer: C.
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