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number prop [#permalink]

27 Oct 2009, 15:58

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which of the following CANNOT be the greatest common divisor of two positive integers x and y ?

A 1
B x
C y
D x-y
E x+y

Do you assume a random value of x and y for this ?

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Re: number prop [#permalink]

27 Oct 2009, 18:19

Ans E.

GCF of x and y can't be greater than the difference between x and y.

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Re: number prop [#permalink]

28 Oct 2009, 13:02

hariharakarthi wrote:

Ans E.

GCF of x and y can't be greater than the difference between x and y.

Are you sure about that rule?

GCF of 2 equal numbers is the number itself > difference of the two numbers (0)

I would say the GCF of two numbers can't be greater than either of the numbers.
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Re: number prop [#permalink]

28 Oct 2009, 17:49

Bhuvi wrote:

which of the following CANNOT be the greatest common divisor of two positive integers x and y ?

A 1
B x
C y
D x-y
E x+y

Do you assume a random value of x and y for this ?

Thats E: (x +y). Greatest common divisor (GCD) of two integers can never be the sum of these integers. For example:

1 and 1 cannot have GCD of 2.
1 and 5 cannot have GCD of 6.
2 and 3 cannot have GCD of 5.
2 and 5 cannot have GCD of 7.
5 and 5 cannot have GCD of 10.
15 and 25 cannot have GCD of 40.
Similarly, x and y cannot have GCD of (x+y).

However (x-y) is possible: Suppose x = 4 and y = 6. The GDC is x-y = 6-4= 2.

1, x, and y can easily be the GCD of integers x and y.

atish wrote:

hariharakarthi wrote:

Ans E.
GCF of x and y can't be greater than the difference between x and y.

Are you sure about that rule?
GCF of 2 equal numbers is the number itself > difference of the two numbers (0)
I would say the GCF of two numbers can't be greater than either of the numbers.

Thats correct.
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Re: number prop [#permalink]

29 Oct 2009, 04:39

GCD of two nos cannot be greater than the two nos.

I will choose option E

Re: number prop [#permalink] 29 Oct 2009, 04:39

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