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Which of the following CANNOT be the greatest common divisor

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Which of the following CANNOT be the greatest common divisor [#permalink] New post 08 Feb 2011, 00:43
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C
D
E

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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
[Reveal] Spoiler: OA
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Re: problem solving [#permalink] New post 08 Feb 2011, 01:55
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GCD of two postive numbers will always be less than or equal to the smaller of the two numbers.

If x and y are two +ve integers.

if (x < y)
GCD(x,y) <= x

if (y < x)
GCD(x,y) <= y

if (y = x)
GCD(x,y) = y = x

In any case;

GCD must be less than the sum of the two numbers

GCD(x,y) < (x+y)

Ans: "E"
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Re: problem solving [#permalink] New post 08 Feb 2011, 02:28
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Lolaergasheva wrote:
Which of the following cannot be the GCD of two positive integers x and y?
a 1
b x
c y
d x-y
e x+y


Divisor of a positive integer cannot be more than that integer (for example integer 4 doesn't have a divisor more than 4, the largest divisor it has is 4 itself), so greatest common divisor of two positive integers x and y can not be more than x or y.

Answer: E.
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Re: problem solving [#permalink] New post 09 Feb 2011, 09:22
E.

X+y will be greater than either x or y and hence it cannot be the answer.
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Re: Could you explain? [#permalink] New post 26 Nov 2011, 06:15
The greatest common divisor of x and y must be a divisor of x, so it can't be larger than x. Since x+y is larger than x, it cannot be the greatest common divisor of x and y.
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Re: Which of the following CANNOT be the greatest common divisor [#permalink] New post 24 Jul 2012, 09:42
Manhattan's way of visualizing the GCF comes in handy in this type of question. Even if you do not recall by theory that the GCF cannot be greater than either terms, you can figure that out.
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Re: Which of the following CANNOT be the greatest common divisor [#permalink] New post 31 Aug 2013, 05:28
Expert's post
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Re: Which of the following CANNOT be the greatest common divisor [#permalink] New post 07 Feb 2014, 20:49
Which of the following CANNOT be the greatest common divisor of two positive integers x and y?

method 1: use examples/counter examples.
A. 1 (x=2;y=3)
B. x (x=2; y = 4)
C. y (x=4; y = 2)
D. x-y (x = 4; y =2)
E. x+y -> NOT POSSIBLE.

Concept: Factors of a number are always less than or equal to that number. HCF of x and y can never be greater than the smaller number.
Re: Which of the following CANNOT be the greatest common divisor   [#permalink] 07 Feb 2014, 20:49
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