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# If x and y are positive integers does x equal to y?

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Re: If x and y are positive integers does x equal to y? [#permalink]
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If x and y are positive integers does x equal to y?

Solution -

Considering Statement (1) alone -
(1) The sum of the greatest common divisor of x and y and the least common multiple of x and y equals to the sum of x and y
If x = 4 and y = 2, GCD = 2 and LCM = 4. In this case, sum of the GCD and LCM of x and y is equal to sum of x and y. Answer to question will be Yes.
If x = 4 and y = 4, GCD = 2 and LCM = 4. In this case, sum of the GCD and LCM of x and y is NOT equal to sum of x and y. Answer to question will be No.

Statement (1) does not have a consistent answer. Statement (1) alone is not sufficient.

Considering Statement (2) alone -
(2) The greatest common divisor of x and y equals to the least common multiple of x and y.
If x = 2 and y = 2, GCD = 2 and LCM = 2. Similar will be the case with prime numbers such as 3, 5, 7, etc.
GCD of any positive integers x and y will be equal to LCM of x and y only when both x and y are the same prime numbers. i.e when both x and y are equal and prime.

Statement (2) alone is sufficient. It gives a Yes answer to the question.

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Re: If x and y are positive integers does x equal to y? [#permalink]
Bunuel wrote:
If x and y are positive integers does x equal to y?

(1) The sum of the greatest common divisor of x and y and the least common multiple of x and y equals to the sum of x and y
(2) The greatest common divisor of x and y equals to the least common multiple of x and y

Plugging in method.

(1)If $$x=2$$ and $$y=2$$ yes
if $$x=1$$ and $$y =2$$ no
INSUFF.

(2) Only possible when both $$x$$and $$y$$ are equal.
i.e. $$x=2\hspace{2mm} y = 2$$
$$x=3 \hspace{2mm} y =3$$

SUFF.

Ans- B

Hope it's clear.
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Re: If x and y are positive integers does x equal to y? [#permalink]
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Re: If x and y are positive integers does x equal to y? [#permalink]
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