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# M16-25

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Math Expert
Joined: 02 Sep 2009
Posts: 58381

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16 Sep 2014, 00:59
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Difficulty:

55% (hard)

Question Stats:

51% (00:57) correct 49% (00:51) wrong based on 100 sessions

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Is the product of two positive numbers $$x$$ and $$y$$ larger than their sum?

(1) $$x$$ and $$y$$ are integers

(2) $$y \gt x \gt 1$$

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Math Expert
Joined: 02 Sep 2009
Posts: 58381

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16 Sep 2014, 00:59
Official Solution:

Statement (1) by itself is insufficient.

Statement (2) by itself is insufficient. If $$x$$ and $$y$$ are large, the answer to the question is "yes". If $$x = 1.1$$ and $$y = 1.2$$, the answer to the question is "no".

Statements (1) and (2) combined are sufficient. The smallest possible $$x$$ is 2, the smallest possible $$y$$ is 3. Even these small values of $$x$$ and $$y$$ give $$xy \gt x + y$$. As $$x$$ and $$y$$ increase, the difference between their product and their sum will only grow.

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Joined: 23 Jun 2011
Posts: 16
Concentration: Finance, Other
WE: Information Technology (Health Care)

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16 Nov 2015, 09:37
case 1:
y=9,x=1.
Sum=10,Product =9 i.e Product<Sum.
case 2:
y=9,x=3.
Sum=12,Product=27 i.e Product>Sum.

Please correct me if I am wrong.
Math Expert
Joined: 02 Sep 2009
Posts: 58381

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16 Nov 2015, 22:15
karan14 wrote:
case 1:
y=9,x=1.
Sum=10,Product =9 i.e Product<Sum.
case 2:
y=9,x=3.
Sum=12,Product=27 i.e Product>Sum.

Please correct me if I am wrong.

(2) says that y > x > 1.
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Joined: 18 Mar 2018
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02 Feb 2019, 16:16
1
From this, is it correct to state these rules?

The product of x and y (xy) will always be LARGER than their sum (x+y) if they are both larger than 2

The product of x and y (xy) will always be SMALLER than their sum (x+y) if they are both between 0 and 1

Please let me know if I am correct in my thinking
Re: M16-25   [#permalink] 02 Feb 2019, 16:16
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# M16-25

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