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# M28-05

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Math Expert
Joined: 02 Sep 2009
Posts: 52906

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16 Sep 2014, 00:28
00:00

Difficulty:

35% (medium)

Question Stats:

58% (00:48) correct 42% (00:49) wrong based on 223 sessions

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Is $$x = 0$$?

(1) $$xy = x$$

(2) $$x+y=x$$

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Joined: 02 Sep 2009
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16 Sep 2014, 00:28
Official Solution:

(1) $$xy = x$$. Re-arrange and factor out $$x$$ to get $$x(y-1)=0$$. So, either $$x=0$$ (and $$y$$ can take any value) OR $$y=1$$ (and $$x$$ can take any value). Not sufficient.

(2) $$x+y=x$$. This statemnt implies that $$y=0$$. Not sufficient to answer whether $$x=0$$.

(1)+(2) As from (2) $$y=0\neq{1}$$ then according to (1) $$x=0$$. Sufficient.

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17 Oct 2015, 13:04
I think this is a high-quality question and I agree with explanation. I'm confused as to why I cannot divide statement 1 by zero to get to y=1. I know that x=0 is clearly a possibility i just don't get why I cannot divide both sides by X.
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18 Oct 2015, 10:27
2
danjbon wrote:
I think this is a high-quality question and I agree with explanation. I'm confused as to why I cannot divide statement 1 by zero to get to y=1. I know that x=0 is clearly a possibility i just don't get why I cannot divide both sides by X.

If you divide (reduce) xy = x by x, you assume, with no ground for it, that x does not equal to zero thus exclude a possible solution.

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero.
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Schools: ISB '18 (A)
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03 Dec 2016, 19:41
why we cannot have a situation where both x and y are zero??it satisfies both the equations..and it has not been explicitly mentioned x and y are different??
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05 Dec 2016, 01:00
mohitks89 wrote:
why we cannot have a situation where both x and y are zero??it satisfies both the equations..and it has not been explicitly mentioned x and y are different??

But we have precisely the situation you describe: when we combine the statements we get that x = y = 0.
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15 Oct 2018, 10:13
What if x = 0 and y = 1 or y = 0 and x = 1
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15 Oct 2018, 20:05
bpdulog wrote:
What if x = 0 and y = 1 or y = 0 and x = 1

Those values do not satisfy given statements.
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Re: M28-05   [#permalink] 15 Oct 2018, 20:05
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# M28-05

Moderators: chetan2u, Bunuel

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