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Is xm < ym ?

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Joined: 01 Sep 2010
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Is xm < ym ? [#permalink]

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26 Jul 2017, 08:10
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67% (00:38) correct 33% (00:45) wrong based on 212 sessions

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Is $$xm < ym$$ ?

(1) $$x > y$$

(2) $$m < 0$$
[Reveal] Spoiler: OA

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Joined: 24 Jun 2008
Posts: 1346
Re: Is xm < ym ? [#permalink]

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26 Jul 2017, 08:20
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Using both statements, if we take the inequality in Statement 1:

x > y

and multiply by m on both sides, we need to reverse the inequality, because, as Statement 2 tells us, m < 0. So we get

xm < ym

which is what we wanted. Statement 1 is not sufficient alone because we need to know if m is positive or negative, and Statement 2 is not sufficient alone since we have no information about x or y. So the answer is C.
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Re: Is xm < ym ? [#permalink]

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03 Aug 2017, 08:06
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carcass wrote:
Is $$xm < ym$$ ?

(1) $$x > y$$

(2) $$m < 0$$

this is more simple method

xm<ym
move ym to the left
xm-ym<0
m(x-y)<0

now we can analyse , applying case 1 and 2.
Intern
Joined: 23 Apr 2017
Posts: 3
Re: Is xm < ym ? [#permalink]

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13 Aug 2017, 02:29
Hi,

m(x-y)<0 -- > m<0 or x>y
do we need 2 conditions together or each condition alone is suff??

as it is m<0 OR x>y can we not select D as the answer?

Thanks.
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Joined: 11 Sep 2015
Posts: 2049
Re: Is xm < ym ? [#permalink]

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13 Aug 2017, 07:42
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carcass wrote:
Is $$xm < ym$$ ?

(1) $$x > y$$

(2) $$m < 0$$

Target question: Is xm < ym?
Another approach is to rephrase the target question.

Take the inequality and subtract ym from both sides to get: xm - ym < 0
Factor out the m to get m(x - y) < 0
In other words....
REPHRASED target question: Is m(x - y) a NEGATIVE value?

Statement 1: x > y
Subtract y from both sides to get: x - y > 0
So, x - y is a POSITIVE value
Does this provide enough information to determine whether or not m(x - y) a NEGATIVE value?
No. We still don't know anything about the value of m
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: m < 0
In other words, m is NEGATIVE
Does this provide enough information to determine whether or not m(x - y) a NEGATIVE value?
No. We don't know anything about the value of (x - y)
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x - y is a POSITIVE value
Statement 2 tells us that m is a NEGATIVE value
So, m(x - y) = (NEGATIVE)(POSITIVE) = some NEGATIVE VALUE
In other words, m(x - y) is definitely a NEGATIVE value
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

[Reveal] Spoiler:
C

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Re: Is xm < ym ?   [#permalink] 13 Aug 2017, 07:42
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