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# Is xm < ym ?

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Is xm < ym ?  [#permalink]

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26 Jul 2017, 08:10
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Is $$xm < ym$$ ?

(1) $$x > y$$

(2) $$m < 0$$

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Joined: 11 Sep 2015
Posts: 4320
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

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Re: Is xm < ym ?  [#permalink]

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26 Jul 2017, 08:20
5
1
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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2
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.
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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: 22 Jan 2018
Posts: 20
Re: Is xm < ym ?  [#permalink]

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02 May 2018, 20:29
1
GMATPrepNow wrote:
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

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In this case, we can subtract ym from both sides even though we don't know their signs?
Math Expert
Joined: 02 Sep 2009
Posts: 61243
Re: Is xm < ym ?  [#permalink]

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02 May 2018, 22:45
In this case, we can subtract ym from both sides even though we don't know their signs?

We are concerned about the sign of a variable when multiplying/dividing an inequality by it. However we can safely add/subtract a variable from both sides of an inequality regardless of its sign.

9. Inequalities

For more check Ultimate GMAT Quantitative Megathread

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Re: Is xm < ym ?  [#permalink]

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03 May 2018, 06:01
Top Contributor
1
In this case, we can subtract ym from both sides even though we don't know their signs?

When it comes to solving inequalities, we can safely add or subtract ANY value from both sides, and the resulting inequality will be perfectly valid.
However, if we multiply or divide both sides by a NEGATIVE value, then we must REVERSE the direction of the inequality symbol.

More here:

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Re: Is xm < ym ?  [#permalink]

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28 May 2018, 08:51
Hi!! Is this approach correct?

xm<ym
xm-ym<0
m(x-y)<0
is m<0 and x<y?

1. x>y but does not tell us the value of m hence not sufficient

2. M>0 but does not tell us for x or y hence not sufficent.

Combining 1+2, we get x>y and M>0 hence a definite yes.

Bunuel
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Re: Is xm < ym ?  [#permalink]

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07 Jun 2018, 18:48
1
asfandabid wrote:
Hi!! Is this approach correct?

xm<ym
xm-ym<0
m(x-y)<0
is m<0 and x<y?

1. x>y but does not tell us the value of m hence not sufficient

2. M>0 but does not tell us for x or y hence not sufficent.

Combining 1+2, we get x>y and M>0 hence a definite yes.

Bunuel
VeritasPrepKarishma

Evaluate this properly: m(x-y)<0
This means the product of m and (x - y) is negative. So, either m is positive and (x - y) negative OR m is negative and (x - y) positive.
The two statements together tell us hat (x - y) is positive and m is positive.

So we know for sure that m(x-y) is positive. Sufficient.
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Re: Is xm < ym ?  [#permalink]

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09 Nov 2018, 10:58
carcass wrote:
Is $$xm < ym$$ ?

(1) $$x > y$$

(2) $$m < 0$$

1) Given: x > y,
now if m is positive, multiplying both sides with m will not change the sign, thus xm > ym
but if m is negative, multiplying both sides with m will change the sign, thus xm < ym

so both cases are possible depending on the value of m. NOT SUFFICIENT.

2) Given: m <0, clearly NOT SUFFICIENT as not information about x and y is given.

Combining 1) and 2)
from two we know that m<0, hence out of the two cases in option 1, only this 'xm < ym' remain true. so BOTH STATEMENTS COMBINED ARE SUFFICIENT.
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Re: Is xm < ym ?  [#permalink]

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08 Jun 2019, 03:45
Can't I take out the M from both sides by multiplying with 1/m ? That leaves x<y.. hence I chose A. Can someone clarify

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Re: Is xm < ym ?  [#permalink]

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25 Jun 2019, 10:21
1
An important rule of Inequalities:

If m> n. Is m+k>n+k.
Yes Always

If m>n, Is mr>nr?
Yes if r>0 No if r<0
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Is xm < ym ?  [#permalink]

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05 Nov 2019, 04:10
Jinnraj wrote:
Can't I take out the M from both sides by multiplying with 1/m ? That leaves x<y.. hence I chose A. Can someone clarify

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Don’t do that when it comes to Inequality questions .

Because , the constant m is going to decide the sign of Inequality ,

If m is -ve , then multiplying both sides (left hand side and Right hand side ) will change the sign of Inequality .

Hope this helps
Is xm < ym ?   [#permalink] 05 Nov 2019, 04:10
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