GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Jul 2018, 00:04

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Is xm < ym ?

Author Message
TAGS:

Hide Tags

Board of Directors
Joined: 01 Sep 2010
Posts: 3428
Is xm < ym ? [#permalink]

Show Tags

26 Jul 2017, 09:10
4
1
Top Contributor
2
00:00

Difficulty:

15% (low)

Question Stats:

72% (00:41) correct 28% (00:40) wrong based on 330 sessions

HideShow timer Statistics

Is $$xm < ym$$ ?

(1) $$x > y$$

(2) $$m < 0$$

_________________
CEO
Joined: 12 Sep 2015
Posts: 2630
Re: Is xm < ym ? [#permalink]

Show Tags

13 Aug 2017, 08:42
5
Top Contributor
1
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

RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – Founder of gmatprepnow.com

General Discussion
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1345
Re: Is xm < ym ? [#permalink]

Show Tags

26 Jul 2017, 09:20
3
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.
_________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Senior Manager
Joined: 29 Jun 2017
Posts: 343
Re: Is xm < ym ? [#permalink]

Show Tags

03 Aug 2017, 09:06
1
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.
Intern
Joined: 23 Apr 2017
Posts: 3
Re: Is xm < ym ? [#permalink]

Show Tags

13 Aug 2017, 03:29
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.
Intern
Joined: 22 Jan 2018
Posts: 23
Re: Is xm < ym ? [#permalink]

Show Tags

02 May 2018, 21:29
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

RELATED VIDEO FROM OUR COURSE

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: 47006
Re: Is xm < ym ? [#permalink]

Show Tags

02 May 2018, 23:45
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

_________________
CEO
Joined: 12 Sep 2015
Posts: 2630
Re: Is xm < ym ? [#permalink]

Show Tags

03 May 2018, 07:01
Top Contributor
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:

_________________

Brent Hanneson – Founder of gmatprepnow.com

Intern
Joined: 11 Dec 2016
Posts: 33
Re: Is xm < ym ? [#permalink]

Show Tags

28 May 2018, 09:51
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
VeritasPrepKarishma
GMAT Club Legend
Joined: 16 Oct 2010
Posts: 8119
Location: Pune, India
Re: Is xm < ym ? [#permalink]

Show Tags

07 Jun 2018, 19:48
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.
_________________

Karishma
Private Tutor for GMAT
Contact: bansal.karishma@gmail.com

Re: Is xm < ym ?   [#permalink] 07 Jun 2018, 19:48
Display posts from previous: Sort by

Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.