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

It is currently 22 Nov 2019, 13:25

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If mn ≠ 0, is m > n? (1) 1/m < 1/n (2) m^2 > n^2

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Senior SC Moderator
User avatar
V
Joined: 14 Nov 2016
Posts: 1347
Location: Malaysia
GMAT ToolKit User
If mn ≠ 0, is m > n? (1) 1/m < 1/n (2) m^2 > n^2  [#permalink]

Show Tags

New post 22 May 2017, 08:35
1
10
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

48% (02:10) correct 52% (01:32) wrong based on 275 sessions

HideShow timer Statistics

If mn ≠ 0, is m > n?

(1) 1/m < 1/n
(2) m^2 > n^2

_________________
"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Rules for posting in verbal forum | Please DO NOT post short answer in your post!

Advanced Search : https://gmatclub.com/forum/advanced-search/
Most Helpful Expert Reply
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4083
Location: Canada
Re: If mn ≠ 0, is m > n? (1) 1/m < 1/n (2) m^2 > n^2  [#permalink]

Show Tags

New post 22 May 2017, 09:04
5
Top Contributor
2
hazelnut wrote:
If mn ≠ 0, is m > n?

(1) 1/m < 1/n
(2) m² > n²


Target question: Is m > n?

Given: mn ≠ 0

Statement 1: 1/m < 1/n
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of m and n that satisfy statement 1. Here are two:
Case a: m = 2 and n = 1. In this case m > n
Case b: m = -3 and n = 1. In this case m < n
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: m² > n²
Before I start choosing numbers to test, I'll see if I can REUSE my numbers from statement 1.
Yes I can! Those same values satisfy the conditions in statement 2.
Case a: m = 2 and n = 1. In this case m > n
Case b: m = -3 and n = 1. In this case m < n
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: m = 2 and n = 1. In this case m > n
Case b: m = -3 and n = 1. In this case m < n
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer:

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
General Discussion
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4469
Re: If mn not equal to 0, is m>n?  [#permalink]

Show Tags

New post 17 Aug 2017, 16:53
3
Gnpth wrote:
If \(mn\neq{0}\) is m>n?

1. \(\frac{1}{m} < \frac{1}{n}\)
2. \(m^2> n^2\)

Dear Gnpth,

I'm happy to respond. :-) This is brilliant question!

Statement #1: \(\frac{1}{m} < \frac{1}{n}\)
I think this is the trickier of the two statements.

Here positive/negative sign is crucial.
Case I: if m = 5 and n = 2, then: \(\frac{1}{5} < \frac{1}{2}\) and m > n
Case II: if m = -5 and n = 2, then: \(-\frac{1}{5} < \frac{1}{2}\) but m < n

Two different choices consistent with the statement produce two different answers. Thus, this statement, alone and by itself, is insufficient.

Statement #2: \(m^2> n^2\)[/quote]
Clearly, positive/negative signs make a difference here. We can use the same two choices.
Case I: if m = 5 and n = 2, then: \(5^2> 2^2\) and and m > n
Case II: if m = -5 and n = 2, then: \((-5)^2> 2^2\) but m < n

Again, two different choices consistent with the statement produce two different answers. Thus, this statement, alone and by itself, is insufficient.

Combining the statements produces no additional restraints, and both pairs still can be used with the combination. Thus, everything is insufficient.

OA = (E)

A truly wonderful question!

Does all this make sense?
Mike :-)
_________________
Mike McGarry
Magoosh Test Prep


Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59268
Re: If mn ≠ 0, is m > n? (1) 1/m < 1/n (2) m^2 > n^2  [#permalink]

Show Tags

New post 14 Aug 2017, 04:49
1
1
rekhabishop wrote:
hazelnut wrote:
If mn ≠ 0, is m > n?

(1) 1/m < 1/n
(2) m^2 > n^2


Calling the master of Algebra!

All hail Bunuel !!
Please help us with a logical (algebraic) solution. :)


If mn ≠ 0, is m > n?

(1) 1/m < 1/n.

Two cases:
If m and n have the same sign (so if both are negative, or both are positive), then when cross multiplying we'll get n < m. Answer: YES.
If m and n have different signs signs (so if n is positive and m is negative), then when cross multiplying we'll get n > m. Answer: NO.
Not sufficient.

(2) m^2 > n^2.
Take the square root from both sides: |m| > |n|. This implies that m is further from 0 than n is. Clearly insufficient to say which is greater.

(1)+(2) The second statement still allows m and n to have the same sign (m = 2 and n = 1) as well as m and n to have different signs (m = -2 and n = 1) thus we can still have two different answers: n < m and n > m. Not sufficient.

Answer: E.
_________________
Manager
Manager
avatar
S
Joined: 25 Apr 2016
Posts: 59
Re: If mn ≠ 0, is m > n? (1) 1/m < 1/n (2) m^2 > n^2  [#permalink]

Show Tags

New post 22 May 2017, 08:46
1
statement 1st will boils down to (n-m)/mn <0 => (n-m) and mn are of opposite sign => not sufficient and statement 2nd implies( m^2 -n^2) >0 => (m+n)(m-n) >0 and that isn't sufficient and taking them together won't lead to any unique solution either -> option ->E
Manager
Manager
avatar
B
Joined: 30 Apr 2013
Posts: 75
Re: If mn ≠ 0, is m > n? (1) 1/m < 1/n (2) m^2 > n^2  [#permalink]

Show Tags

New post 12 Aug 2017, 06:19
Hi Brent,

in statement one 1)

case a ) if M=2 and N=1 . then how come M > N ? could you please clarify
Current Student
avatar
B
Joined: 22 Sep 2016
Posts: 156
Location: India
GMAT 1: 710 Q50 V35
GPA: 4
Re: If mn ≠ 0, is m > n? (1) 1/m < 1/n (2) m^2 > n^2  [#permalink]

Show Tags

New post 14 Aug 2017, 04:22
hazelnut wrote:
If mn ≠ 0, is m > n?

(1) 1/m < 1/n
(2) m^2 > n^2


Calling the master of Algebra!

All hail Bunuel !!
Please help us with a logical (algebraic) solution. :)
_________________
Desperately need 'KUDOS' !!
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8202
If mn ≠ 0, is m > n? (1) 1/m < 1/n (2) m^2 > n^2  [#permalink]

Show Tags

New post 14 Aug 2017, 05:01
hazelnut wrote:
If mn ≠ 0, is m > n?

(1) 1/m < 1/n
(2) m^2 > n^2



Hi..

Algebraic approach..
Given that neither of m and n is 0, they can be negative, positive..

Let's see the statements..
1) \(\frac{1}{m}<\frac{1}{n}.....\frac{1}{n}-\frac{1}{m}.....\frac{m-n}{mn}>0\)
So two cases..
mn>0... m-n>0, m>n.....
That is if both n and m are of SAME sign, m>n
mn<0.. m-n<0, m<n...
That is if both are of different sign, m<n..
Insufficient

2) \(m^2>n^2.....m^2-n^2>0......(m-n)(m+n)>0\)..
Two cases..
m+n>0...m-n>0, m>n...
That is if both are POSITIVE, or one is ATLEAST positive, m>n
m+n<0... m-n<0..
So if both are NEGATIVE m<n...
Again different possibilities
Insufficient

Combined..
Find the common in both statements..
A) when both are NEGATIVE, m<n
B) when both are of different sign, m>n
Again insufficient

E

Just for info

Ofcourse when both are positive ans is different from each statement, so not possible..
It seems Bunuel has already replied in a crisp manner, this is on same line slightly in detail
_________________
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2549
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
If mn ≠ 0, is m > n? (1) 1/m < 1/n (2) m^2 > n^2  [#permalink]

Show Tags

New post 14 Aug 2017, 05:06
Great question.

The bottom line is => If you don't know the signs of the inequality then do not change the sides.
i.e => If 1/m<1/n
then it does not mean n<m unless we know the signs for the involved numbers.



As for this question -> Here is an easy way out
Taking two examples => (100,1) and (-100,1) => Push the E option.

_________________
Senior Manager
Senior Manager
User avatar
G
Joined: 06 Jul 2016
Posts: 356
Location: Singapore
Concentration: Strategy, Finance
GMAT ToolKit User
Re: If mn ≠ 0, is m > n? (1) 1/m < 1/n (2) m^2 > n^2  [#permalink]

Show Tags

New post 14 Aug 2017, 05:07
hazelnut wrote:
If mn ≠ 0, is m > n?

(1) 1/m < 1/n
(2) m^2 > n^2


Number plugging was faster IMO!

1) \(\frac{1}{m}\) < \(\frac{1}{n}\)
m = 2, n = 1 => Yes
m = -2, n = 1 => No
Insufficient.

2) \(m^2\) > \(n^2\)
m = 2, n = 1 => Yes
m = -2, n = 1 => No
Insufficient.

1+2)
Nothing new. Insufficient.
E is the answer
_________________
Put in the work, and that dream score is yours!
Senior Manager
Senior Manager
User avatar
P
Joined: 29 Jun 2017
Posts: 417
GPA: 4
WE: Engineering (Transportation)
GMAT ToolKit User Reviews Badge
Re: If mn ≠ 0, is m > n? (1) 1/m < 1/n (2) m^2 > n^2  [#permalink]

Show Tags

New post 14 Aug 2017, 05:19
Clearly its E

1) 1/m<1/n
(m-n)/mn >0
numerator and denominator both have to be simultaneously positive or negative to be the statement to be true. A,D ruled out

2) m^2>n^2
m<-n and m>n and therefore B is out

combine them

put m=-2 n=1 and also m=2 and n=1
both the condition will satisfy

clearly we cant say if m>n or not. C is out

E is answer
_________________
Give Kudos for correct answer and/or if you like the solution.
Current Student
User avatar
P
Status: Chasing my MBB Dream!
Joined: 29 Aug 2012
Posts: 1096
Location: United States (DC)
WE: General Management (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
If mn not equal to 0, is m>n?  [#permalink]

Show Tags

New post 17 Aug 2017, 13:59
Top Contributor
If \(mn\neq{0}\) is m>n?

1. \(\frac{1}{m} < \frac{1}{n}\)
2. \(m^2> n^2\)
_________________
VP
VP
User avatar
V
Joined: 23 Feb 2015
Posts: 1310
GMAT ToolKit User Premium Member
Re: If mn ≠ 0, is m > n? (1) 1/m < 1/n (2) m^2 > n^2  [#permalink]

Show Tags

New post 05 Nov 2019, 12:52
hazelnut wrote:
If mn ≠ 0, is m > n?

(1) 1/m < 1/n
(2) m^2 > n^2


Official Explanation:
The constraint in the question stem indicates that neither m nor n equals zero.
(1) INSUFFICIENT: You can solve algebraically/theoretically or you can Test Cases. If you solve algebraically, be careful:
you have to account for multiplying the inequality by a negative.
If m and n are both positive, then \(m > n\).
If m and n are both negative, the sign flips twice, so \(m > n\) again.
If only one is negative, then the sign flips once and \(m < n\). In this case, m must be the negative number, since any positive
is greater than any negative.
Alternatively, Test Cases:
If m = 3 and n = 2, then statement (1) is true and the answer to the question is Yes, \(m > n\).
If m = −3 and n = 2, then statement (1) is true and the answer to the question is No, m is not greater than n.

(2) INSUFFICIENT: This statement indicates nothing about the signs of the two variables. Either one could be positive or
negative.

(1) AND (2) INSUFFICIENT. If you are solving algebraically, test the scenarios that you devised for statement (1).
If m and n are both positive, then \(m > n\) and \(m^2 > n^2\). Both statements allow this scenario.
If m and n are both negative, then \(m > n\) but and \(m^2\) is not greater than \(n^2\). Discard this scenario, since it makes statement
(2) false.
If m is negative and n is positive, then \(m < n\). It could also be true that \(m^2 > n^2\), as long as m's magnitude is larger than
n's. If you're not sure Test Cases (see below).
Alternatively, test cases. Start by testing whether the cases you already tried for statement (1) also apply to statement (2).
If m = 3 and n = 2, then \(m > n\) and m² > n². Both statements allow this scenario.
If m = −3 and n = 2, then \(m < n\) and m² > n². Both statements allow this scenario.
Because there are scenarios in which \(m > n\) and \(m < n\), both statements together are still insufficient to answer the question. If
you forgot to account for the positive and negative cases, you may end up with (A) or (D) as your (incorrect) answer.
The correct answer is (E).
_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”
Henry Wadsworth Longfellow

SEARCH FOR ALL TAGS
GMAT Club Bot
Re: If mn ≠ 0, is m > n? (1) 1/m < 1/n (2) m^2 > n^2   [#permalink] 05 Nov 2019, 12:52
Display posts from previous: Sort by

If mn ≠ 0, is m > n? (1) 1/m < 1/n (2) m^2 > n^2

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne