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

 It is currently 13 Oct 2019, 19:19

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

If a*b = a/b - b/a and m > n > 0, then which of following must be true

Author Message
TAGS:

Hide Tags

Current Student
Joined: 12 Aug 2015
Posts: 2574
Schools: Boston U '20 (M)
GRE 1: Q169 V154
If a*b = a/b - b/a and m > n > 0, then which of following must be true  [#permalink]

Show Tags

Updated on: 16 Oct 2018, 00:50
11
00:00

Difficulty:

85% (hard)

Question Stats:

56% (02:21) correct 44% (02:10) wrong based on 186 sessions

HideShow timer Statistics

If $$a#b=\frac{a}{b}-\frac{b}{a}$$ and $$m>n>0$$, then which of following must be true?

(I) $$\frac{1}{m}#\frac{1}{n} > \frac{1}{n} #\frac{1}{m}$$

(II) $$\frac{1}{m} #\frac{1}{n} < \frac{1}{n} #\frac{1}{m}$$

(III) $$m#n<0$$

(IV) $$m#n>0$$

A) I and III
B) I and IV
C) II and III
D) II and IV
E) only IV

_________________

Originally posted by stonecold on 19 Apr 2017, 10:24.
Last edited by Bunuel on 16 Oct 2018, 00:50, edited 2 times in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Aug 2009
Posts: 7943
Re: If a*b = a/b - b/a and m > n > 0, then which of following must be true  [#permalink]

Show Tags

19 Apr 2017, 18:55
1
stonecold wrote:
If $$a*b=\frac{a}{b}-\frac{b}{a}$$ and $$m>n>0$$, then which of following must be true?

(I)$$\frac{1}{m}*\frac{1}{n} > \frac{1}{n} *\frac{1}{m}$$

(II)$$\frac{1}{m} *\frac{1}{n} < \frac{1}{n} *\frac{1}{m}$$

(III)$$m*n<0$$
(IV)$$m*n>0$$

A)I and III
B)I and IV
C)II and III
D)II and IV
E)only IV

ONLY one out of III and IV & one out of I and II.
So just check for only one of them.
Let's see between III n IV
M*n= m/n-n/m...
Now m>n, so m/n will be GREATER than 1 and n/m will be lesser than 1..
This means m/n-n/m will be GREATER than 0..
Hence IV is correct..

Also we can straight way take that when we take reciprocal of these numbers 1/n becomes greater than 1/m and hence the INEQUALITY sign will change from > to <.. II is correct
But say you want to check out..
Make it easier by taking m and n as fraction
So m =1/2 and n=1/3....m>n...
So 1/m becomes 2 and 1/n becomes 3..
Now you can check between 2*3 & 3*2

So II and IV are correct, hence D
_________________
Retired Moderator
Joined: 22 Aug 2013
Posts: 1431
Location: India
Re: If a*b = a/b - b/a and m > n > 0, then which of following must be true  [#permalink]

Show Tags

20 May 2017, 22:38
Please note that since m>n>0, m/n >1 and n/m<1

(1/m)*(1/n) = (1/m)/(1/n) - (1/n)/(1/m) = (n/m) - (m/n)
This is <0 because n/m <1 and m/n>1

(1/n)*(1/m) = (1/n)/(1/m) - (1/m)/(1/n) = (m/n) - (n/m)
This is >0 because m/n >1 and n/m<1

So II is true

Also, m*n = m/n - n/m
This is >0 because m/n > 1 > n/m

So IV is also true

Manager
Joined: 18 Feb 2018
Posts: 109
Re: If a*b = a/b - b/a and m > n > 0, then which of following must be true  [#permalink]

Show Tags

14 Oct 2018, 05:00
What does a and b have to do with m and n? The question is unclear.
Intern
Joined: 09 Apr 2018
Posts: 31
GPA: 4
Re: If a*b = a/b - b/a and m > n > 0, then which of following must be true  [#permalink]

Show Tags

15 Oct 2018, 23:32
1
GittinGud wrote:
What does a and b have to do with m and n? The question is unclear.

It basically tells you the operations you have to perform. You can think of a and b as placeholders that are just there to demonstrate how the equation works and m, n as you actual inputs.

Hope this helps.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9695
Location: Pune, India
Re: If a*b = a/b - b/a and m > n > 0, then which of following must be true  [#permalink]

Show Tags

16 Oct 2018, 00:43
stonecold wrote:
If $$a*b=\frac{a}{b}-\frac{b}{a}$$ and $$m>n>0$$, then which of following must be true?

(I) $$\frac{1}{m}*\frac{1}{n} > \frac{1}{n} *\frac{1}{m}$$

(II) $$\frac{1}{m} *\frac{1}{n} < \frac{1}{n} *\frac{1}{m}$$

(III) $$m*n<0$$

(IV) $$m*n>0$$

A) I and III
B) I and IV
C) II and III
D) II and IV
E) only IV

The format of the question is incorrect. It is not given as a function or user defined operator. You cannot use a standard operator as a user defined operator that too without explaining explicitly. We can guess that the relation given for a and b is supposed to hold for m and n too to solve it but an actual GMAT question would need to be formatted differently.

Given the question as is, I would just say that m > n > 0 so m and n are positive and hence m*n > 0. This is the ONLY statement that will be true.

If you define a new operator such as
a#b = a/b - b/a

now, you can worry about (1/m) # (1/n) and (1/n)#(1/m)

(1/m) # (1/n) = n/m - m/n = (n - m)/mn (since n < m, this is negative)
(1/n)#(1/m) = m/n - n/m = (m - n)/mn (since m > n, this is positive)

So II is correct.

m#n = m/n - n/m = (m - n)/mn (since m > n, this is positive)
So IV is correct.

_________________
Karishma
Veritas Prep GMAT Instructor

Re: If a*b = a/b - b/a and m > n > 0, then which of following must be true   [#permalink] 16 Oct 2018, 00:43
Display posts from previous: Sort by