It is currently 20 Nov 2017, 08:53

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Basic Inequality Question - Multiplying Inequalities

Author Message
TAGS:

### Hide Tags

Intern
Joined: 22 Mar 2013
Posts: 11

Kudos [?]: 1 [0], given: 15

Basic Inequality Question - Multiplying Inequalities [#permalink]

### Show Tags

26 Jun 2013, 08:29
Hi guys, I have a basic question that can probably be answered pretty quickly. I tried google searching but could not find my answer.

My question is, the guide has this rule: "Only multiply inequalities together if both sides of both inequalities are positive."

What if both inequalities were negative?

If m and n are both positive, is mn < 10?
(1) m < 2
(2) n < 5

For instance, in the example above what if both "m" and "n" were negative? Could you solve the problem? Why or Why not?

Kudos [?]: 1 [0], given: 15

Director
Joined: 14 Dec 2012
Posts: 832

Kudos [?]: 1630 [1], given: 197

Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Re: Basic Inequality Question - Multiplying Inequalities [#permalink]

### Show Tags

26 Jun 2013, 09:13
1
KUDOS
tmipanthers wrote:
Hi guys, I have a basic question that can probably be answered pretty quickly. I tried google searching but could not find my answer.

My question is, the guide has this rule: "Only multiply inequalities together if both sides of both inequalities are positive."

What if both inequalities were negative?

If m and n are both positive, is mn < 10?
(1) m < 2
(2) n < 5

For instance, in the example above what if both "m" and "n" were negative? Could you solve the problem? Why or Why not?

see this rule is because inequality sign changes when a negative thing is multipled...

example:
3 > 2===>now in this case if you multiple both sides with a negative number lets us suppose -2
then LHS=-6
RHS=-4
YOU CAN CLEARLY SEE THAT RHS > LHS ==>Initially LHS>RHS.
So guide is actually asking to keep caustion ...because we people forget to change the inequality some times.

If m and n are both negative, is mn < 10?
(1) m < 2
(2) n < 5

now as you if m and n are negative ..then there product will be postive..
product of two numbers <10
(1) m < 2==>we dont know about n hence ==not sufficient
(2) n < 5==> we dont know about M hence==not sufficient

now combining m is negative and m<2 and n is negative too and n<5
again not sufficient
take n=-10
m=-2===>mn=20==which is greater than 10.NO
Now take m=-1..n=-3
==mn=3===which is <10.YES.
ans E

KUDOS if it helped
_________________

When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...

learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment

Kudos [?]: 1630 [1], given: 197

Intern
Joined: 22 Mar 2013
Posts: 11

Kudos [?]: 1 [0], given: 15

Re: Basic Inequality Question - Multiplying Inequalities [#permalink]

### Show Tags

26 Jun 2013, 09:20
Thank you very much Shaileshmishra! That was very helpful. In fact, do you mind if I ask you another question on inequalities.

The guide also says: "Note that you can only take the square root of an inequality for which both sides are definitely not negative, since you cannot take the square root of a negative number."

I am confused about the scope of this rule.
If I am given this
"x^2>9"

Then that means |x| > 3

Can I not say then X > 3 or x <-3?
It seems I am taking the square root anyways but allowing for both a positive and negative possibilities of X. Is this correct? In what situation does the rule I just posted control if not this one?

I hope I made my question clear enough!

Kudos [?]: 1 [0], given: 15

Director
Joined: 14 Dec 2012
Posts: 832

Kudos [?]: 1630 [1], given: 197

Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Re: Basic Inequality Question - Multiplying Inequalities [#permalink]

### Show Tags

26 Jun 2013, 09:36
1
KUDOS
tmipanthers wrote:
Thank you very much Shaileshmishra! That was very helpful. In fact, do you mind if I ask you another question on inequalities.

The guide also says: "Note that you can only take the square root of an inequality for which both sides are definitely not negative, since you cannot take the square root of a negative number."

I am confused about the scope of this rule.
If I am given this
"x^2>9"

Then that means |x| > 3

Can I not say then X > 3 or x <-3?
It seems I am taking the square root anyways but allowing for both a positive and negative possibilities of X. Is this correct? In what situation does the rule I just posted control if not this one?

I hope I made my question clear enough!

hi,
see the book rule is perfectly fine.
actually the defenition of square root holds only for positive numbers, see the attached graph ==>it is defined only for positive values of X.
"x^2>9"....(1)
Then that means |x| > 3
this is perfectly done....
in equation one x^2==>this thing is greater than 9===>means we can say that it is positive===>x^2 is positive ..now as the rule says you can take the square root of positive number. so you have done perfectly fine.==>we dont have to worry about the value of x ===>we have to think as we are taking square root of x^2 then x^2 must be positive.
just keep always in your mind: sqrt of x^2 = mod of x==>as you have done.

one example :
x^2>-16....==> then in this case dont take sqr root of -16...as it is negative....this example lil weird ,but i think i made my point

kudos appreciated.
Attachments

why.gif [ 3 KiB | Viewed 1235 times ]

_________________

When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...

learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment

Kudos [?]: 1630 [1], given: 197

Intern
Joined: 22 Mar 2013
Posts: 11

Kudos [?]: 1 [0], given: 15

Re: Basic Inequality Question - Multiplying Inequalities [#permalink]

### Show Tags

26 Jun 2013, 10:05
shaileshmishra wrote:
tmipanthers wrote:
Thank you very much Shaileshmishra! That was very helpful. In fact, do you mind if I ask you another question on inequalities.

The guide also says: "Note that you can only take the square root of an inequality for which both sides are definitely not negative, since you cannot take the square root of a negative number."

I am confused about the scope of this rule.
If I am given this
"x^2>9"

Then that means |x| > 3

Can I not say then X > 3 or x <-3?
It seems I am taking the square root anyways but allowing for both a positive and negative possibilities of X. Is this correct? In what situation does the rule I just posted control if not this one?

I hope I made my question clear enough!

hi,
see the book rule is perfectly fine.
actually the defenition of square root holds only for positive numbers, see the attached graph ==>it is defined only for positive values of X.
"x^2>9"....(1)
Then that means |x| > 3
this is perfectly done....
in equation one x^2==>this thing is greater than 9===>means we can say that it is positive===>x^2 is positive ..now as the rule says you can take the square root of positive number. so you have done perfectly fine.==>we dont have to worry about the value of x ===>we have to think as we are taking square root of x^2 then x^2 must be positive.
just keep always in your mind: sqrt of x^2 = mod of x==>as you have done.

one example :
x^2>-16....==> then in this case dont take sqr root of -16...as it is negative....this example lil weird ,but i think i made my point

kudos appreciated.

Superb explanation! Thank you again.

Kudos [?]: 1 [0], given: 15

Re: Basic Inequality Question - Multiplying Inequalities   [#permalink] 26 Jun 2013, 10:05
Display posts from previous: Sort by