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.

now in your question:

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.

NO DEFINITE ANSWER...HENCE NOT SUFFICIENT

ans E

KUDOS if it helped

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