Inequality Dilema

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vineetbatra: Master | Next Rank: 500 Posts; Posts: 355; Joined: Thu Feb 19, 2009 12:42 pmFollowed by: 1 member; Thanked: 2 times

by vineetbatra » Fri Jan 29, 2010 4:34 am

Friends,

I have amajor problem solving inequalities, the biggest problem is where to start. Should I solve them Algebrically or by plugging in numbers. If Plugging then what numbers to use. Can someone please explain, with a few examples and scenarios.

I did go through MGMAT guide but that didn't really help too much. I have a test in a week and any help will be much appreciated.

Thanks,

Vineet

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Source: Beat The GMAT — Data Sufficiency | Fri Jan 29, 2010 4:34 am

sars72: Master | Next Rank: 500 Posts; Posts: 241; Joined: Wed Jan 27, 2010 10:10 pmFollowed by: 2 members; Location: Chennai; Thanked: 23 times; GMAT Score:690

by sars72 » Fri Jan 29, 2010 4:42 am

With inequalities, there are a host of ways one can go about solving. Plugging in, Algebraic and Graphic are the more popular methods of solving inequalities.

I for one prefer a combo of plugging in and algebraic, whichever works best. No one option is the best for all. Each problem is unique and while for one plugging in may give you the answer in 10 seconds, it may take forever on problems which could have been easily solved algebraically. So, there's no BEST method.

One thing you've got to remember is that you have to change the sign when you multiply or divide both sides of the inequality by a negative value, you have to change the sign. Another important point to note is that you cannot multiply or divide both sides of an inequality by an unknown, say variable 'x', becuase you do not, at the time of solving, know whether it is positive or not!

Best way for learning inequalities, as is the case for most other topics, is to practice solving problems. Start with low level before working your way up. You will find loads of problems on the forum. But, start with OG problems.

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vineetbatra: Master | Next Rank: 500 Posts; Posts: 355; Joined: Thu Feb 19, 2009 12:42 pmFollowed by: 1 member; Thanked: 2 times

by vineetbatra » Fri Jan 29, 2010 8:02 am

Thanks for the reply Sars, well I know all the rules, just that I spend too much time trying to figure out where to start from.

Then I start, take too much time, panic and move one, I am usually able to solve 2-3 steps into it, and falter just when I am about to find the answer.

I am not sure how to tackle this.

Vineet

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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

by papgust » Fri Jan 29, 2010 6:59 pm

At one stage, not long before, i was really struggling with inequalities. The key is to really start from bottom. I was madly looking for some good tutorials in net as i don't have a good book. I also got hold of my high school math book (which i feel is the best).

To name a few online tutorials,
https://www.purplemath.com/modules/ineqsolv.htm
https://www.sosmath.com/algebra/inequali ... neq01.html - Very good basics.

Then i started solving problems in a flurry to get into the groove. I was then comfortable with the concept.

As sars72 mentioned, the key is to solve problems but only after you understand the concept. Visualize the number line while solving inequalities. It will really help you.

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fibbonnaci: MBA Student; Posts: 403; Joined: Tue Dec 22, 2009 7:32 pmFollowed by: 22 members; Thanked: 98 times

by fibbonnaci » Fri Jan 29, 2010 8:19 pm

Also you could post those inequalities questions that bother you. you will get great insights from the community, further enhancing your grip on the concepts.

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vineetbatra: Master | Next Rank: 500 Posts; Posts: 355; Joined: Thu Feb 19, 2009 12:42 pmFollowed by: 1 member; Thanked: 2 times

by vineetbatra » Tue Feb 02, 2010 5:42 am

Hello,

Thanks a lot for the replies, after little more analysis I have found that my problem is specifically with inequalities that have more than 1 variables. I can solve them, but the problem is to figure out the right way to solve them so that I do not create a web of different ways in which I get entangled.

I am posting 4 questions, all I need is one approach to solve them, step by step and also the reason for the approach. I will really appreciate if someone can help me.

Thanks,

Vineet

1) if x <> 0, is (X^2 +1 )/X > Y
A x = Y
B. y>0

OA C

2) is x < Y

A. 1/x<1/y
B. x/y<0

OA is C

3) is w-x<y-z
A. Y>W
B. Z<X

OA is C

4) is x^2>y^2
A) x<Y
B Y<0

OA is C

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Tue Feb 02, 2010 6:04 am

vineetbatra wrote:Hello,

Thanks a lot for the replies, after little more analysis I have found that my problem is specifically with inequalities that have more than 1 variables. I can solve them, but the problem is to figure out the right way to solve them so that I do not create a web of different ways in which I get entangled.

I am posting 4 questions, all I need is one approach to solve them, step by step and also the reason for the approach. I will really appreciate if someone can help me.

Thanks,

Vineet

1) if x <> 0, is (X^2 +1 )/X > Y
A x = Y
B. y>0

is the highlighted portion correct bcoz a no can not be bth <0 and >0 at same point of time

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vineetbatra: Master | Next Rank: 500 Posts; Posts: 355; Joined: Thu Feb 19, 2009 12:42 pmFollowed by: 1 member; Thanked: 2 times

by vineetbatra » Tue Feb 02, 2010 6:07 am

This sign means not equal to i.e. x is not equal to 0.

Thanks,

Vineet

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Tue Feb 02, 2010 6:17 am

vineetbatra wrote:Hello,
1) if x <> 0, is (X^2 +1 )/X > Y
A x = Y
B. y>0

first simplify the eqn
(X^2 +1 )=
(x^2+1)/x-y
=(x^2+1-xy)/x........EQN1

s1)X=Y
--->EQN1=1/X SINCE WE DO NOT KNOW ANY THING ELSE ABOUT X IT CAN BE >0 OR <0
NOT SUFF

S2)Y>0
SINCE WE DO NOT KNOW ANY THING ELSE ABOUT X IT CAN BE >0 OR <0

S1)+S2)
1/X = 1/Y (X=Y)
AND SINCE Y>0
X
1/X>0
AND THEREFORE X>0
SUFF
HENCE c

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Tue Feb 02, 2010 6:34 am

vineetbatra wrote:Hello,

3) is w-x<y-z------>W+Z<Y+X
A. Y>W
B. Z<X

SOLN:
1)Y>W
WE DNT HAVE RELATIONSHIP B/N Z AND X
INSUFF

2)Z<X
WE DNT HAVE RELATIONSHIP B/N W AND Y
HENCE INSUFF

1+2)
Y+X>W+Z
SUFF
IMO C

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Tue Feb 02, 2010 8:29 am

vineetbatra wrote:
4) is x^2>y^2
A) x<Y
B Y<0

OA is C

soln:
A)by plugging

s1) let x=3 and y=4 satisfies s1) condition x<y
x^2=9 and Y^2=16
here x^2<y^2
hence no

but if x=-4 and y=-3
x<y satisfies s1)
and x^2=16>9=y^2
hence yes

two diff ans for same condition hence s1) is insuff

s2)
y<0 but we dnt whether x>y or y>x
hence insuff

s1)+S2)
for x<y ; and y<0
if y=-3 x=-5---->x^2>y^2
if y=-5 and x=-6--->x^2>y^2
true for all values y<0 and x<y
hence suff

usually plugging values is always better than direct solving
but one has to be careful for selecting no's , it must satisfy all the given condition and hidden hints
solving by plugging no's always save time

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