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Algebra - Inequalities strategy, help!!!!

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Algebra - Inequalities strategy, help!!!!

by gbb » Sun Mar 22, 2009 11:42 am
Help!!! I’m very bad (slow) in solving algebra-inequalities DS questions. I can get right always spending more than 2minutes.

So, I was wondering if someone has a strategy to approach this type of question. I always try to pick number (very time-consuming! Maybe I’m not picking the right numbers)

So, if someone has a strategy to solve this type of questions I appreciate it!!! Could be anything:
1) to pick always x,y,z numbers (eg. -1,0,1)
2) or playing with algebra
3) or just by identifying patterns of some inequalities (categorize inequalities)
4) anything!

Please, Help!! Stacey, cramya, DanaJ???

Just to illustrate some problems, OG algebra-inequalities questions: 9,18,22,24,31,50,53,64,80,99,109,119,135,139,145

Below follows questions that I got wrong (I’m more interested to see an approach to solve this type of questions and solving the questions can illustrate this approach, but it’s not necessary):

OG DS 50
If x and y are positive, is x/y greater than 1?
(i) xy > 1
(ii) x-y > 0
answer:B

OG DS 80
Is a, b and c are integers, is a-b+c greater than a+b-c?
(i) b is negative
(ii) c is positive
answer:C

OG DS 119
Is 2x-3y < x^2?
(i) 2x-3y = -2
(ii) x>2 and y>0
answer:D

OG DS 139
If x<>y, is x-y/x+y>1?
(i) x>0
(ii) y<0
answer: E

OG DS 145
Is 1/p > r/r^2+2?
(i) p=r
(ii) r>0
answer: C
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by cramya » Sun Mar 22, 2009 1:16 pm
OG DS 80

Is a, b and c are integers, is a-b+c greater than a+b-c?
(i) b is negative
(ii) c is positive
answer:C

I would say simplify whats asked in the question as this may make it easier.

Eg:

Is a-b+c > a+b-c

Both a's cancels

So -b+c > b-c

Add +b to both sides

c > 2b-c

Add c to both sides

2c > 2b

Is c>b

The question simplifies to Is c>b

Now we can clearly see we need both statements to prove this.

Hence C
Last edited by cramya on Sun Mar 22, 2009 1:22 pm, edited 1 time in total.
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by cramya » Sun Mar 22, 2009 1:21 pm
OG DS 50
If x and y are positive, is x/y greater than 1?
(i) xy > 1
(ii) x-y > 0
answer:B

An important rule to keep in mind when manipulating inequalities is that u cant multiply or divide eithr side of an inequalitiy by a variable that u dont know what the sign is.

For example if the variable is positive then the inequalitiy does not change; if its negative the inequalitiy reverses. So the take away is before u multiply or divide both sides of an inequality absolutely u need to know the dign of the variable. If u dont then dont multiply or divide.


Coming to this problem

Is x/y>1

We can multiply both sides by y wihtout affecting the existing inequality since we know y is positive.

So the question boils down to Is x>y

Stmt I
xy > 1

x=10000 y=1
x=1 y=10000

INSUFF

Stmt II

x-y>0

Add y to both sides (addition is ok)

x > y

Exactly what we need

SUFF

B
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by cramya » Sun Mar 22, 2009 1:42 pm
OG DS 139
If x<>y, is x-y/x+y>1?
(i) x>0
(ii) y<0

Pl check my post here.Let me know if u still hv questions.

https://www.beatthegmat.com/variables-t26771.html


Regards,
CR
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by cramya » Sun Mar 22, 2009 1:47 pm
OG DS 139
If x<>y, is x-y/x+y>1?
(i) x>0
(ii) y<0
answer: E


1) Simplify the question

Is x-y/x+y > 1

x-y/x+y - 1>0 (take lcm for 1 and x+y which is x+y)


x-y - ( x+y) / x+y>0

x-y-x-y / x+y > 0

Is -2y / x+y > 0


Stmt I

x>0

No idea if y is positive or negative

INSUFF

Stmt II

y <0

No idea if x is postive or negative

INSUFF

Together

x>0 y<0

-2y is positive

x+y even though we know x is positive and y is negative we have no idea if x+y is positive or negative


x=1000 y =-1 YES

x= 1 y=-1000 NO

HENCE E

Hope this helps!


Regards,
CR
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