Algebra - Inequalities strategy, help!!!! - The Beat The GMAT Forum

Algebra - Inequalities strategy, help!!!!

Expert replies

gbb: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Tue Mar 17, 2009 3:59 pm

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

Like this post

Source: Beat The GMAT — Data Sufficiency | Sun Mar 22, 2009 11:42 am

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

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.

Like this post

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

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

Like this post

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

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

Like this post

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

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

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review