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DS Inequality Questions

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by m7373 » Sat Feb 23, 2008 1:09 pm
I don't understand why i'm having difficulty with DS Inequality Questions even after lots of practice. For example, look at the following:

If x and n are integers, is the sum of x and n less than zero?

(1) x + 3 < n – 1

(2) -2x > 2n

I would appreciate your thoughts on how you might approach a question such as this. Is your first step to plug in answers, simplify, or...?

I know what the answer is, i'm just looking for quick and clever ways to solve these types of questions.

Thanks!
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Source: — Data Sufficiency |
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by joshi.komal » Sun Feb 24, 2008 2:21 am
Hi There,

In any DS question you have to first simplify the question itself and then attack the statements.

So in this question lets translate words into algebra
If x and n are integers, is the sum of x and n less than zero?
Given: x and n integers
Is x + n <0 ?
or Is x < -n ?

Any statement which can answer any of the above question is sufficient
(1) x + 3 < n – 1
or x < n - 4 Does not answer the question but lets try to plug in values
since given that x and n are integers so you should not use fractions but plug in at least 3 types of values NPZ (Negative Positive and Zero)
-- --- N P Z
----- n -2 2 0
----- x -6 -2 -4
-- n+x -8 0 -4
n+x<0 Y N -4

You can see you are getting 2 answers for same question so it is insufficient.


2. -2x > 2n
or -x > n (Since 2 is known and positive)
or x < -n
SUFFICIENT

Hence the answer is B

Hope it helps
Last edited by joshi.komal on Sun Feb 24, 2008 4:51 pm, edited 1 time in total.
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by m7373 » Sun Feb 24, 2008 1:43 pm
thanks for your explanation joshi.komal. Just to double check, the reason why (1) was insufficient was because "n+x" equaled 0 at one point meaning it didn't satisfy our original statement, correct?

thanks
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by joshi.komal » Sun Feb 24, 2008 4:54 pm
m7373 wrote:thanks for your explanation joshi.komal. Just to double check, the reason why (1) was insufficient was because "n+x" equaled 0 at one point meaning it didn't satisfy our original statement, correct?
thanks
Yes thats right... I have also edited my post as there were some display errors :)

Hope it will be better now
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by sampleresume » Sun Apr 13, 2008 5:30 pm
:D :D :D
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by honeysn » Mon Aug 23, 2010 4:49 pm
Hi,

I am still confused on 1st condition. Per explaination above, if I take n=2, then x should be less than -2. This means x+n will be still less than zero. Kindly explain. Looks like 1st is also a sufficient condition. Thanks
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by lakshmi86 » Sat Aug 28, 2010 6:22 am
joshi.komal wrote:Hi There,

In any DS question you have to first simplify the question itself and then attack the statements.

So in this question lets translate words into algebra
If x and n are integers, is the sum of x and n less than zero?
Given: x and n integers
Is x + n <0 ?
or Is x < -n ?

Any statement which can answer any of the above question is sufficient
(1) x + 3 < n � 1
or x < n - 4 Does not answer the question but lets try to plug in values
since given that x and n are integers so you should not use fractions but plug in at least 3 types of values NPZ (Negative Positive and Zero)
-- --- N P Z
----- n -2 2 0
----- x -6 -2 -4
-- n+x -8 0 -4
n+x<0 Y N -4

You can see you are getting 2 answers for same question so it is insufficient.


2. -2x > 2n
or -x > n (Since 2 is known and positive)
or x < -n
SUFFICIENT

Hence the answer is B

Hope it helps
Please tell me why this analysis is wrong?

x+3<n-1
x-n+4<0
(x-n)+positive value <0
so, x-n < 0
x<n
or x>-n => x+n>0
cant we clearly say that x+n is not less than zero if we approach it this way?

Regards,
Lakshmi
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by anantbhatia » Sun Aug 29, 2010 2:40 am
x<n ----->correct till here
or x>-n ------>incorrect.

x<n Multiply both sides by -1 and change the direction of inequality.

therefore, -x>-n

Take a real life eg. 2<3 and -2>-3

eg. another one -1<3 and 1>-3. I hope you have understood. Remember to stick to the basics. They never fail.
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by jayanti » Sat Jul 16, 2011 7:04 am
Hey, can we not take the values on the left hand side and make everything >0.
Pls explain with this method....
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