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I have issues with picking smart numbers for inequalities

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I have issues with picking smart numbers for inequalities [#permalink] New post 02 Apr 2009, 00:42
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I have issues with picking smart numbers for inequalities ques in data sufficiency. Especially when the numbers could be an integer, a fraction, positive or negative. At times, I spend more time than I should just trying out numbers. What strategy or approach should I take when facing such ques? Example a ques from my initial post.

Is x>y?

(1) x=y+2

(2)x/y=y-1
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Re: Picking smart no. for inequalities problem-need help! [#permalink] New post 02 Apr 2009, 14:36
This one is relatively easy question because here LHS=RHS while in some question you will get ineq in st 1 n 2.

Try +ive, -ve and 0. Try values which will not result what you intend so that you can move on to next st.

Say here from 1 you knw that

x-y=2 so x is greater than y.

Lets move on to st 2

x=y^2-y; try y=0 and y =3 you will get 0 and 6 resp. Not suff.

SO A.
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Re: Picking smart no. for inequalities problem-need help! [#permalink] New post 03 Apr 2009, 06:39
hemantsood wrote:
This one is relatively easy question because here LHS=RHS while in some question you will get ineq in st 1 n 2.

Try +ive, -ve and 0. Try values which will not result what you intend so that you can move on to next st.

Say here from 1 you knw that

x-y=2 so x is greater than y.

Lets move on to st 2

x=y^2-y; try y=0 and y =3 you will get 0 and 6 resp. Not suff.

SO A.


I agree, it is not the best example for illustration since I couldn't find a good one at the point of posting. Maybe this one.
If x not equal -y, is (x-y)/(x+y)>1?
(1) x>0
(2) y<0

It can be quite tricky especially when there is 2 or more unknown variable and the unknown variables are numbers and not integers. We do have to consider fractions too, right? Also is there numbers I should avoid picking? Like number 1? :|
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Re: Picking smart no. for inequalities problem-need help! [#permalink] New post 03 Apr 2009, 15:24
Lets reduce this to

1-y/x / 1+y/x

Now what we need to prove this greater than both x and y as signs are important here...

1 tells abt x so not suff assume any number does not matter here...try some value of y closer to x and far away from x.
2 tell abt y less than zero as we need x

Come to both of the statements.

Take (5, -1) 1+1/5/1-1/5 clearly greater than zero ... wow we feel this is sufficient.

Lets reverse it take (1,-5) 1+5/1-5 hmmm not sufficient. Ans E.

I hope you getting the idea try to prove that eq cant be solve by these value .. try to prove that eq is wrong like the french justice system.

For eq involving square ineq use value (0,1) and (1, infi) same for the LHS of zero

For normal eq try 0 positive and negative number... you prob feel what the heck this gonna take time... believe me for first 10 questions you will take time and then it will be fun and after sometime you will be able to solve directly without plugging number and without any paper.
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Re: Picking smart no. for inequalities problem-need help! [#permalink] New post 13 Apr 2009, 22:39
joyseychow wrote:
I have issues with picking smart numbers for inequalities ques in data sufficiency. Especially when the numbers could be an integer, a fraction, positive or negative. At times, I spend more time than I should just trying out numbers. What strategy or approach should I take when facing such ques? Example a ques from my initial post.

Is x>y?

(1) x=y+2

(2)x/y=y-1



As far as picking values are concerned, we have got no choice but pick numbers.
-1,0,1, .5, -.5
And then 2 threshhold numbers.. like in statement 1, the number is 2.
But we can think differently.... whenever possible. Like
try to draw number line whereever possible.
Like in 1, we can easily say that.. x will lie on the right of Y on the number line..hence x will always be greater than Y and is sufficient.

Just putting 2 values as 0 and 1 for Y gives two values..
hence no need to further calculate.
But the problem arises.. only.. when 1 and 2 are together not sufficient..
in that case we need to go for more iterations.

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Re: Picking smart no. for inequalities problem-need help! [#permalink] New post 03 Nov 2011, 09:49
If x not equal -y, is (x-y)/(x+y)>1?
(1) x>0
(2) y<0

Could someone explain it by another way please?
Re: Picking smart no. for inequalities problem-need help!   [#permalink] 03 Nov 2011, 09:49
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