BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

tough inequality

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 659
Joined: Mon Dec 14, 2009 8:12 am
Thanked: 32 times
Followed by:3 members

tough inequality

by Gurpinder » Thu Oct 06, 2011 12:05 pm
if x is NOT = 0, is (x^2 +1)/x > Y?

(1) x = y
(2) y>0

I don't understand how (1) is not sufficient.

To multiply by variable, we need to take the positive and the negative:
(x^2 +1)/x > Y
x^2 +1 > xy ?

And stmt 1 says y=y hence the question becomes, x^2+1>x^2? In which case, YES! regardless of whether x is negative or even a fraction.

now if we take the negative of x:

(-x)(x^2 +1)/x > Y(-x)
-x^2 -1 > -xy
x^2 + 1 < xy which equals x^2 + 1 < x^2

Even here, statement (1) is sufficient to answer the question! how is it insufficient!?
"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.
Top
Source: — Data Sufficiency |
Senior | Next Rank: 100 Posts
Posts: 61
Joined: Tue Apr 13, 2010 3:29 am
Thanked: 8 times

by n@resh » Thu Oct 06, 2011 12:23 pm
Gurpinder wrote:if x is NOT = 0, is (x^2 +1)/x > Y?

(1) x = y
(2) y>0

I don't understand how (1) is not sufficient.

To multiply by variable, we need to take the positive and the negative:
(x^2 +1)/x > Y
x^2 +1 > xy ?

And stmt 1 says y=y hence the question becomes, x^2+1>x^2? In which case, YES! regardless of whether x is negative or even a fraction.

now if we take the negative of x:

(-x)(x^2 +1)/x > Y(-x)
-x^2 -1 > -xy
x^2 + 1 < xy which equals x^2 + 1 < x^2

Even here, statement (1) is sufficient to answer the question! how is it insufficient!?
It's simple, as you endup with two answers from using statement 1, that's the reason why it's not sufficient.
Even statement 2, isn't enough.

Using both statements: x = y and y>0, we can confirm (x^2 +1)/x > Y. for all the values of x and y.
Answer C.
Top
User avatar
Legendary Member
Posts: 659
Joined: Mon Dec 14, 2009 8:12 am
Thanked: 32 times
Followed by:3 members

by Gurpinder » Thu Oct 06, 2011 12:25 pm
thx.

i see what i was doing wrong. i need some coffee!
"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 496
Joined: Tue Jun 07, 2011 5:34 am
Thanked: 38 times
Followed by:1 members

by sl750 » Fri Oct 07, 2011 2:28 am
Gurpinder wrote:if x is NOT = 0, is (x^2 +1)/x > Y?

(1) x = y
(2) y>0

I don't understand how (1) is not sufficient.

To multiply by variable, we need to take the positive and the negative:
(x^2 +1)/x > Y
x^2 +1 > xy ?

And stmt 1 says y=y hence the question becomes, x^2+1>x^2? In which case, YES! regardless of whether x is negative or even a fraction.

now if we take the negative of x:

(-x)(x^2 +1)/x > Y(-x)
-x^2 -1 > -xy
x^2 + 1 < xy which equals x^2 + 1 < x^2

Even here, statement (1) is sufficient to answer the question! how is it insufficient!?
In statement, all it says is x=y, but we don't know the sign of x or y. So you can't multiply the right hand side by x and assume the inequality sign will remain the same

All we get from statement 1 is, Is 1/x >0 ?. x could be positive or negative. Insufficient
Top
Post new topic Post Reply
• Page 1 of 1