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Inequality

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sun Jun 23, 2013 5:06 am
ygdrasil24 wrote:If x is not equal to zero, is (x^2+1)/x > y ?

(1) x=y
(2) y>0
Target question: Is (x^2+1)/x > y ?

This might be a good candidate for rephrasing the target question. (Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100)

Take the inequality (x^2+1)/x > y, and rewrite it as: (x^2)/x + 1/x > y
Simplify: x + 1/x > y

Rephrased target question: Is x + 1/x > y ?

Statement 1: x = y
Take the rephrased target question and replace x with y to get: Is y + 1/y > y ?
Subtract y from both sides: Is 1/y > 0 ?
Since y can be positive or negative, we cannot answer the target question.
Statement 1 is NOT SUFFICIENT

Statement 2: y > 0
We have no information about x, so we cannot answer the target question with certainty
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
From statement 1, we were able to reduce the target question to: Is 1/y > 0 ?
When we add statement 2, we can see that 1/y is definitely greater than 0
So the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
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by ygdrasil24 » Tue Jun 25, 2013 12:27 am
Brent@GMATPrepNow wrote:
ygdrasil24 wrote:If x is not equal to zero, is (x^2+1)/x > y ?

(1) x=y
(2) y>0
Target question: Is (x^2+1)/x > y ?

This might be a good candidate for rephrasing the target question. (Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100)

Take the inequality (x^2+1)/x > y, and rewrite it as: (x^2)/x + 1/x > y
Simplify: x + 1/x > y

Rephrased target question: Is x + 1/x > y ?

Statement 1: x = y
Take the rephrased target question and replace x with y to get: Is y + 1/y > y ?
Subtract y from both sides: Is 1/y > 0 ?
Since y can be positive or negative, we cannot answer the target question.
Statement 1 is NOT SUFFICIENT

Statement 2: y > 0
We have no information about x, so we cannot answer the target question with certainty
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
From statement 1, we were able to reduce the target question to: Is 1/y > 0 ?
When we add statement 2, we can see that 1/y is definitely greater than 0
So the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Thanks Brent.
I have a different approach :
(1) x = y, so (x^2+1)/x > y can be re written as
(x^2+1)/x> x * x
so it becomes Is (x^2+1)>x^2
Whatever sign x has, x^2+1 will always be greater than X^2 .

So A is sufficient, B is not sufficient since we dont know sign of x on LHS so answer for me is A
Whats wrong here ?
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by faraz_jeddah » Tue Jun 25, 2013 3:26 am
ygdrasil24 wrote:
Brent@GMATPrepNow wrote:
ygdrasil24 wrote:If x is not equal to zero, is (x^2+1)/x > y ?

(1) x=y
(2) y>0
Target question: Is (x^2+1)/x > y ?

This might be a good candidate for rephrasing the target question. (Aside: We have a free video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100)

Take the inequality (x^2+1)/x > y, and rewrite it as: (x^2)/x + 1/x > y
Simplify: x + 1/x > y

Rephrased target question: Is x + 1/x > y ?

Statement 1: x = y
Take the rephrased target question and replace x with y to get: Is y + 1/y > y ?
Subtract y from both sides: Is 1/y > 0 ?
Since y can be positive or negative, we cannot answer the target question.
Statement 1 is NOT SUFFICIENT

Statement 2: y > 0
We have no information about x, so we cannot answer the target question with certainty
Statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
From statement 1, we were able to reduce the target question to: Is 1/y > 0 ?
When we add statement 2, we can see that 1/y is definitely greater than 0
So the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Thanks Brent.
I have a different approach :
(1) x = y, so (x^2+1)/x > y can be re written as
(x^2+1)/x> x * x
so it becomes Is (x^2+1)>x^2
Whatever sign x has, x^2+1 will always be greater than X^2 .

So A is sufficient, B is not sufficient since we dont know sign of x on LHS so answer for me is A
Whats wrong here ?

Check the part highlighted in bold. Where did the x in the denominator on LHS go?
It should be (x^2+1) > x^3
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by ygdrasil24 » Tue Jun 25, 2013 9:09 pm
Nopes,
The question contains only x in deonominator so when taken on RHS it should become x2
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by faraz_jeddah » Tue Jun 25, 2013 10:06 pm
aah yes.. but you did make a typo :cry:

Hmm well heres my reasoning - you dont know the sign of x, so you cant say for sure that the '>' sign will stay the same.
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by Brent@GMATPrepNow » Wed Jun 26, 2013 5:47 am
faraz_jeddah wrote: Thanks Brent.
I have a different approach :
(1) x = y, so (x^2+1)/x > y can be re written as
(x^2+1)/x > x * x
so it becomes Is (x^2+1)>x^2
Whatever sign x has, x^2+1 will always be greater than X^2 .

So A is sufficient, B is not sufficient since we dont know sign of x on LHS so answer for me is A
Whats wrong here ?
When we replace y with x we can rephrase the target question as: Is (x^2+1)/x > x?
However, we cannot multiply both sides by x to get: Is x^2 + 1 > x^2?
We cannot multiply both sides by x since we don't know whether x is positive or negative.
If x is positive, then the target question becomes Is x^2 + 1 > x^2?
If x is negative, then the target question becomes Is x^2 + 1 < x^2?

To see, why statement 1 is not sufficient, let's go back there:
Statement 1: x=y
There are several pairs of values that meet this condition. Here are two:
Case a: x = 1 and y = 1, in which case (x^2+1)/x > y
Case b: x = -1 and y = -1, in which case (x^2+1)/x < y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Cheers,
Brent
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