If x is not equal to zero, is (x^2+1)/x > y ?
(1) x=y
(2) y>0
C
Source : MGMAT[/list]
Inequality
This topic has expert replies
- ygdrasil24
- Senior | Next Rank: 100 Posts
- Posts: 42
- Joined: Tue Dec 06, 2011 8:06 am
- Thanked: 3 times
- Followed by:1 members
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Target question: Is (x^2+1)/x > y ?ygdrasil24 wrote:If x is not equal to zero, is (x^2+1)/x > y ?
(1) x=y
(2) y>0
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
- ygdrasil24
- Senior | Next Rank: 100 Posts
- Posts: 42
- Joined: Tue Dec 06, 2011 8:06 am
- Thanked: 3 times
- Followed by:1 members
Thanks Brent.Brent@GMATPrepNow wrote:Target question: Is (x^2+1)/x > y ?ygdrasil24 wrote:If x is not equal to zero, is (x^2+1)/x > y ?
(1) x=y
(2) y>0
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
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 ?
- faraz_jeddah
- Master | Next Rank: 500 Posts
- Posts: 358
- Joined: Thu Apr 18, 2013 9:46 am
- Location: Jeddah, Saudi Arabia
- Thanked: 42 times
- Followed by:7 members
- GMAT Score:730
ygdrasil24 wrote:Thanks Brent.Brent@GMATPrepNow wrote:Target question: Is (x^2+1)/x > y ?ygdrasil24 wrote:If x is not equal to zero, is (x^2+1)/x > y ?
(1) x=y
(2) y>0
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
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
- ygdrasil24
- Senior | Next Rank: 100 Posts
- Posts: 42
- Joined: Tue Dec 06, 2011 8:06 am
- Thanked: 3 times
- Followed by:1 members
- faraz_jeddah
- Master | Next Rank: 500 Posts
- Posts: 358
- Joined: Thu Apr 18, 2013 9:46 am
- Location: Jeddah, Saudi Arabia
- Thanked: 42 times
- Followed by:7 members
- GMAT Score:730
aah yes.. but you did make a typo
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.
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.
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
When we replace y with x we can rephrase the target question as: Is (x^2+1)/x > x?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 ?
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