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

Redeem

Is x > y?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Sun Jan 09, 2011 12:25 pm
Thanked: 1 times

Is x > y?

by diaca » Fri Jan 28, 2011 12:56 pm
Is x > y?

(1) sqrt (x)> y
(2) x^3 > y

Source Manhattan Gmat
I don't get part of the explanation given in the test.

C
Thanks
Top
Source: — Data Sufficiency |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Fri Jan 28, 2011 2:10 pm
diaca wrote:Is x > y?

(1) √x > y
(2) x³ > y
Whenever powers of variables are concerned, check for values greater than 1 and less than 1.

Statement 1: √x > y
If x > 1, then x > √x > y => x > y
If x < 1, then √x > x => x may not be greater than y

Not sufficient

Statement 2: x³ > y
If x > 1, then x³ > x but x may or may not be greater than y
If x < 1, then x > x³ > y

Not sufficient

1 & 2 Together: If x > 1, x³ > x > √x > y => x > y
And if x < 1, √x > x > x³ > y => x > y

Sufficient.

The correct answer is C.
Last edited by Anurag@Gurome on Sat Aug 20, 2011 7:00 pm, edited 1 time in total.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Master | Next Rank: 500 Posts
Posts: 131
Joined: Fri Jun 18, 2010 10:19 am
Location: New York, NY
Thanked: 10 times

by aleph777 » Fri Jan 28, 2011 2:15 pm
The thing about a sqrt is that it can only ever reveal the absolute value of a number.

Statement 1 says that sqrt x > y. I think the question expects you to think, ok, let's square both sides, and then we have the sqrt canceled out and: x > y^2, which means x must be greater than y. But when you square a sqrt, you end up with |x|. In other words, you can't tell whether the natural value of x is positive or negative. Thus, x could be 5 and y could be 2, in which case, x > y, but x could also equal -5. The absolute value hides the sign of x, so we can't tell just yet. Insufficient.

Statement 2 says x^3 > y. That could mean -2^3 > -20, or it could mean that 2^3 > 3. Etc. Insufficient, as well.

Combined, however, sqrt x > y tells us that the absolute value of x is greater than y, and x^3 > y tells us that even if x is negative, its negative value cubed is still greater than y. Therefore, -2^3 > y, 2^3 >y 0^3 > y, etc.

Sufficient. C
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 35
Joined: Sun Dec 02, 2007 1:06 pm

by jaguar123 » Sat Aug 20, 2011 5:59 am
Will the GMAT Test us for root of negative fractions?
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Sat Aug 20, 2011 6:01 am
jaguar123 wrote:Will the GMAT Test us for root of negative fractions?
GMAT does not require to deal with imaginary numbers. Hence roots of any negative number is not defined for GMAT.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
User avatar
Senior | Next Rank: 100 Posts
Posts: 35
Joined: Mon Jul 11, 2011 11:47 am
Thanked: 1 times
Followed by:1 members

by AVbyT » Sat Aug 20, 2011 9:20 am
Anurag@Gurome wrote:
diaca wrote:Is x > y?

(1) √x > y
(2) x³ > y
Whenever powers of variables are concerned, check for values greater than 1 and less than 1.

Statement 1: √x > y
If x > 1, say x = 4, then x > √x > y => x > y
If x < 1, say x = 1/4, then √x > x => x may not be greater than y

Not sufficient

Statement 2: x³ > y
If x > 1, say x = 8, then x³ > x > y => x > y
If x < 1, say x = 1/8, then x > x³ => x may not be greater than y

Not sufficient

1 & 2 Together: If x > 1, x³ > x > √x > y => x > y
And if x < 1, √x > x > x³ > y => x > y

Sufficient.

The correct answer is C.

Hello Anurag@Gurome - I think there's a slight error in your explanation for Statement 2:

Statement 2: x³ > y
If x>1, say x = 2 => x³= 8. Now y=6 or 1 so in this condition x may or may not be greater than y
However, if x<1, say x = 1/2 => x³ = 1/8 and in this case x (will always be greater than) > x³ and since x³>y so will x > y.

You got the right answer but reversed the explanation for the conditions in Statement 2.

Yea?

- Amit
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pm
Location: Milpitas, CA
Thanked: 1854 times
Followed by:523 members
GMAT Score:770

by Anurag@Gurome » Sat Aug 20, 2011 6:58 pm
AVbyT wrote:You got the right answer but reversed the explanation for the conditions in Statement 2.
Thanks Amit.
Editing my reply.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Post new topic Post Reply
• Page 1 of 1