If x and y are positive, is x^3 > y?
(1) square root of x > y
(2) x > y
x^3 > y
This topic has expert replies
- MartyMurray
- Legendary Member
- Posts: 2131
- Joined: Mon Feb 03, 2014 9:26 am
- Location: https://martymurraycoaching.com/
- Thanked: 955 times
- Followed by:140 members
- GMAT Score:800
First, since we know x and y are both positive, we don't have to worry about 0 or negative numbers.Abhijit K wrote:If x and y are positive, is x³ > y?
(1) √x > y
(2) x > y
Statement 1 is tricky. If √x > y, then it seems that x³ would also be greater than y, but things are not so simple, because fractions can work differently from whole numbers.
If x = 1/4 and y = 1/3, then √x = 1/2 and 1/2 > 1/3.
However (1/4)³ is way less than 1/3.
So Statement 1 is insufficient.
Statement 2 also seems to indicate that x³ > y. For instance, if x = 2 and y = 1, then x³ > y.
But once again given fractional values of x and y, x could be greater than y and x³ could be less than y. For instance if x = 1/2 and y = 1/3, then x³ = (1/2)³ = 1/8 which is less than 1/3.
So Statement 2 is insufficient.
Combining the statements we can still find examples that make x³ > y and fractions that fit both statements and result in x³ < y.
For example if x = 1/2 and y = 1/3, then x > y and √x > y, but (1/2)³ = 1/8 which is less than 1/3.
So the statements in combination are still insufficient.
Choose E.
Last edited by MartyMurray on Mon Mar 23, 2015 8:50 am, edited 5 times in total.
Marty Murray
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
Perfect Scoring Tutor With Over a Decade of Experience
MartyMurrayCoaching.com
Contact me at [email protected] for a free consultation.
- DavidG@VeritasPrep
- Legendary Member
- Posts: 2663
- Joined: Wed Jan 14, 2015 8:25 am
- Location: Boston, MA
- Thanked: 1153 times
- Followed by:128 members
- GMAT Score:770
This is a classic number-picking question.
S1: square both sides to get x > y^2
x = 2, y^2 = 1
x^3 = 8 y = 1, so YES, x^3 is bigger
x = 1/2, y^2 = 1/4
x^3 = 1/8, y= 1/2, so NO, x^3 is not bigger
S1: Not Sufficient
S2: Reuse x = 2, y = 1
x^3 = 8, y = 1, YES, x^3 is bigger
x = 1/2, y = 1/3
x^3 = 1/8, y = 1/3, NO, x^3 is not bigger
Together: We know: x > y^2 and x > y
x = 2, y = 1 satisfies both
x^3 = 8, y = 1, YES, x^3 is bigger
x = 1/2, y = 1/3 satisfies both (y^2 = 1/9, and 1/2 > 1/9)
x^3 = 1/8, y = 1/3, NO, x^3 is not bigger
Still not sufficient.
Answer is E
S1: square both sides to get x > y^2
x = 2, y^2 = 1
x^3 = 8 y = 1, so YES, x^3 is bigger
x = 1/2, y^2 = 1/4
x^3 = 1/8, y= 1/2, so NO, x^3 is not bigger
S1: Not Sufficient
S2: Reuse x = 2, y = 1
x^3 = 8, y = 1, YES, x^3 is bigger
x = 1/2, y = 1/3
x^3 = 1/8, y = 1/3, NO, x^3 is not bigger
Together: We know: x > y^2 and x > y
x = 2, y = 1 satisfies both
x^3 = 8, y = 1, YES, x^3 is bigger
x = 1/2, y = 1/3 satisfies both (y^2 = 1/9, and 1/2 > 1/9)
x^3 = 1/8, y = 1/3, NO, x^3 is not bigger
Still not sufficient.
Answer is E
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Question stem: Is y < x³?Abhijit K wrote:If x and y are positive, is x³ > y?
(1) √x > y
(2) x > y
This problem can also be solved GRAPHICALLY.
The red region in the figure above consists of all points such that y < x³.
Question stem, rephrased:
Is y a positive value in the red region?
Statement 1: y < √x
Statement 2: y < x
The dark purple region in the figure above consists of all points such that y < √x and y < x.
We need to determine whether this dark purple region lies completely below the graph of y = x³.
Statements combined:
Putting together y < √x, y < x and y = x³, we get:
The dark green region in the figure above consists of all points such that y < √x and y < x.
Some of the dark green region lies ABOVE y = x³ (implying that y can be GREATER than x³), while some of the dark green region lies BELOW y = x³ (implying that y can be LESS than x³).
Thus, the two statements combined are INSUFFICIENT.
The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3