Q.Is x > y?
(1) x ^ 1/2 > y
(2) x^3 > y
Q.Is X > Y?
(!) x^2 >y
(2) x^ 1/2 < y
For questions like these, what are the suitable numbers that we need to test for . I take positive and negative fractions like x = 1/4, y = 1/3etc. Sometimes I get stuck due to these numbers only.
Please suggest any approach to take on these inequality questions.
Inequality
This topic has expert replies
- prachi18oct
- Master | Next Rank: 500 Posts
- Posts: 269
- Joined: Sun Apr 27, 2014 10:33 pm
- Thanked: 8 times
- Followed by:5 members
- 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
For this problem, I posted two approaches here:prachi18oct wrote:Q.Is x > y?
(1) x ^ 1/2 > y
(2) x^3 > y
https://www.beatthegmat.com/x-y-t280459.html
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
- 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
Test a value for x whose square and root can be calculated easily.prachi18oct wrote:
Q.Is X > Y?
(!) x^2 > y
(2) x^ 1/2 < y
Let x=4.
The statements become:
Statement 1: 16 > y
Statement 2: 2 < y
Both statements are satisfied if y=3, in which case x>y.
Both statements are satisfied if y=5, in which case x<y.
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
-
- GMAT Instructor
- Posts: 2630
- Joined: Wed Sep 12, 2012 3:32 pm
- Location: East Bay all the way
- Thanked: 625 times
- Followed by:119 members
- GMAT Score:780
There are lots of ways to see that neither statement alone is sufficient. (Number picking is probably the easiest. For instance, in the first one, x could be negative and y positive, or vice versa. In the second, we could have y = 4 and √x = 1, or we could have y = 3 and √x = 2.)Is x > y?
S1:: x² > y
S2:: y > √x
Taking the two together, we have
x² > y > √x
This makes it easier to test numbers. We could have √x = 2 and y = 3, in which case x = 4 and x > y. But we could also have √x = 2 and y = 15, in which case x = 4 (as before) but now y > x.
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
Aside: Once we combine the statements, we get: √x < y < x²
If we ignore the y, we see that √x < x²
When it comes to the squares and square roots of positive numbers, there are three possible cases:
case a: If 0 < k < 1, then √k > k²
case b: If k = 1, then √k = k²
case c: If 1 < k, then √k < k²
Since the combined statements tell us that √x < x², we can conclude that 1 < x
When we test certain values of x that are greater than 1 (as others have done above), we see that the combined statements are still insufficient.
Cheers,
Brent
If we ignore the y, we see that √x < x²
When it comes to the squares and square roots of positive numbers, there are three possible cases:
case a: If 0 < k < 1, then √k > k²
case b: If k = 1, then √k = k²
case c: If 1 < k, then √k < k²
Since the combined statements tell us that √x < x², we can conclude that 1 < x
When we test certain values of x that are greater than 1 (as others have done above), we see that the combined statements are still insufficient.
Cheers,
Brent