Is 2x - 3y < x^2
1) 2x - 3y = -2
2) x>2 and y>0
inequality
This topic has expert replies
-
- Master | Next Rank: 500 Posts
- Posts: 116
- Joined: Tue Mar 31, 2009 10:50 am
- 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 2x - 3y < x²?LulaBrazilia wrote:Is 2x - 3y < x²?
1) 2x - 3y = -2
2) x > 2 and y > 0
Statement 1: 2x - 3y = -2
We can now take the target question, and replace 2x - 3y with -2 to get: Is -2 < x²?
Since x² must be greater than or equal to zero (as with all SQUARED numbers), we can conclude that it MUST be the case that -2 < x²
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x > 2 and y > 0
This one is a little trickier.
First recognize that if y > 0, then 3y = some positive value. So, if we take 2x and SUBTRACT 3y, we get a lesser value.
In other words, we can be certain that 2x - 3y < 2x
Now let's compare 2x and x²
If x > 2 (as we're told in statement 2), x² MUST be greater than 2x (test it out if you're not convinced)
In other words, it MUST be the case that 2x < x²
Now that we're derived two inequalities, we can combine them to get 2x - 3y < 2x < x²
From this, we can see that it MUST be the case that 2x - 3y < x²
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer = D
Cheers,
Brent
- Patrick_GMATFix
- GMAT Instructor
- Posts: 1052
- Joined: Fri May 21, 2010 1:30 am
- Thanked: 335 times
- Followed by:98 members
Statement 1 tells us that the left side of the inequality in the original Q is negative. Since the right side (x^2) must be at least 0, we know that it must be greater than the left side 2x-3y must be less than x^2. we can definitively answer the Q.
Statement 2 is most useful if we manipulate the original question to say: is -3y < x^2 - 2x ?. Since y>0, the left side will be negative. Since x>2, x^2 > 2x and the right side will be positive. So we know for sure that -3 < x^2 - 2x and we can answer the Q definitively.
Each statement is sufficient; the answer is D. The solution below is taken from the GMATFix App.
-Patrick
Statement 2 is most useful if we manipulate the original question to say: is -3y < x^2 - 2x ?. Since y>0, the left side will be negative. Since x>2, x^2 > 2x and the right side will be positive. So we know for sure that -3 < x^2 - 2x and we can answer the Q definitively.
Each statement is sufficient; the answer is D. The solution below is taken from the GMATFix App.
-Patrick
- Check out my site: GMATFix.com
- To prep my students I use this tool >> (screenshots, video)
- Ask me about tutoring.