Hi,
How would you answer this question?
Is x/3+3/x>2
(1) x<3
(2) x>1
Cheers,
ds - > question
This topic has expert replies
- MAAJ
- Master | Next Rank: 500 Posts
- Posts: 243
- Joined: Sun Jul 12, 2009 7:12 am
- Location: Dominican Republic
- Thanked: 31 times
- Followed by:2 members
- GMAT Score:480
Is it (x/3) + (3/x) > 2 ?
ccassel wrote:Hi,
How would you answer this question?
Is x/3+3/x>2
(1) x<3
(2) x>1
Cheers,
"There's a difference between interest and commitment. When you're interested in doing something, you do it only when circumstance permit. When you're committed to something, you accept no excuses, only results."
- vineeshp
- Legendary Member
- Posts: 965
- Joined: Thu Jan 28, 2010 12:52 am
- Thanked: 156 times
- Followed by:34 members
- GMAT Score:720
From 1) x < 3
If we choose x=2 --> x/3 + 3/x > 2
But if x = -2 (still satisfies x < 3) we can get that x/3 + 3/x < 0 hence !>2.
From 2)
x>1
At x=1 ( I know this is not valid, bt only for illustration)
x/3 + 3/x = 3 1/3
At x=2
x/3 + 3/x = 13/6 = 2 1/6
At x=3
x/3 + 3/x = 2
At x=4
x/3 + 3/x = 4/3 + 3/4 = 25/12 = 2 1/12
So expression attains minimum value of 2 at x = 3.
But it still does not prove that x/3 + 3/x > 2.
If you combine 1 and 2.
We just deduced that x/3 + 3/x decreases from 3 1/3 at x = 1 and stops at 2 when x = 3. So in between these values x/3 + 3/x > 2.
Hence C.
If we choose x=2 --> x/3 + 3/x > 2
But if x = -2 (still satisfies x < 3) we can get that x/3 + 3/x < 0 hence !>2.
From 2)
x>1
At x=1 ( I know this is not valid, bt only for illustration)
x/3 + 3/x = 3 1/3
At x=2
x/3 + 3/x = 13/6 = 2 1/6
At x=3
x/3 + 3/x = 2
At x=4
x/3 + 3/x = 4/3 + 3/4 = 25/12 = 2 1/12
So expression attains minimum value of 2 at x = 3.
But it still does not prove that x/3 + 3/x > 2.
If you combine 1 and 2.
We just deduced that x/3 + 3/x decreases from 3 1/3 at x = 1 and stops at 2 when x = 3. So in between these values x/3 + 3/x > 2.
Hence C.
Vineesh,
Just telling you what I know and think. I am not the expert.
Just telling you what I know and think. I am not the expert.
- manpsingh87
- Master | Next Rank: 500 Posts
- Posts: 436
- Joined: Tue Feb 08, 2011 3:07 am
- Thanked: 72 times
- Followed by:6 members
taking lcm we have (x^2+9)/3x >2;ccassel wrote:Hi,
How would you answer this question?
Is x/3+3/x>2
(1) x<3
(2) x>1
Cheers,
1) if x<3; i.e. it includes all the value to the left of 3 on the number line..!!
if x=1 we have 10/3=3.33>2;
if x=-1 we have 10/-3, -3.33<2
as two different results are possible here for different values of x hence 1 is not sufficient to answer the question.
2)x>1; all the values to the right of 1 on the number line.. now consider x=3;
9+9/9=2 2 is not<2; and for all other values we have results greater than 2, hence 2 alone is also not sufficient to answer the question.
combining 1 and 2 we have
1<x<3;
for all the values between 1 and 3; x is greater than 2 hence both together are sufficient to answer the question...!!!!
C
O Excellence... my search for you is on... you can be far.. but not beyond my reach!
- manpsingh87
- Master | Next Rank: 500 Posts
- Posts: 436
- Joined: Tue Feb 08, 2011 3:07 am
- Thanked: 72 times
- Followed by:6 members
my approach here is to combine two different fractions into one...!!for example if we have to solve the question like 1/3+1/2+1/4+1/6 then our approach should be to combine four different fractional terms into one i.e. to minimize the number of terms in the question..!!!ccassel wrote:manpsingh87 - Why did you calculate the lcm of x/3+3/x>2? How do you get that result?
Thanks in advance for the tips.
Cheers,
O Excellence... my search for you is on... you can be far.. but not beyond my reach!