Is the eqn > 2

Problem is
is x/3 + 3/x > 2 ?

Stmt 1: x < 3

This is insufficient coz of the following cases:
let x = 2
2/3 + 3/2
> 2

let x = 0
value is indeterminate
So insufficient


Stmt 2. x > 1

For all values of x > 1, the value of 3/x + x/3 is > 2.
Sufficient.


So ans is B.

What is the OA ?

thanks
-V

vittalgmat wrote:Stmt 2. x > 1

For all values of x > 1, the value of 3/x + x/3 is > 2.
Sufficient.


So ans is B.

Wrong.

If x = 3, then 3/x + x/3 = 2, which disqualifies the inequality. Hence statement 2 is insufficient on its own.

Both statements together specify the lower and upper boundaries for x to satisfy the inequality. Choose C.

-BM-

IMO A. Is x/3 + 3/x >2 ? could be simplified to x^2 - 6x+9 >0?

which could be further simplified as x-3 >0 => so the question is x>3?

St 1 tells is x<3 ...Hence sufficient
St 2 x>1 doesn't help much.

Hence A.

GID09 wrote:IMO A. Is x/3 + 3/x >2 ? could be simplified to x^2 - 6x+9 >0?

which could be further simplified as x-3 >0 => so the question is x>3?

I don't think you can treat the question stem as a known fact. Try plugging a negative value into the question stem and you will see that the inequality does not hold.

-BM-

BM, Could you explain what you mean by "Try plugging a negative value into the question stem and you will see that the inequality does not hold" ?

I was just rearranging the variables without disturbing the inequality right?

Thanks,
GID09

GID09 wrote:BM, Could you explain what you mean by "Try plugging a negative value into the question stem and you will see that the inequality does not hold" ?

I was just rearranging the variables without disturbing the inequality right?

hi GID09,

in your solution, you did the following:

"is x/3 + 3/x > 2 ?" was changed to -> "is x^2 - 6x + 9 > 2?".

when you manupulated the inequality, you assumed x to be positive. thats where the problem is. we don't know whether x is positive or negative. if x is negative, you will have to flip the sign when you multipled the inequality with x, and you will arrive at a different inequality.

the point of the question is to prove whether (x/3 + 3/x) is always greater than 2. Without any boundaries for x, (x/3 + 3/x) can take values less than 2 or greater than 2.

All we know in statement 1 is that x<3. But is this sufficient? For eg. say x = -1, then (x/3 + 3/x) will be a negative value, i.e. less than 2. but if x = 2, then (x/3 + 3/x) is greater than 2. so statement 1 is insufficient on its own.

hope this explanation helps.

-BM-

BM, I agree. Thanks!

bluementor wrote: Wrong.

If x = 3, then 3/x + x/3 = 2, which disqualifies the inequality. Hence statement 2 is insufficient on its own.

Both statements together specify the lower and upper boundaries for x to satisfy the inequality. Choose C.

-BM-

The OA is C.

But i still dont understand one thing.

Statement 1. This is insufficient which can be determined by plugging in values 2 and 0 for x which leads to different results.

Statement 2. This is where i am lost. If i plug in 3, it would yield that x/3 + 3/x = 2. So 2=2 and would lead to an answer of NO. But when we plug in 2 for x, this would yield that x/3 + 3/x = 0.66 + 1.5 = 2.16> 2 and would lead to an answer of YES. So this statement is insufficient.

Now taking both statements together, we get 1<x<3, plug in 2 we get an answer of YES the eqn is > 2. Now substitute x = 1.5, we get 1.5/3 + 3/1.5 = 0.5 + 2 = 2.5 > 2. Similarly if we plug in x = 2.5 we get 2.5/3 + 3/2.5 = 0.83 + 1.2 = 2.03 > 2. So yes. Hence both together are sufficient.

Although i got this right, the explanation said "Using statement 2, if we substitute x=3, then it would result in the eqn being 2=2, so x cannot be 3 hence this statement is insufficient because it violates the inqeuality." --> I also see that bluementor also gave the same explanation. But i dont understand this. The question asks if the eqn is > 2 and if the eqn is = 2, then the question is answered as NO its is not greater than 2. Whats with this "disqualify the inequality." Please explain this to me.

I hope i didn't make it too complicated to understand.

Thanks in advance..

bluementor wrote:

vittalgmat wrote:Stmt 2. x > 1

For all values of x > 1, the value of 3/x + x/3 is > 2.
Sufficient.


So ans is B.

Wrong.

If x = 3, then 3/x + x/3 = 2, which disqualifies the inequality. Hence statement 2 is insufficient on its own.

Both statements together specify the lower and upper boundaries for x to satisfy the inequality. Choose C.

-BM-

Damn!! so silly of me!!! .. careless error!!.
Thanks BM for pointing it out.
Will be more careful next time.

rgds
-V

hk wrote:
Although i got this right, the explanation said "Using statement 2, if we substitute x=3, then it would result in the eqn being 2=2, so x cannot be 3 hence this statement is insufficient because it violates the inqeuality." --> I also see that bluementor also gave the same explanation. But i dont understand this. The question asks if the eqn is > 2 and if the eqn is = 2, then the question is answered as NO its is not greater than 2. Whats with this "disqualify the inequality." Please explain this to me.

I hope i didn't make it too complicated to understand.

Thanks in advance..

hk, sorry for replying so late. I only saw your message this morning.

Anyway, I guess Ian has already clearified your doubt. Post back if something still bothers you.

-BM-