Is x/3 + 3/x >2
(1) x<2
(2) x>1
[spoiler]OA: C ; IMO B[/spoiler]
Here is my solution to reach B:
x/3 + 3/x >2
Cross multiplying the left hand side, we get
(x^2 + 9) / 3x > 2
we know x^2 will always be positive and 9 is also positive, so numerator will always be positive and greater than 9 for sure.
Now if x is -ve then eqn is false as denominator will be -ve.
And if x is +ve then eqn will be true as denominator will be +ve and offcourse x^2 + 9 will be many times greater.
In short question is asking, is X -ve or +ve ?
(1) x<2 ---> x can be positive or it can be -ve as well.(checked for max value 2 as well and answer is coming YES too)
(2) x>1 --> This says X is always +ve , meaning eqn is true.
Hence went with B.
Where am I going wrong.
Tricky DS from Grockit
This topic has expert replies
My solution is C.
I restate the formula by multiplying it with 3 to:
x+9/x>2
First checking statement 1:
X=1
1+9>6
X=-1
-1-9<6
false
Second checking statement 2:
x=2
2+4,5 > 6
Attention: number is getting smaller --> further testing
X=3
3+3 > 6
false
Checking both statements together:
extreme cases already tested X=1 and X=2
Thus answer is C.
I restate the formula by multiplying it with 3 to:
x+9/x>2
First checking statement 1:
X=1
1+9>6
X=-1
-1-9<6
false
Second checking statement 2:
x=2
2+4,5 > 6
Attention: number is getting smaller --> further testing
X=3
3+3 > 6
false
Checking both statements together:
extreme cases already tested X=1 and X=2
Thus answer is C.
Last edited by BastiG on Fri Aug 27, 2010 9:07 pm, edited 1 time in total.
loveusonu wrote:Is x/3 + 3/x >2
In short question is asking, is X -ve or +ve ? --> wrong conclusion. This is only true for the first statement but not for second. There it is important which number you choose.
- loveusonu
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does that mean I can't cross multiply in inequalities, same like we can't mlutiply\divide X uless known +ve or -ve??BastiG wrote:loveusonu wrote:Is x/3 + 3/x >2
In short question is asking, is X -ve or +ve ? --> wrong conclusion. This is only true for the first statement but not for second. There it is important which number you choose.
Because Cross multiplying x/3 + 3/x >2 leads to a different conclusion(as stated above)
Sonu
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When you want something desperately, the whole Universe conspires in helping to give it to you - The Alchemist
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When you want something desperately, the whole Universe conspires in helping to give it to you - The Alchemist
No you can cross-multiply. But look at the formula:loveusonu wrote:does that mean I can't cross multiply in inequalities, same like we can't mlutiply\divide X uless known +ve or -ve??BastiG wrote:loveusonu wrote:Is x/3 + 3/x >2
In short question is asking, is X -ve or +ve ? --> wrong conclusion. This is only true for the first statement but not for second. There it is important which number you choose.
Because Cross multiplying x/3 + 3/x >2 leads to a different conclusion(as stated above)
(x^2 + 9) / 3x > 2
If you input x=3
then
(9+9)/9=2
If You input x=4
then
(16+9)/12=2,08
Thus the second statement is insufficient.
- kvcpk
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Let me share a simple concept here.loveusonu wrote:Is x/3 + 3/x >2
(1) x<2
(2) x>1
a + 1/a >=2 whenever, a is positive.
a+1/a = 2 when a=1 else a+1/a>2
Now,
in tis case, a=x/3
Hence x/3 + 1/(x/3) >=2 when x/3 is positive.
x/3 + 1/(x/3) =2 when x/3=1 -> x=3
Else, x/3 + 1/(x/3) >2 for all positive x.
Hope this helps!!
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don't be afraid of failure and don't abandon it.
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don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)