inequality

[beater]

Is x>3?

1. (x-3) (x-2) (x-1) > 0
2. x>1

[yalanand]

I feel answer is E


1) Suppose x=1.9 then still the given equation is greater than 0..and x< 3

2) Not sufficient as explained above..

Combining both of them Not sufficient.

[welcome]

To prove X >3.

1) (X-3) (X-2) (X-1) >0

To make this hapenne..
1. X should not equal to 3 or 2 or 1.
2. either all of then are +ve or at least 2 of them are -ve.

But cant say whether X>3 or not, because for X=4 this relation is true, but it is also tru for X=1.7. so NOT SUFF

2) X>1, simpally X=2 is false but x=4 is true for the statement given. so NOT SUFF


but combining both will say this,
X>1 and X is not 1,2,3 it means x>3.

Ans : C

[logitech]

Is x-3 > 0

1. (x-3) (x-2) (x-1) > 0

- - +
+ + +

are the only two ways we can have a positive product

we don't know which so INSUF

2. x>1[/quote]

Hmm

x-1> 0 means

x>1 so we still can not find out whether x>3 ( on another note, if this option was x>4 , we would choose B )

1+2 together


- - +
+ + +

so we have one POSITIVE for sure so we are left with

- - or + +

we now that x >1 but if it is less than 2

we will have

- -

if x is greater than 3 we will have

+ +

Do we know anything about where x lies ? NO

E

[logitech]

To prove X >3.

1) (X-3) (X-2) (X-1) >0

To make this hapenne..
1. X should not equal to 3 or 2 or 1.
2. either all of then are +ve or at least 2 of them are -ve.

But cant say whether X>3 or not, because for X=4 this relation is true, but it is also tru for X=1.7. so NOT SUFF

2) X>1, simpally X=2 is false but x=4 is true for the statement given. so NOT SUFF


but combining both will say this,
X>1 and X is not 1,2,3 it means x>3.

Ans : C

This is a very nice solution but we are NOT told that X can be only integer.

[welcome]

logitech,
Where is this mentioned that X should be an integer. Or it is some kind of rule or assumption. Please tell me the details.

Thanks in advance.

[logitech]

logitech,
Where is this mentioned that X should be an integer. Or it is some kind of rule or assumption. Please tell me the details.

Thanks in advance.

Well nothing is mentioned about X so it can be any number. Fraction or integer.