Data Sufficiency

Q, Is X -ve number??

1, 9x > 10x

2, x+3 is +ve

the answer is A according to gmat off guide

my Q is its easy if we take into account only integers to arrive to the ans A.

but how do u decide not to check for fractions

i.e if x =1/90

then 1 becomes 1/9 > 1/10

which is true

does the word number in the question suggest to check only for intergers,

if we need to check for fractions will the Q be only

is X +ve ??

Fractions are just "smaller" integers, I guess.

A can be re-written as:

9x > 10x - subtract 9x from each side

0 > x - x is clearly negative.

For such a simple exercise, I recommend you just solve it algebraically. Plugging in numbers is a risky strategy and should be used with caution! What if you pick the wrong numbers? I've already written something about it here.

Q, Is X -ve number??

1, 9x > 10x

2, x+3 is +ve

Just divide the first inequality by X. If x is positive We get:

9 > 10. Which is not possible

x must be negative because the sign would flip when dividing by a negative number.

9 < 10. Suff.

2. x + 3 > 0

x > -3

X can be any number, positive or negative or zero, greater than -3. Insuff.

Adeel, here's where you've gone wrong:

adeel wrote:i.e if x =1/90
then 1 becomes 1/9 > 1/10

If x=1/90 then

9x = 9/90 = 1/10
10x = 10/90 = 1/9

(1) Says 1/10>1/9, which is not true, hence 1/90 is not a valid solution for x