Data Sufficiency

@garuhape: finally, third and last question I got A

Is x/12>y/40 ?

12=2^2 *3; 40=2^3 *5; [(2^3) * 3*5]= 120
x/12 - y/40 >0; (10x-3y)/120 >0 OR 10x-3y>0 ? <--- this is our question as of now
st(1) 10x<3y-6 --> 10x-3y<-6 Sufficient, as it's clear that 10x-3y<0
st(2) 12x-7>4y --> 12x-4y>7 OR 4(3x-y)>7, 3*(3x-y)>3*(7/4), 9x-3y>21/4 <--- this expression can be -ve Only if x>21/4 But we don't know by how much x should be larger -Not Sufficient

IOM A

garuhape wrote: 3. Is x/12>y/40 ?
10x < 3y -6
12x - 7 > 4y[/b]

no-no clock, I answer only x=-3; and x=1.5 two critical points within set. They keep inequality condition. Intervals are not precise. I would agree on math mistake if the solution intervals were found, BUT here's only set with two critical points - believe or not // agree?

clock60 wrote:@ night reader
may be it is better to put aside this
it closer to the truth, but probably you commit math mistake, you answer -3<x<1.5. as i see
try x=1.45
3*1.45-2=2,35
|2*1.45-5|=|-2.1|=2.1
2.35>2,1 not true

@ reader i agree but only partly, my answer to this, is that x(-3;1,4 (7/5)) including -3, and 1,4, within this interval any given x will result in proper inequility, out of this range not.
but in your answer x=1.5 does not fit inequality, try to insert x=1.45, or x=1.5 as i did in previous post and you see that it is not needed range, that is why i think that it is your math mistake somewhere

you are correct, math mistake
I need to get full 48 hours sleep before my GMAT in two weeks, otherwise I will mark my score to the hell ...
finally it's x E {-3;1.4} the miscalculation was after discriminant section

clock60 wrote:@ reader i agree but only partly, my answer to this, is that x(-3;1,4 (7/5)) including -3, and 1,4, within this interval any given x will result in proper inequility, out of this range not.
but in your answer x=1.5 does not fit inequality, try to insert x=1.45, or x=1.5 as i did in previous post and you see that it is not needed range, that is why i think that it is your math mistake somewhere

1. Find the solution set for the following inequality |3x - 2| ≤ |2x - 5|?

Alternate Approach :
I am sure most of you are quite comfortable with drawing the line : y = |x| {If you are not, it is simply y=x for x>=0, and y=-x, for x<0}

Using this approach, as shown in the diagram we have to just solve two equations :
1) For point "A" : 3x-2 = -(2x-5) => x =7/5
2) For point "B" : -(3x-2) = -(2x-5) => x = -3

The values of x which lie between A and B is the solution set : -3 ≤ x ≤7/5

[Note : Please note that while drawing the lines, it helps to consider that the slopes for the lines |3x-2| (which is 3) are more than that of the lines |2x-5| (which is 2). This help us to understand that there is a point "B" which is the intersection point of the two lines. If the slope of the lines were equal the two lines would never meet and if the slopes were in opposite order, the two lines would intersect in another way (clearly not as "B")]

[/img]