teal wrote:
Is the product of a positive and a negative integer less than -10?
(1) The positive integer is greater than 3
(2) The negative integer is less than -2
To answer this question, we need the solid understanding that as the magnitude of negative numbers increases, their value decreases. so, in the negative number universe, -3>-10. With this in mind, we are ready to take on this question. So let us begin.
S1. take x=-ve and y=+ve. We can take y=4 as per this statement since the only constraint is that y>3. We should actively try and get opposing answers to 'yes/no' kind of questions. Let's do yes first.
so we established that y=4; let us assume x=-10 (as it can be any negative number). x*y=4*-10=-40 <-10. Remember the rule negative nu,ber rule above.
Now let's see of we can get a 'no' and call it a day: y is till 4, let us take x=-1 (remember, we are purposely trying to prove no here)
xy=4*-1=-4 which is NOT less than -10. Hence disproved and this has rendered the statement insufficient. Strike A and D off.
S2. Take x=-3 (-3<-2). again let's purposely try and get a yes and no.
Yes first: y= 10 (since there are no constraints on y). xy= -3*10= -30<-10. ok.
No: y= 1: xy= -3*1= -3 which is NOT <-10. Hence disproved and this has rendered the statement insufficient. Strike B off as well.
Now combining the two, we can solve for 3 or 4 cases and we will notice that all of them answer in 'Yes' therefore the answer here is C.