yourshail123 wrote:Thanks Brent for sharing the video, it does give some useful tips, such as the 'Good Numbers' and prime numbers. Of course these values -10,-1,-1/2,0,1/2,1,10 are very important in most of the questions; however, there are certain typical examples which ask for other values than the above.
Yes, there is no thumb rule; and there is where I am having hard time. For me, mostly, the problems where even/odd or squares/powers numbers are required which needs picking values, adding inequality to it causes more confusion.
For example, below ques:
If ab ≠0, does a = b?
(1) x^a = x^b
(2) x = x^2
Here, while evaluating Statement 1) I simply missed to check for x=0/x=1.
It irritates when such small values cost so dearly on a simple question. And I always go wrong on such types.
It seems my applicative skill is lagging behind even if I am conceptually clear.
I think I see the problem now.
Before you start plugging in values, you should see if you can do a little work up front that helps limit the numbers you plug in.
For example, in statement 1, we have
x^a = x^b
At this point, it may be difficult to find values to plug in that yield conflicting answers to the target question.
To make the task easier, we can do some work first.
Divide both sides by x^b to get
(x^a)/(x^b) = 1
Simplify to get
x^(a-b)= 1
At this point, we can see that we have several possibilities:
Case 1: a-b = 0, in which case
a does equal b
Case 2: x = 1, in which case
a may or may not equal b
Case 3: x = -1 and a-b is an even integer, in which case
a may or may not equal b
At this point, it's much easier to plug in values.
Similarly, we shouldn't start plugging in values for statement 2 (
x = x^2), until we first do some work.
Subtract x from both sides to get
0 = x^2 - x
Factor the right side to get
0 = x(x - 1)
At this point, we can see that x must equal 0 or 1.
The takeaway here is that we shouldn't jump directly into plugging in values until we first try to do a little work.
Cheers,
Brent
