Inequalities- Under One Minute Video Lecture - Banking Exams

hello everyone welcome to the session I
hope your preparation for Kat exam is
going on very good and to further
enhance your preparation I'm going to
discuss a very tricky question from
inequalities and that will make you
comfortable with the inequalities topic
this is the question from Karen Walker
2003 in this question it is given that V
is a variable ranging from minus 1 to 1
U is a variable ranging from minus 2 to
minus 0.5 Z ranges from minus 2 to minus
0.5 W is equal to we said upon you then
which of the following is necessarily
true four options are given in this
question and we have to find the range
for W that means we have to find the
minimum value of W possible for W and
the maximum possible value for W now see
W is equal to V is that upon you for
this question I am going to discuss two
different approaches first one will be a
bit linear as compared to the second one
so first approaches see in this question
we have to find the minimum possible
value for W and the maximum possible
value for W and W is a fraction we set
up on you
now just see if I want to maximize any
fraction then I have to maximize the
magnitude of the numerators and minimize
the magnitude of the denominators now in
this case we have two numerators V and
said we have to maximize the magnitudes
of these two numerators and U is the
only denominator and I have to minimize
the magnitude of U now if I observe
carefully value of Z will be negative
always because in this it is given that
it will range from minus 2 to minus 0.5
again when you of you would also be
negative always ranging from minus 2 to
minus 0.5 that means whatever will be
the value of Z or u that will cancel
each other negative sign will get
cancelled with each other of V and the
sorry of Z and you
and I'll have positive result of these
two values now depending on the value of
V I'll get positive or negative value
for W so now I have to observe only the
magnitude part for Z and you I don't
have to take tension about the sign for
Z n you know as V and Z both are
numerators I have to maximize the
magnitude of the numerators in order to
maximize that value of W maximum value
of V can be 1 magnitude vise make some
value of Z magnitude vise will be 2 and
maximum sorry I have to consider the
minimum value of U and the minimum value
of U is 0.5 because I know that negative
sign of Z and you will cancel each other
and we can be positive at this FLS
negative so this will be the maximum
possible value for W and this will be 4
so in this way I got the maximum
possible value for W and for this from
this only I know that second option
would be my answer if I have to further
see what will be the minimum possible
value for W no as I know that is sine of
Z and you will not affect the value of W
only V will matter for the sign of W and
if I take the value of V as minus 1 then
that value of W would be minus 4 and
this is the minimum possible value for W
because I already have maximized the
overall value of the friction and with
negative sign it will mean that this is
the minimum possible value for W so both
the minimum and the maximum values I am
getting an option number 2 that means
option number 2 is my answer so this is
the first approach and moving on to the
second approach for this question this
is a bit prettier approach just check
Vee is in the numerator and we can be
negative as well as positive and minimum
magnitude and maximum possible value of
the minimum possible value and maximum
possible value of V is minus 1 and 1
magnitude is again fun that means if I
have to check but can be the minimum and
maximum value of W then I have to see
that in which option I am getting
magnitude for both minimum and maximum
possible values is same because I know V
when your field will only change the
sign of that magnitude now in second
option minimum possible value is W
before and maximum possible value is for
sign is just the meta here so I have to
see in which option both minimum and
maximum magnitude is same and this thing
I am getting in second option that means
second option is the answer and this
thing I have observed only on the basis
of V because I know that sign of V will
matter and the minimum and possible in
the minimum and maximum value of W so in
from that approach second option is my
answer so friends I have discussed both
approaches for this cushion this
question was a bit trickier question
from cat exam and to know more about
inequalities and how to handle questions
based on options from the topic of
inequalities you can watch my full video
so thank you very much for attending the
session all the best thank you very much