## Saturday, 29 October 2011

### Numbers-8 (CAT-2001)

If x>5 and y<-1, then which of the following statements is true:
(1)(x+4y) > 1      (2) x > -4y        (3) -4x < 5y        (4) None of these
Solution follows here:

Solution:
We need to know some basics about inequalities:
“If we multiply with a positive number on both sides, the inequality remains same.
But, if we multiply with a negative number, the inequality changes”
Given x>5 and y<-1
Now we check the given options one by one:
option-1         (x+4y) > 1
x>5;   y<-1 =>4y<-4
If we take x=6 and 4y = -7, then x+4y = -1 < 1
But, if we take x=8 and 4y = -5, then x+4y = 3 > 1
So it is ambiguous, option is wrong
option-2         x > -4y
x>5;     y<-1  => -4y>4
If we take x=6 and -4y = 5, then x > -4y
But, if we take x=6 and -4y = 7 (which is also possible), then x < -4y
So it is ambiguous, option is wrong
option-3         -4x < 5y
x>5 => -4x < -20;       y<-1 => 5y < -5
If we take -4x=-21 and 5y = -6, then -4x < 5y
But, if we take -4x=-21 and 5y = -22, then -4x > 5y
So it is ambiguous, option is wrong