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

Answer (4)

Concept:

In the case of third option,we need to check for “-4x<5y”

Left part of the inequality (ie., -4x) is less than -20 => all possibilities are to the left of -20 on number line.

Right part of the inequality (ie., 5y) is less than -5 => all possibilities are to the left of -5 on number line.

We can compare the two values only if the respective possibilities lie on opposite directions of number line and there should not be any common possibilities between the two.