If b < 2 and 2x - 3b = 0, which of the following must be true?

(A) x > -3

(B) x < 2

(C) x = 3

(D) x < 3

(E) x > 3

Sol: given 2x-3b=0 or x =3b/2 and b<2

St 1: x>-3 lets consider possible value of b if b =-24 then x =-36 so x>-3 could be true but not must be true

St2: x<2 if b=1.9 the x= 3*1.9/2 or x> 2 so this condition could be true but not must be true

St3: x=3 for x =3 we need b=1 which is possible but again falls under could be true cause b can take any value

Less than 2

St4:x<3 -------> or 3b/2<3 we get

(3b-6)/2< 0 or 3b-6< 0

Or b< 2 which is same as the original given condition so we need not look beyond option D but for curiosity lets look at E as well

St 5: x> 3 or 3b/2>3 or (3b-6)/2 >0

3b-6>0 or b>2 clearly not true

Ans D

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