Question

Find the solution set for [3x] + [4x] + [5x] = 14, where [] indicates the greatest integer function.

• A. $x<\frac{3}{2}$
• B. $1\le x$ < $\frac{4}{3}$
• C. x > $\frac{3}{2}$
• D. $\frac{5}{4}\le$x < $\frac{27}{20}$

Answer 1

The correct option is D $\frac{5}{4}\le$x < $\frac{27}{20}$

It is convenient to check with the values taken between the intervals given in the choice, x = 1 gives [3x] + [4x] + [5x] = 12 $\ne$ 14). So, options (a), (b) are eliminated.
For x > 3/2 , we get a higher value than 14.
$x=\frac{5}{4}$ gives [3x] + [4x] + [5x] = 14