Question

If [x] stands for the greatest integer less or equal to x, then in order than the set of equations

x – 3y = 4 ; 5x + y = 2 ; [2p]x – [e]y = [2a] may be consistent, then ‘a’ should lie in –

• A. $\left\lbrack 3,\frac{7}{2} \right)$
• B. $\left( 3,\frac{7}{3} \right)$
• C. $\left( 3,\frac{7}{3} \right\rbrack$
• D. None of these

Answer 1

Answer: (A)

$\left\lbrack 3,\frac{7}{2} \right)$

Answer 2

On solving x – 3y = 4 and 5x + y = 2, we get x = $\frac{5}{8}$, y = –$\frac{9}{8}$. As [2p] = 6 and (5) = 2. So that the three equations are

consistence if [2p].$\frac{5}{8}$ + [e] $\frac{9}{8}$= [2a] or [2a] = 6

This gives 6 £ 2a < 7 or 3 £ a < $\frac{7}{2}$.

Hence (1) is correct answer.