Question

When a natural number $x$ is divided by $5$, the remainder is $2$. When a natural number y is divided by $5$, the remainder is 4. The remainder is $z$ when $x+y$ is divided by $5$. Then the value of $\frac{2z-5}{3}$ is

• A. $-1$
• B. $1$
• C. $-2$
• D. $2$

Answer 1

Answer: (A)

$-1$

Given

$x\equiv 2mod\left(5\right)$ and $y\equiv 4mod\left(5\right)$ ...... (1)

and $x+y\equiv zmod\left(5\right)$ ....... (2)

Adding x and y from (1) we get

$x+y\equiv 6mod\left(5\right)\equiv 1mod\left(5\right)$

Equating with equation (2) we get

$z=1$

$\therefore$ $\frac{2z-5}{3}=\frac{2-5}{3}=\frac{-3}{3}=-1$