NTSE Stage 2 SAT 2015 Question Paper

When a natural number x is divided by ‘5’, the remainder is 2
∴ $\mathrm{x}=5\mathrm{P}+2$ ... (i)
When a natural number y is divided by ‘5’ the remainder is 4
∴ $;\mathrm{y}=5\mathrm{Q}+4$ ... (ii)
When x + y is divided by ‘5’, the remainder is z
Adding Eq. (i) and (ii), we get
$\mathrm{x}+\mathrm{y}=5\left(\mathrm{P}+\mathrm{Q}\right)+6$
Now when x + y is divided by ‘5’ remainder will be 1
∴ $\mathrm{z}=1$
Hence the value of $\frac{2\mathrm{z}-5}{3}$
$=\frac{2\left(1\right)-5}{3}=-1$