A number when divided........

Number Theory Level 2

A number when divided by a divisor leaves a remainder of 5 and when divided by twice the divisor leaves a remainder of 45. Find the divisor?

All of the above 10 20 40

1 solution

Andrea Palma
May 10, 2015

Write

$n = q\cdot d + 5$ $n = q^\prime \cdot 2d + 45$

subtract the equations and get

$(q - 2q^\prime)d = 40$

So the divisor $d$ is a divisor of $40$ . Since $45$ is a remainder of the division by $2d$ we have necessarily $45 < 2d$ . This inequality is true for only one divisor $d$ of $40$ , namely $d = 40$ .

$n = 125$ and $d = 40$ suit the assumptions.

Andrea Palma - 6 years, 1 month ago

A number when divided........

1 solution

0 pending reports