A logic problem by Ilham Saiful Fauzi

Logic Level 3

Let $P=abcd$ and $Q=badc$ are 4-digit number with $a$ and $b$ are not equal to zero, such that $P=4Q$ . Find the value of $P-Q$

1 solution

A Former Brilliant Member
Jun 8, 2016

I am taking $Q$ as first.

• $b$ will 1 and 2 because If the number exceeds 2 that $P$ will be 5 digit number.

Now taking $c$ and multiplying it by $4$ .
Here all numbers eliminates lefting $2$ .

• $c$ will be $2$ .

•And,since $c$ is $2$ , $d$ is $8$ .

•Now, simple multiplying $1a82×4=a128$ , this gives $a=7$ .

Now, $P-Q=7128-1782=\boxed{5346}$ .