Find each value

Algebra Level 2

$'abc'$ represents a three digit number where $a, b, c$ are the digits of it and $'bc'$ also represents a two digit number where $b$ and $c$ are the digits of it. If $abc=(bc)^2$ and $bc=c^2$ , then which digits are represented by $a, b, c$ ?

This problem is a part of the set Problems for everyone!!!

a=7; b=6; c=5

a=6; b=5; c=2

a=6; b=2; c=5

a=4; b=5; c=6

1 solution

S P
May 24, 2018

It is given that $bc=c^2$

Hence, $c=5 ~ \text{or} ~ 6$ because any power of $5 ~ \text{and} ~ 6$ has units digit as $5 ~ \text{and} ~ 6$ which we want

$\therefore b=2~\text{or}~3$ because $5^2=25~\text{and}~ 6^2=36$

Now we are given $abc=(bc)^2$ and $25^2=625~\text{and}~36^2=1296$

Since, $(bc)^2$ must be a three digit number $bc=25$ and $a=6$

Hence, $\boxed{a=6;b=2;c=5}$

Find each value

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