WMC 2018 Senior Problem 27

Level 2

Order the following from smallest to largest

$\left(a\right)2^{10}\times{10}^6$

$\left(b\right)\ 2^3\times200\times{10}^6$

$\left(c\right)\ 9\times{10}^8$

$\left(d\right)\ 8^5\times64000$

$(e) 2^3\times3^3\times4^3\times5^3\times{10}^3$

c,a,b,e,d

a,c,e,d,b

a,c,b,e,d

c,b,a,e,d

c,a,e,b,d

2 solutions

Julian Yu
Oct 20, 2018

These can be rewritten as:

a) $10^6\cdot 1024$

b) $10^6\cdot 1600$

c) $10^6\cdot 900$

e) $10^6\cdot 1728$ .

So clearly, $c<a<b<e$ . We can show that $e<d$ by dividing both sides by $8\cdot 64000$ , and it can be confirmed that $3^3\cdot 5^3<8^4$ .

X X
Oct 19, 2018

$(a,b,c,d,e)=(1024000000,1600000000,900000000,2097152000,1728000000)$