# I am an even number between 300 and 400. i have three different digits. the sum of my digits is five times my hundred digits. what number can i be?

1
by charlottetupaz2

2015-09-21T20:14:31+08:00

if it is a number between 300 and 400  and if it is even then it would be between

302-398.

In which case, we've already identified the number in the hundreds place as 3.

the number would be

3xy

x being the digit in the tens place and y in the units place

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if the sum of the digits is five times the hundred digit then

3+x+y = 5(3)

3+x+y =15

x + y = 15 - 3

x + y = 12

that being x + y = 12, we can have investigation through trial and error

we'll have:

3xy

since it is even then we'll base the assumptions in its units digit

if y = 0

x = 12

not correct since we can't have two digits for the tens place

if y = 2

x = 10

not correct with same reason as the first

if y = 4

x = 8

can be since it qualifies to the condition that no digit shall be the same as the other

if y = 6

x = 6

doesn't satisfy the 'I have three different digits' statement

if y = 8

x = 4

can be

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so the number can either be

348 or 384