Is it an even question?
XYZ is a three-digit even number with digits X, Y and Z such that X:
-
Is not six
-
Is an even multiple of ONE of Y or Z
-
Has a difference of 5 with ONE of Y or Z
What is the sum of all possible values of XYZ?
Clarification: Even multiple means that X is Y or Z times an even number.
The answer is 2158.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Since Z is even, it takes values 0, 2, 4, 6, 8
If we assume that X has a difference of 5 with Z, X can take values 5, 7, 9
Since none of these values are even, X cannot have a difference of 5 with Z.
Therefore, X has a difference of 5 with Y.
If X has a difference of 5 with Y, the possible pairs are 0-5, 1-6, 2-7, 3-8, 4-9
X cannot be 6. Similarly, if it is 1, then it is not an even multiple of 6.
Hence, X must be a multiple of Z.
X can take values 4 (corresponding to Z =2), 8 (corresponding to Z = 2 or Z = 4)
Y can take values 9 and 3.
The possible numbers are 834, 832, 492
The sum of these numbers is 2158