a is the hundreds digit of the three digit integer x, b is the tens digit of x, and c is the units digit of x. a = 2b = 4c, and a > 0.
What is the difference between the two greatest possible values of x?

A. 124
B. 297
C. 394
D. 421
E. 842

OA to be updated after some discussion.
Kudos for correct solution


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Hi all,

Let me show how I did it - and I am quite happy as I HATE number properties questions ...

First of all we have to start somewhere. And since this is a 3-digit number then it must be 100<x<999.

We also know that a=2b=2c. So, c will be 1/4 of a and b will be 1/2 of a. We are interested in a then!

In 999, the last digit is 9. So, a can never be 4 times 9, because it would be 36, making b 18. This is not a 3-digit number. In other words, we are looking for 2s to divide and multiply.

So, 8 is the greatest multiple of 2, from 1 to 9.
If a=8, then b=4 and c=2 --> x = 842

We cannot have a=2, as then c would be 1/2.

So, the lowest possibe a=4, making b=2 and c=1 --> x = 421.

Finally, 842 - 421 = 421, ANS D

Just to add to this solution =>
I think There are only two possible values of x here they are => 842 and 421
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