a is the hundreds digit of the three digit integer x, b

The 3 digit number is x=abc.

Since a=2b=4c. Lets start plugging in numbers for C.

For example : if C=3 then A=4c= 12. We need only single digit numbers.

So C cannot be greater than 2.

we need to find the difference between 2 greatest possible values of x.

so if c=1,

then a=4, and b=2.

so X= 421.

and if c=2,

then a=8, and b=4.

so x= 842.

The difference-> 842-421= 421.

The answer is D.
_________________

Similar questions to practice:
if-x-0-abcd-where-a-b-c-and-d-each-represent-a-nonzero-127399.html
if-x-0-rstu-where-r-s-t-and-u-each-represent-a-nonzero-109735.html
if-the-three-digit-integer-x-abc-where-a-b-and-c-131904.html
if-y-0-jkmn-where-j-k-m-and-n-each-represent-a-nonzero-130018.html
what-is-the-two-digit-positive-integer-whose-tens-digit-is-a-128766.html
if-a-0-abc-where-a-b-and-c-are-digits-of-a-is-a-greater-138282.html
in-the-correctly-worked-addition-problem-above-a-b-c-d-128953.html
if-z-is-a-three-digit-positive-integer-what-is-the-value-of-69999.html
ab-cd-aaa-where-ab-and-cd-are-two-digit-numbers-and-aa-136903.html
if-in-the-addition-problem-above-a-b-c-d-e-f-x-y-a-97479.html

Hope this helps.
_________________

As this question is written, I was confused by the portion "the different between the two greatest possible values of x"?
Isn´t the word "greatest" redundant?

Aren´t only two possible values for x, namely 842 and 421?

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

Ratio of a:b:c= 4:2:1

Two possible greatest single digit values for a are 8 and 4

if a is 8, then x= 842
if a is 4, then x= 421

difference= 842-421= 421

D is the answer
_________________

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

Frame the number and assume a(hundred's) b(ten's) c(unit's) place in terms of c as 4c 2c c.
Now substitute c=2 once and c=1.
The numbers obtained in each iteration (842 -421) using the above values gives 421.
Option D.

Our 3-digit number looks like this: abc

If a = 4c, then c cannot be greater than 2. Otherwise, a will not be a digit.
For example, if we let c = 3, then a = 12, and 12 is not a digit.

So, there are ONLY TWO possible values for c.
Case a: c = 1
If a = 2b = 4c, the a = 4, b = 2 and c = 1
So, the resulting 3-digit number (aka x) is 421

Case b: c = 2
If a = 2b = 4c, the a = 8, b = 4 and c = 2
So, the resulting 3-digit number (aka x) is 842

What is the difference between the two greatest possible values of x?
There are only 2 possible values of x.
Their DIFFERENCE = 842 - 421 = 421

Answer: D

Cheers,
Brent
_________________

We see that the value of c is the smallest. Since a > 0, b and c are also greater than 0; therefore,

If c = 1, we have a = 4, b = 2, and hence, x = 421.

If c = 2, we have a = 8, b = 4, and hence, x = 842.

Since c can’t be 3 or more (otherwise a would be a two-digit number), there are only 2 possible values of x, and their difference is 842 - 421 = 421.

Answer: D

_________________

We see that the value of c is the smallest. Since a > 0, b and c are also greater than 0; therefore,

If c = 1, we have a = 4, b = 2, and hence x = 421.

If c = 2, we have a = 8, b = 4, and hence x = 842.

Since c can’t be 3 or more (otherwise a would be a two-digit number), there are only 2 possible values of x, and their difference is 842 - 421 = 421.

Answer: D
_________________

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________