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

Question

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.
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Tip: Don't stop till you have exhausted all answer choices to arrive at the correct one.

Gnpth · Answer

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.

Bunuel · Answer

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minwoswoh · Answer

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?

pacifist85 · Answer

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 = 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

Divyadisha · Answer

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

stonecold · Answer

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

FB2017 · Answer

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.

BrentGMATPrepNow · Answer

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

ScottTargetTestPrep · Answer

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

ScottTargetTestPrep · Answer

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

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

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

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