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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 [#permalink]

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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

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

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Re: a is the hundreds digit of the three digit integer x, b [#permalink]

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New post 03 Aug 2014, 00:38
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WoundedTiger wrote:
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

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


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.
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Re: a is the hundreds digit of the three digit integer x, b [#permalink]

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New post 03 Aug 2014, 00:58
WoundedTiger wrote:
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

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


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Hope this helps.
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a is the hundreds digit of the three digit integer x, b [#permalink]

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New post 03 Jan 2015, 19:51
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?
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Re: a is the hundreds digit of the three digit integer x, b [#permalink]

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New post 06 Feb 2015, 10:10
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

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Re: a is the hundreds digit of the three digit integer x, b [#permalink]

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Re: a is the hundreds digit of the three digit integer x, b [#permalink]

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New post 23 Jun 2016, 09:56
WoundedTiger wrote:
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

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


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
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Re: a is the hundreds digit of the three digit integer x, b [#permalink]

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New post 11 Aug 2016, 07:41
Divyadisha wrote:
WoundedTiger wrote:
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

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


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
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Re: a is the hundreds digit of the three digit integer x, b [#permalink]

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New post 11 Aug 2017, 02:54
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.

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Re: a is the hundreds digit of the three digit integer x, b   [#permalink] 11 Aug 2017, 02:54
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