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a is the hundreds digit of the three digit integer x

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a is the hundreds digit of the three digit integer x

by gmattesttaker2 » Sun Jun 22, 2014 8:27 pm
Hello,

Can you please assist with this:

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: 421

Thanks a lot,
Sri
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by Brent@GMATPrepNow » Sun Jun 22, 2014 8:39 pm
gmattesttaker2 wrote:Hello,

Can you please assist with this:

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: 421


Thanks a lot,
Sri
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

Cheers,
Brent
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by gmattesttaker2 » Sun Jun 22, 2014 9:14 pm
Brent@GMATPrepNow wrote:
gmattesttaker2 wrote:Hello,

Can you please assist with this:

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: 421


Thanks a lot,
Sri
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

Cheers,
Brent
Hello Brent,

Thank you very much for the excellent explanation.

Best Regards,
Sri
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