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What's the diff between the 2 greatest possible values of x?

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What's the diff between the 2 greatest possible values of x?

by vinhaha » Fri May 20, 2016 5:38 am
hi, can anyone help out on this question? i don't understand the explanation. thanks in advance!

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?

Solution:
[spoiler]Solution: D.

If a = 2b = 4c and a, b, and c must all be nonzero single digit integers - if they weren't, they couldn't be digits - then c is either 1 or 2. If c = 1, then b = 2 and a = 4, giving us 421. If c = 2, then b = 4 and a = 8, giving us 842.

The difference between the numbers is thus 842 - 421 = 421 = (D).[/spoiler]
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by DavidG@VeritasPrep » Fri May 20, 2016 5:57 am
vinhaha wrote:hi, can anyone help out on this question? i don't understand the explanation. thanks in advance!

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?
Say c = 1. Now our equation looks like this a = 2b = 4. If 2b = 4, then b = 2. And we can see that a = 4. So if a = 4, b = 2, and c = 1, the value of the three-digit number is 421.

Say c = 2. Now our equation looks like this a = 2b = 8. If 2b = 8, then b = 4. And we can see that a = 8. So if a = 8, b = 4, and c = 2, the value of the three-digit number is 842.

842 - 421 = 421.

(If c = 3, our equation would look like this a = 2b = 12. Well, a can't be 12, because we're told that a must be a digit!, so we need not worry about this scenario, or any scenario in which c > 2.)
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by [email protected] » Fri May 20, 2016 9:43 am
Hi vinhaha,

David's properly explained the math behind this question, so I won't rehash any of that work here. When posting questions, it's important to post the FULL prompt (including the answer choices). Sometimes, the answers themselves provide a big 'hint' as to how you can go about solving the problem and can sometimes provide a shortcut to help you avoid some of the 'math' involved. Without having that information, we're forced to answer this question with math.

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