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]
What's the diff between the 2 greatest possible values of x?
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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.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 = 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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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.
GMAT assassins aren't born, they're made,
Rich
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.
GMAT assassins aren't born, they're made,
Rich