askhokha wrote:

Q How many three-digit positive integers can be divided by 2 to produce a new integer with the same tens digit and units digit as the original integer?

None

One

Two

Three

Four

The answer is four. Can you please explain in detail how this was achieved. Will really appreciate the help. Thank you!

We are looking for a three digit number \(abc\) such that \(abc = 2*xbc\), where \(xbc\) is also a three digit number.

This means \(100a+10b+c=200x+20b+2c\), from which \(100(a-2x)=10b+c.\)

Since \(0\leq10b+c\leq99\) and \(100(a-2x)\geq0\), the only possibility is \(b=c=0\) and \(a=2x.\)

So, \(a\) can 2, 4, 6, or 8.

Answer E (total of 4 numbers - \(200, 400, 600, 800\)).

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PhD in Applied Mathematics

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