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If A and B are integers and 2A - B = B - A than which of the following

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If A and B are integers and 2A - B = B - A than which of the following [#permalink] New post   06 Sep 2022, 01:45
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If A and B are integers and 2A - B = B - A, than which of the following is true?

A. B<A
B. A<B
C. A and B are even.
D. A is even and B is either even or odd.
E. B is even.


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If A and B are integers and 2A - B = B - A than which of the following [#permalink] New post   06 Sep 2022, 04:14
Given:
A and B are integers
and \(2*A - B = B - A\) => 3A = 2B

We are required to determine the option which is true.

since \(3*A = 2*B\) (and A, B are integers) it is evident that A is even integer while B can be either Even or Odd integer
so Option D is correct

Lets analyze the other options
A. B<A - we know that \(B= 1.5 * A\), but we don't know the actual values of A and B. not true
B. A<B - Similar reasons as above. not true
C. A and B are even. As discussed above, B can be either Even or Odd. not true
E. B is even. not true
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Re: If A and B are integers and 2A - B = B - A than which of the following [#permalink] New post   06 Sep 2022, 05:00
\( 2A - B = B - A\)

\(3A = 2B\)

\(\frac{A}{B} = \frac{2}{3}\)

The ratio of A to B is 2:3. We are not told if A or B are negative, only that they are integers which means we cannot determine if \(A>B\) or if \(B>A\). However, we do know A will always be even and B could be either even or odd.

Only answer choice D will always hold.

Answer D
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Re: If A and B are integers and 2A - B = B - A than which of the following [#permalink] New post   18 Sep 2022, 23:49
1. reduce the equation to 3A = 2B

2. Look at the answer choices. They are either about which is big or about which even or odd.

3. Take a few test cases for big or small - A can be 2 and B can be 3 or A can be -2 and B can be -3 . Now A is bigger is one case and B is bigger in another case. So, eliminate first two choices.

4. Take a few test cases for even or odd - A has be even because the other side of 3A is an even number. So, take two even numbers for A - 2 & 4. If A = 2, B=3 but if A=4 , B = 6 - So, B can be odd or even.

So, A must be even and B can be odd or even.

Choice D is the answer.
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Re: If A and B are integers and 2A - B = B - A than which of the following [#permalink]
18 Sep 2022, 23:49
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