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06 Sep 2022, 01:45
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Difficulty:
55%
(hard)
Question Stats:
58% (01:36) correct
42%
(01:23)
wrong
based on 147
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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.
Are You Up For the Challenge: 700 Level Questions
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.
Are You Up For the Challenge: 700 Level Questions
06 Sep 2022, 04:14
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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
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
06 Sep 2022, 05:00
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\( 2A - B = B - A\)
\(3A = 2B\)
\(\frac{A}{B} = \frac{2}{3}\)
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
\(3A = 2B\)
\(\frac{A}{B} = \frac{2}{3}\)
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
