There are certain rules that we need to remember.
1. Anything multiplied by Even is even.
2. Even + Even = Even
3. \(\frac{Even}{Even}\) = Even or Odd. For example, \(\frac{6}{2} = 3\) and \(\frac{4}{2} = 2\)
Now, let's see the options.
Option A: \(\frac{b}{cd} = Y\)
Assuming value of b = 12 and c = d = 2, we get \(\frac{12}{2 \times 2} = 3\)
Option B: \((\frac{b}{c})(d) = Y\)
This is a tricky option as one might think that \(\frac{Even}{Even}\) can be Even or Odd and when it is multiplied by Even, it will always result in Even.
Let's disprove this!
Assume value of b = 6 and c = 4 and d = 2, we get \(\frac{6}{4 } \times 2 = 3\)
Option B can be true.
Option C: \(\frac{b + c}{d} = Y\)
B+C = even + even = even. Now as we have seen in option A, \(\frac{Even}{Even}\) can be odd. So, this option is also possible.
Option D: \(\frac{Y – b}{c} = d\)
Rearranging the terms, we get \(Y = cd + b\)
Now, cd = even \(\times\) even = even and B = even. So, EVEN + EVEN can never be ODD.
Option D CANNOT be true.Option E: \(\frac{b + c + d}{2} = Y\)
B + C + D = even + even + even = even
Now \(\frac{Even}{2}\) can be ODD.
OA, DGreenlightTestPrep wrote:
If \(b\), \(c\) and \(d\) are even integers, and \(Y\) is an odd integer, which of the following CANNOT be true?
A) \(\frac{b}{cd} = Y\)
B) \((\frac{b}{c})(d) = Y\)
C) \(\frac{b + c}{d} = Y\)
D) \(\frac{Y – b}{c} = d\)
E) \(\frac{b + c + d}{2} = Y\)