Vincen wrote:If a and b are two consecutive even integers such that a > b and 3a < 2b. then which of the following describes the range of possible values for b?
A) b > 0
B) b < 0
C) b < -6
D) b > 6
E) b < 4
The OA is C.
I need help. Experts can you explain this PS question to me? Thanks.
It is given that a and b are two consecutive even integers such that a > b and 3a < 2b.
3a < 2b => 1.5a < b
Given that a > b, if a were positive, 1.5a
> b; however, it is given that 1.5a
< b. It implies that a and b are negative even integers.
The correct answer must be either B or C.
To choose between B and C, let's choose a test value for b that lies between 0 and -6.
Say b = -4, thus a = -2 (consecutive even and a > b).
Test this in 1.5a < b.
At a = -2 and b = -4, 1.5a < b => 1.5*(-2) ? -4 => -3
> -4. This is incorrect possible value of b, thus b must not lie between 0 and -6. Thus, the correct answer is
C.
Hope this helps!
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