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.
If a and b are two consecutive
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It is given that a and b are two consecutive even integers such that a > b and 3a < 2b.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.
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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We want a common term in each inequality in order to chain them together, so multiply the first inequality by 3.
With that, we've got 3a > 3b and 2b > 3a. That chains into 2b > 3a > 3b, or 2b > 3b.
2b > 3b isn't possible for any positive b, so b is negative. But if b = -2, then a = 0 and 2b > 3a doesn't hold. Likewise, if b = -6, then a = -4 and 2b > 3a doesn't hold, so b < -6.
With that, we've got 3a > 3b and 2b > 3a. That chains into 2b > 3a > 3b, or 2b > 3b.
2b > 3b isn't possible for any positive b, so b is negative. But if b = -2, then a = 0 and 2b > 3a doesn't hold. Likewise, if b = -6, then a = -4 and 2b > 3a doesn't hold, so b < -6.
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We could also set a in terms of b at the outset: a = b + 2, since a > b and they're consecutive evens.
With that, replace a with b + 2 in the second inequality:
2b > 3 * (b + 2)
2b > 3b + 6
-6 > b
With that, replace a with b + 2 in the second inequality:
2b > 3 * (b + 2)
2b > 3b + 6
-6 > b
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Since a and b are consecutive even integers and a > b, we can say that a = b + 2.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
We can substitute b + 2 for a in the inequality 3a < 2b and we have:
3(b+2) < 2b
3b + 6 < 2b
b < -6
Answer: C
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