Can someone please walk me through the work on statement 1. Thanks
If b is an even integer, is b<0?
1. b^24b+4<16
2. b^2>9
OA = A
Inequalities with Exponents
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From Statement 1:tonebeeze wrote:Can someone please walk me through the work on statement 1. Thanks
If b is an even integer, is b<0?
1. b^24b+4<16
2. b^2>9
OA = A
b^2  4b + 4 < 16
b^2  4b  12 < 0
(b  6)(b + 2) < 0
We now have a product which is negative. So one factor must be negative, the other positive. Since b6 is certainly smaller than b+2, it must be that b6 is the negative factor, and b+2 is the positive factor. So b6 < 0, and b < 6, and b+2 > 0, so b > 2. Combining these we know 2 < b < 6. Since b must be an even integer, b can only be 0, 2 or 4. So it is certainly *not* true that b<0, and we have a definite answer to the question, so Statement 1 is sufficient.
Statement 2 is not sufficient; b^2 > 9 is true whenever b > 3 or b < 3.
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From the stem
b={...4, 2, 0, 2, 4...}
Question
is b = 2 or 4 or 6...
Attack statement 2 first because, off the bat it seems like it would not work
(2)
b^2 > 9
b=...6 or 4 or 4 or 6...
Since we get both positives and negatives in our set, INSUFFICIENT
(1)
b^2  4b + 4 < 16
b^2  4b + 12 < 0
(b  6)(b + 2) < 0
Since we must have a positive multiplied by a negative to get a value less than zero, one of b6 or b+2 must be less than zero
If b>6, both parenthetical expressions are positive. If b < 2, both parenthetical expressions are negative. So we must have 2 < b < 6. But note that leaves us with the set b= {0, 2, 4} which is always positive or 0. Therefore the answer to the target question is no and this is SUFFICIENT.
That was kind of a tough one. There may be a more straightforward approach...
b={...4, 2, 0, 2, 4...}
Question
is b = 2 or 4 or 6...
Attack statement 2 first because, off the bat it seems like it would not work
(2)
b^2 > 9
b=...6 or 4 or 4 or 6...
Since we get both positives and negatives in our set, INSUFFICIENT
(1)
b^2  4b + 4 < 16
b^2  4b + 12 < 0
(b  6)(b + 2) < 0
Since we must have a positive multiplied by a negative to get a value less than zero, one of b6 or b+2 must be less than zero
If b>6, both parenthetical expressions are positive. If b < 2, both parenthetical expressions are negative. So we must have 2 < b < 6. But note that leaves us with the set b= {0, 2, 4} which is always positive or 0. Therefore the answer to the target question is no and this is SUFFICIENT.
That was kind of a tough one. There may be a more straightforward approach...