sanju09 wrote:If -2 < a < 11 and 3 < b < 12, then which of the following is NOT true?
A. 1 < a + b < 23
B. -14 < a - b < 8
C. -7 < b - a < 14
D. 1 < b + a < 23
E. -24 < a b < 132
If -14 < a-b < 8 (option B) is multiplied by -1, we get:
14 > -a+b > -8
14 > b-a > -8
-8 < b-a < 14.
Implication:
If B is true, then C is NOT true, since C indicates that -7 < b-a < 14.
In other words:
B and C cannot both be true.
Test whether B or C is true.
If we multiply 3 < b < 12 by -1, we get:
-3 > -b > -12
-12 < -b < -3
Adding together -2 < a < 11 and -12 < -b < -3, we get:
-2 + (-12) < a-b < 11 + (-3)
-14 < a-b < 8.
Since B is true, we know that C is NOT true.
The correct answer is
C.
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