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If 4 < a < 8 and -3 < b < -1, indicate all of the following [#permalink]
Carcass wrote:
If \(4 < a < 8\) and \(-3 < b < -1\), indicate all of the following expressions that must be true.

Indicate all that apply

A. a + b > 0

B. a - b > 0

C. b - a > 0

D. b - a < 0

E. 2b + a < 0


\(4 < a < 8\) and \(-3 < b < -1\)

A. \(a + b > 0: YES\)
Inequalities with same sign can be added
So, \(4 + (-3) < a + b < 8 + (-1)\)
i.e. 1 < a + b < 7


B. \(a - b > 0: YES\)
Inequalities with opposite sign can be subtracted
So, \(4 - (-1) < a - b < 8 - (-3)\)
i.e. 5 < a - b < 11


C. \(b - a > 0: NEVER\)
Inequalities with opposite sign can be subtracted
So, \(-3 - (8) < b - a < -1 - (4)\)
\(-11 < b - a < -5\)


D. \(b - a < 0: YES\)
We just saw \(-11 < b - a < -5\)


E. \(2b + a < 0: NOT ALWAYS\)
Multiply b with 2 and add a to it
\(-6 + 4 < 2b + a < -2 + 8\)
\(-2 < 2b + a < 6\)
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If 4 < a < 8 and -3 < b < -1, indicate all of the following [#permalink]
this question is testing positive and negative value bigger than or less than zero
4<a<8 and −3<b<−1
a can be 5 and b can be -2
ONLY A,B,D are correct
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Re: If 4 < a < 8 and -3 < b < -1, indicate all of the following [#permalink]
1
gd2906 wrote:
but for option choice A, A could be 0, and B could be -2 and that would be < than 0??



- A cannot be 0 because question specifies that: 4 < a < 8.
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Re: If 4 < a < 8 and -3 < b < -1, indicate all of the following [#permalink]
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