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If −5 ≤ a ≤ 12 and −10 ≤ b ≤ 25, which of the following represents all

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If −5 ≤ a ≤ 12 and −10 ≤ b ≤ 25, which of the following represents all  [#permalink]

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New post 18 Feb 2019, 04:06
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If −5 ≤ a ≤ 12 and −10 ≤ b ≤ 25, which of the following represents all possible values of a – b ?

A. −30 ≤ a – b ≤ 22
B. −30 ≤ a – b ≤ 5
C. −13 ≤ a – b ≤ 5
D. 5 ≤ a – b ≤ 22
E. 5 ≤ a – b ≤ 30

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Re: If −5 ≤ a ≤ 12 and −10 ≤ b ≤ 25, which of the following represents all  [#permalink]

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New post 18 Feb 2019, 04:14
Bunuel wrote:
If −5 ≤ a ≤ 12 and −10 ≤ b ≤ 25, which of the following represents all possible values of a – b ?

A. −30 ≤ a – b ≤ 22
B. −30 ≤ a – b ≤ 5
C. −13 ≤ a – b ≤ 5
D. 5 ≤ a – b ≤ 22
E. 5 ≤ a – b ≤ 30



IMO A
−30 ≤ a – b ≤ 22
gives all range possible of a-b
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If −5 ≤ a ≤ 12 and −10 ≤ b ≤ 25, which of the following represents all  [#permalink]

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New post 19 Feb 2019, 11:02
Bunuel wrote:
If −5 ≤ a ≤ 12 and −10 ≤ b ≤ 25, which of the following represents all possible values of a – b ?

A. −30 ≤ a – b ≤ 22
B. −30 ≤ a – b ≤ 5
C. −13 ≤ a – b ≤ 5
D. 5 ≤ a – b ≤ 22
E. 5 ≤ a – b ≤ 30


You shouldn't subtract inequalities, but add, therefore

we convert the \(b\) into \(-b\) (to avoid confusion, make sure the signs point to the same direction):
\(-25\leq{-b}\leq{10}\)

then add the inequalities:
\(-5+(-25)\leq{a+(-b)}\leq{12+10}\)
or
\(-30\leq{a-b}\leq{22}\)
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Re: If −5 ≤ a ≤ 12 and −10 ≤ b ≤ 25, which of the following represents all  [#permalink]

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New post 21 Feb 2019, 18:09
Bunuel wrote:
If −5 ≤ a ≤ 12 and −10 ≤ b ≤ 25, which of the following represents all possible values of a – b ?

A. −30 ≤ a – b ≤ 22
B. −30 ≤ a – b ≤ 5
C. −13 ≤ a – b ≤ 5
D. 5 ≤ a – b ≤ 22
E. 5 ≤ a – b ≤ 30


To maximize (a - b), we choose a such that it is its largest positive value (so a = 12), and we choose b such that it is its smallest negative value (-10), so that when we subtract b from a, the result will be the greatest possible (positive) number. Thus, the largest possible value of a - b is 12 - (-10) = 22.

To minimize (a - b), we choose a such that it is its smallest negative value (so a = -5), and we choose b such that it is its largest positive value (25), so that when we subtract b from a, the result will be the smallest possible (negative) value. Thus, the smallest value of a - b is - 5 - 25 = -30.

Answer: A
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Re: If −5 ≤ a ≤ 12 and −10 ≤ b ≤ 25, which of the following represents all   [#permalink] 21 Feb 2019, 18:09
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