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If a and b are integers and a = |

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If a and b are integers and a = |b + 11| + |12 - b|, does a equal 23?

a. b < 12

2. b > -11

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Re: If a and b are integers and a = |  [#permalink]

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New post 27 Mar 2019, 03:26
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If a and b are integers and a = |b + 11| + |12 - b|, does a equal 23?

a. b < 12

2. b > -11



From option (a), if b< 12 then a=23 till b=-11 but after that i.e if b=-12 then a=25 so only (a) is not sufficient
similarly From option (b), if b> -11 then a=23 till b=12 but after that i.e if b=13, then a= 25 so only (b) is not sufficient
But if we consider both a and b then a=23 if -11<b<12
So OA: (C)
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If a and b are integers and a = |  [#permalink]

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New post 08 Oct 2019, 04:55
AkshdeepS wrote:
If a and b are integers and a = |b + 11| + |12 - b|, does a equal 23?

a. b < 12
2. b > -11


\(a = |b + 11| + |12 - b|\)
\(b≥0:b+11≥0…b≥-11\)
\(b<0:b+11<0…b<-11\)
\(b≥0:12-b≥0…-b≥-12…b≤12\)
\(b<0:12-b<0…b>12\)

\(|b+11|\): ___neg__-11___pos___12__pos__
\(|12-b|\): ___pos__-11___pos___12___neg__

\([A]b<-11: a=-(b+11)+(12-b)…a=-b-11+12-b…a=-2b+1…\)
\((a≥0)…-2b+1≥0…-2b≥-1…b≤1/2=valid\)
\(b=-20:a=|-20+11|+|12-(-20)|…a=|-9|+|32|=41≠23\)

\([B]-11≤b≤12: a=(b+11)+(12-b)…a=23\)
\(b=-11:a=|-11+11|+|12-(-11)|…a=|0|+|23|=23\)
\(b=0:a=|0+11|+|12-0|…a=|11|+|12|=23\)

\([C]b>12: a=(b+11)-(12-b)…a=2b+1…(a≥0)…2b+1≥0…b≥1/2=valid\)
\(b=13:a=|13+11|+|12-(13)|…a=|24|+|-1|=25\)

(1) b < 12: \(b\) could fall in range \(b<-11\) or \(-11≤b≤12\); insufic.

(2) b > -11: \(b\) could fall in range \(-11≤b≤12\) or \(b>12\); insufic.

(1&2) \(-11<b<12\) so \(a=23\); sufic.

Answer (C)
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If a and b are integers and a = |   [#permalink] 08 Oct 2019, 04:55
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