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# If a and b are integers and a = |

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Status: It's near - I can see.
Joined: 13 Apr 2013
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If a and b are integers and a = |  [#permalink]

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27 Mar 2019, 02:04
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75% (hard)

Question Stats:

49% (02:06) correct 51% (01:51) wrong based on 41 sessions

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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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Location: India
Schools: ISB '20
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WE: Programming (Computer Software)
Re: If a and b are integers and a = |  [#permalink]

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27 Mar 2019, 03:26
2
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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Joined: 24 Nov 2016
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If a and b are integers and a = |  [#permalink]

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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.

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