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If for integers a, b, c, and d, a + b + c + d = 4, does d = 1?

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If for integers a, b, c, and d, a + b + c + d = 4, does d = 1?  [#permalink]

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New post 19 Nov 2019, 02:04
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44% (01:47) correct 56% (01:32) wrong based on 43 sessions

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Re: If for integers a, b, c, and d, a + b + c + d = 4, does d = 1?  [#permalink]

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New post 19 Nov 2019, 03:23
If for integers a, b, c, and d, \(a + b + c + d = 4\), does \(d = 1\)?


(1) \(abc = 1\). This means a, b and c are either 1 or -1.
say abc=1*1*1=1, then d=1
say abc=(-1)*(-1)*1=1, then (-1)+(-1)+1+d=4....d=5

(2) \(ad = 1\)...
ad=1=(-1)(-1)....d=-1
ad=1*1=1...d=1

Combined
d can be only 1
Suff
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Re: If for integers a, b, c, and d, a + b + c + d = 4, does d = 1?  [#permalink]

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New post 19 Nov 2019, 04:37
Bunuel wrote:
If for integers a, b, c, and d, \(a + b + c + d = 4\), does \(d = 1\)?


(1) \(abc = 1\)

(2) \(ad = 1\)


(1) \(abc = 1\) insufic
abc=1: (a,b,c)=(1,1,1);(1,-1,-1);(-1,-1,-1)
d=(1);(1-2+d=4…d=5);(-3+d=4…d=7)

(2) \(ad = 1\) insufic
ad=1: (a,d)=(1,1);(-1,-1)

(1&2) sufic
(a,d)=(1,1); (b,c)=(1,1).

Ans (C)
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Re: If for integers a, b, c, and d, a + b + c + d = 4, does d = 1?  [#permalink]

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New post 19 Nov 2019, 08:57
#1 \(abc = 1\)
a,b =-1 and c=1
d=3
a,b,c=1 , d = 1
insufficeint
#2
ad=1
both either +1 or -1
insufficeint
from 1 &2
+1 , yes d=1
IMO C



Bunuel wrote:
If for integers a, b, c, and d, \(a + b + c + d = 4\), does \(d = 1\)?


(1) \(abc = 1\)

(2) \(ad = 1\)


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Re: If for integers a, b, c, and d, a + b + c + d = 4, does d = 1?   [#permalink] 19 Nov 2019, 08:57
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