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

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Math Expert
Joined: 02 Sep 2009
Posts: 59712
If for integers a, b, c, and d, a + b + c + d = 4, does d = 1?  [#permalink]

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19 Nov 2019, 02:04
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Difficulty:

55% (hard)

Question Stats:

40% (01:37) correct 60% (01:34) wrong based on 38 sessions

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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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Joined: 02 Aug 2009
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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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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) $$ad = 1$$...

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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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

(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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19 Nov 2019, 08:57
#1 $$abc = 1$$
a,b =-1 and c=1
d=3
a,b,c=1 , d = 1
insufficeint
#2
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) $$ad = 1$$

Are You Up For the Challenge: 700 Level Questions
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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