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

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

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16 May 2013, 07:19
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Difficulty:

65% (hard)

Question Stats:

59% (02:07) correct 41% (01:40) wrong based on 138 sessions

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

(1) abc = 1

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

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16 May 2013, 07:54
1
yogirb8801 wrote:
If for integers a, b, c, and d, a + b + c + d = 4, does d = 1?

(1) abc = 1

Given :- a+b+c+d = 4

statement 1:- abc = 1

Two cases are possible
a=1,b=1,c=1 then d = 1 YES

a=-1,b=-1,c=1 then d= 5 NO

So A alone is not sufficient . AD are ousted.

Two cases are possible
a = 1,d = 1 YES
a = -1,d=-1 NO.

so B alone is not sufficient B is ousted

Combine both the statements.

We will get only one case possible which satisfies all the three conditions.
How??

ad = 1 implies two cases a=-1,b=-1 or a=1,b=1

if a=-1 and d = -1 then apply the first condition. then b,c will have -1 and 1 It doesnot satisfy a + b+c+d = 4;

if a=1 and d = 1 then apply second condition then b,c will have 1 ,1 .It satisfies a+b+c+d = 4.So d = 1. YES

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

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16 May 2013, 07:55
If for integers a, b, c, and d, a + b + c + d = 4, does d = 1?

(1) abc = 1. Since each unknown is an integer, then either a=b=c=1 or two of them equal 1 and the third one -1. Now, if a=b=c=1, then d=1 but if a=b=-1 and c=1, then d=5. Not sufficient.

(2) ad = 1 --> a=d=1 or a=d=-1. Not sufficient.

(1)+(2) The common value of d from (1) and (2) is 1. Sufficient.

Hope it's clear.
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Re: If for integers a, b, c, and d, a + b + c + d = 4  [#permalink]

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29 Mar 2017, 02:30
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Re: If for integers a, b, c, and d, a + b + c + d = 4 &nbs [#permalink] 29 Mar 2017, 02:30
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