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# What is the value of abcd+a+b+c+d ?

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Intern
Joined: 12 Feb 2013
Posts: 6
What is the value of abcd+a+b+c+d ? [#permalink]

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25 Apr 2013, 05:31
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Difficulty:

35% (medium)

Question Stats:

62% (01:01) correct 38% (00:56) wrong based on 203 sessions

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What is the value of abcd+a+b+c+d ?

(1) a^2 + b^2 + c^2 + d = 249

(2) d>= 249
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Re: What is the value of abcd+a+b+c+d ? [#permalink]

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25 Apr 2013, 05:37
1
What is the value of abcd+a+b+c+d ?

(1) a^2 + b^2 + c^2 + d = 249
Clearly not sufficient, the combinations are endless

(2) d>= 249
Clearly no sufficient, no info about other terms

1+2) Now $$a^2 + b^2 + c^2 + d = 249$$ and $$d\geq{249}$$ remeber that a squared number cannot have a negative value, and its least value is 0.
With this the only combination that respect 1 and 2 is $$0+0+0+249=249$$, if you (for example) say that d=250 than $$a^2 + b^2 + c^2$$ must be nagative => impossible (at least it equals 0). so $$d=249$$ $$a,b,c=0$$ Sufficient
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Intern
Joined: 12 Feb 2013
Posts: 6
Re: What is the value of abcd+a+b+c+d ? [#permalink]

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25 Apr 2013, 05:42
Zarrolou wrote:
What is the value of abcd+a+b+c+d ?

(1) a^2 + b^2 + c^2 + d = 249
Clearly not sufficient, the combinations are endless

(2) d>= 249
Clearly no sufficient, no info about other terms

1+2) Now $$a^2 + b^2 + c^2 + d = 249$$ and $$d\geq{249}$$ remeber that a squared number cannot have a negative value, and its least value is 0.
With this the only combination that respect 1 and 2 is $$0+0+0+249=249$$, if you (for example) say that d=250 than $$a^2 + b^2 + c^2$$ must be nagative => impossible (at least it equals 0). so $$d=249$$ $$a,b,c=0$$ Sufficient
C

Of course ! Thank you!
The last four days instead of get better I get worst ! And I am going to take the exam in three days ! :O
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Joined: 10 Oct 2012
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Re: What is the value of abcd+a+b+c+d ? [#permalink]

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25 Apr 2013, 05:45
alex90 wrote:
What is the value of abcd+a+b+c+d ?

(1) a^2 + b^2 + c^2 + d = 249

(2) d>= 249

From F.S 1, for the given equation, we can arrive at a conclusive value for abcd+a+b+c+d . Insufficient.

From F.S 2, Clearly Insufficient.

Both together,we know that for d = 249, a^2 + b^2 + c^2 = 0. Sum of squares can only be zero of all of them are individually zero. Also, we get a unique value for the expression in the Question Stem.

Again, for all the values of d>249, we would end up getting a^2 + b^2 + c^2<0 ; which is not possible for square of real numbers. Thus, d = 249. Sufficient.

C.
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Re: What is the value of abcd+a+b+c+d ? [#permalink]

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12 Sep 2017, 05:19
Zarrolou wrote:
What is the value of abcd+a+b+c+d ?

(1) a^2 + b^2 + c^2 + d = 249
Clearly not sufficient, the combinations are endless

(2) d>= 249
Clearly no sufficient, no info about other terms

1+2) Now $$a^2 + b^2 + c^2 + d = 249$$ and $$d\geq{249}$$ remeber that a squared number cannot have a negative value, and its least value is 0.
With this the only combination that respect 1 and 2 is $$0+0+0+249=249$$, if you (for example) say that d=250 than $$a^2 + b^2 + c^2$$ must be nagative => impossible (at least it equals 0). so $$d=249$$ $$a,b,c=0$$ Sufficient
C

Wonderful explanation - thanks.
I missed this point while solving the question.
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Re: What is the value of abcd+a+b+c+d ?   [#permalink] 12 Sep 2017, 05:19
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