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

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

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New post 25 Apr 2013, 05:31
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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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New post 25 Apr 2013, 05:37
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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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Re: What is the value of abcd+a+b+c+d ? [#permalink]

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

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New post 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.

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

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New post 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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