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

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Re: What is the value of abcd+a+b+c+d ? [#permalink]
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alex90
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]
Zarrolou
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]
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Its a beautiful DS question emerging a beauty of GMAT that Quant section is not mathematics it is a quant reasoning here you can easily save time by using reasoning skill that not any single statement were able to give a conclusive answer but it seems taking together also you are not able to get answer but think again if d greater than or EQUAL the main point is d is equal to 249 than combining both we can easily get the answer
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Re: What is the value of abcd+a+b+c+d ? [#permalink]
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Re: What is the value of abcd+a+b+c+d ? [#permalink]
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