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xcusemeplz2009
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If a, b, c, d are each positive, a+b+c+d=8, a^2+b^2+c^2+d^2= Updated on: 09 Jul 2013, 10:13
Originally posted by xcusemeplz2009 on 07 Dec 2009, 11:57.
Last edited by Bunuel on 09 Jul 2013, 10:13, edited 2 times in total.
Added the OA.
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95% (hard)

Question Stats:

47% (02:48) correct 53% (02:55) wrong based on 77 sessions

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If a, b, c, d are each positive, a+b+c+d=8, a^2+b^2+c^2+d^2=25 and c=d, then what is the greatest value of c?

(A) 1/2
(B) 3/2
(C) 5/2
(D) 7/2

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kp1811
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If a, b, c, d are each positive, a+b+c+d=8, a^2+b^2+c^2+d^2= 07 Dec 2009, 12:11
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xcusemeplz2009
If a,b,c,d are each +ve, a+b+c+d=8,a^2+b^2+c^2+d^2=25 and c=d ..Then what is the greatest value of c..?
(A)1/2 (B) 3/2 (C) 5/2 (D) 7/2

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c -7/2

d = 7/2 ,a and b = 1/2

sum of these will be 8 and sum of there squares will be 25
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If a, b, c, d are each positive, a+b+c+d=8, a^2+b^2+c^2+d^2= 08 Dec 2009, 09:20
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can this be a gmat prob ???
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kp1811
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If a, b, c, d are each positive, a+b+c+d=8, a^2+b^2+c^2+d^2= 08 Dec 2009, 09:58
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nikhilpoddar
can this be a gmat prob ???
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don't think so...but you never know :lol:
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If a, b, c, d are each positive, a+b+c+d=8, a^2+b^2+c^2+d^2= 07 Dec 2010, 02:55
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Can someone please take a look at this one? I think there should be some shortcut or simplification.
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Bunuel
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If a, b, c, d are each positive, a+b+c+d=8, a^2+b^2+c^2+d^2= 07 Dec 2010, 05:01
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xcusemeplz2009
If a,b,c,d are each +ve, a+b+c+d=8, a^2+b^2+c^2+d^2=25 and c=d ..Then what is the greatest value of c..?
(A)1/2 (B) 3/2 (C) 5/2 (D) 7/2

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This is not a GMAT question so I wouldn't worry about it at all. Anyway below is an algebraic solution for it:

Given: \(a+b+2c=8\) and \(a^2+b^2+2c^2=25\).

\(a+b+2c=8\) --> \(b=8-a-2c\) --> \(a^2+(8-a-2c)^2+2c^2=25\) --> \(2a^2+4a(c-4)+(6c^2-32c+39)=0\). Now, this quadratic equation to have real solutions for \(a\) its discriminat must be more than or equal to zero: \(d=4^2*(c-4)^2-4*2(6c^2-32c+39)\geq{0}\) --> \(4c^2-16c+7\leq{0}\) --> \({\frac{1}{2}}\leq{c}\leq{\frac{7}{2}}\) --> \(c_{max}=\frac{7}{2}\).

Answer: D.
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If a, b, c, d are each positive, a+b+c+d=8, a^2+b^2+c^2+d^2= 07 Dec 2010, 19:43
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nikhilpoddar
can this be a gmat prob ???
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GMAT problems sometimes look tricky. Nevertheless, all of them can be easily solved. Something like this isn't fun to do.. just tedious... so very slim chance that it will appear on GMAT... If you do get stuck on something, don't fret. Use options.
Here try 7/2 since it is the greatest value. Make d also 7/2 and split the leftover 1 from the sum of 8 evenly between a and b. It will work. It is not a neat little problem but still intuitive.
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If a, b, c, d are each positive, a+b+c+d=8, a^2+b^2+c^2+d^2= 17 Aug 2013, 13:32
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I tried hit and trial method.

let a= 1
b=2
c=3

1+2+6=9
a^2 + b^2 + 2 c^2= 1 + 4 + 18 = 23

c should be near to 3 and 7/2 is the nearest value.
Its not a foolproof way, but good to guess a possible answer :P

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