Bunuel wrote:
If \(a + b + c + d = 12\), what is the value of \(\sqrt{a^2+b^2+c^2+d^2}\) ?
(1) \(ab = cd = ad\)
(2) \(|a| = |b| = |c| = |d|\)
Given information: a+b+c+d=12
To determine value of: \(\sqrt{a^2+b^2+c^2+d^2}\)
(1) \(ab = cd = ad\)
Best way to go about this is to test values
a b c d ab cd ad \(\sqrt{a^2+b^2+c^2+d^2}\)
3 3 3 3 9 9 9 6
4 2 4 2 8 8 8 Root(40)
NOT SUFFICIENT(2) \(|a| = |b| = |c| = |d|\)
a b c d \(\sqrt{a^2+b^2+c^2+d^2}\)
3 3 3 3 6
6 6 6 -6 12
NOT SUFFICIENT(1) + (2) together:
Now combining all information together, we have:
a) ab=cd=ad
b) a + b + c + d=12
c) |a|=|b|=|c|=|d|
From the above, we can infer the following cases
a) a, b, c and d all have the same absolute value
b) Either they are all negative (NOT POSSIBLE because then original sum=12 condition will not satisfy)
c) a and c are negative (NOT POSSIBLE because all same absolute value and 2 negative will lead to sum as 0, not 12)
d) b and d are negative (NOT POSSIBLE same reason as c)
e) All positive and equal in value (Only possible and viable option)
So based on this, we can say that the only values that fit are when each a, b, c and d are all equal to 3, which will give us 1 definite answer
SUFFICIENTAnswer - C