In a certain city, 5% of all the persons in town have unlisted phone numbers. If you select 100 names at random from that city's phone directory, how many people selected will have unlisted phone numbers? 

From the given equations,

(a+b+c)2=a2+b2+c2+2(ab+bc+ca)
(6)2=14 + 2(ab + bc + ca)
36 - 14 = 2(ab + bc + ca)
22/2 = ab + bc + ca
ab + bc + ca = 11

a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
= (6) (14 - 11)
=(6)(3)
=18

Since, a3 + b3 + c3 - 3abc = 18

36 - 3abc = 18

-3abc = 18 - 36

-3abc = -18

abc = 6.

Here the answer is 98.

The logic in the given puzzle:

2+3 = 8
3+7 = (7+2)x3 = 27
4+5 = (5+3)x4 = 32
5+8 = (8+4)x5 = 60
6+7 = (7+5)x6 = 72

Similarly,

7+8 = (8+6)x7 = 98.

The answer here is 1.

Logic Followed in the given puzzle ::

The logic here is the number of circles in each 4 digit number mentioned.

8801 has 5

5261 has 1

and so on

The Answer is 46.

Logic ::

First number on the right hand side is the second number in the left side of equation ( and ) second number on the right side is the sum of two numbers on the left side of the equation.

Hence, 2 + 4 = 4(2+4) = 46.

A + B = 15 .... (1)

B x C = 84 .... (2)

C ÷ 4 = 3  .... (3)

B + D = 18 .... (4)

From (3), we get C = 12

From (2), we get B = 84/12 = 7

From (1), we get A = 15 - 7 = 8

From (4), we get D = 18 - 7 = 11

Hence, D = 11.

The logic in this puzzle is summing the result of [subtraction of upper two digits] & [addition of lower two digits] 

Hence, the result is  

(5 - 3) + (2 + 8) = 2 + 10 = 12.

A - A - A = 20
B - B - B = 15
C - C - C = 25

A = -20
B = -15
C = -25

=> A + B + C = (-20)+(-15)+(-25) = -20 - 15 - 25 = -60.

5 + 5 = 10

5x 2 + 2 = 12

5 x 2 - 1 x 5 = 5

Hence, ∆ = 1.